0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : run_vampire %s %d THM
0.12/0.34	% Computer : n018.cluster.edu
0.12/0.34	% Model    : x86_64 x86_64
0.12/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory   : 8042.1875MB
0.12/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 1920
0.12/0.34	% WCLimit    : 240
0.12/0.34	% DateTime   : Wed Jul 30 02:00:04 EDT 2025
0.12/0.34	% CPUTime    : 
0.12/0.36	This is a THF_ problem
0.12/0.36	Running higher-order theorem proving
0.12/0.37	Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.guXwhKhjpX/E---3.1_2233.p -m 16384 -t 240
0.12/0.38	ipcrm: permission denied for id (71106560)
0.12/0.38	ipcrm: permission denied for id (71303170)
0.12/0.38	ipcrm: permission denied for id (71401476)
0.22/0.39	ipcrm: permission denied for id (71598087)
0.22/0.39	ipcrm: permission denied for id (71630857)
0.22/0.39	ipcrm: permission denied for id (71696396)
0.22/0.41	ipcrm: permission denied for id (72056856)
0.22/0.41	ipcrm: permission denied for id (72089625)
0.22/0.41	ipcrm: permission denied for id (72155162)
0.22/0.41	ipcrm: permission denied for id (72187931)
0.22/0.41	ipcrm: permission denied for id (72253469)
0.22/0.41	ipcrm: permission denied for id (72319006)
0.22/0.42	ipcrm: permission denied for id (72384543)
0.22/0.42	ipcrm: permission denied for id (72450080)
0.22/0.42	ipcrm: permission denied for id (72581158)
0.22/0.43	ipcrm: permission denied for id (72810541)
0.22/0.44	ipcrm: permission denied for id (72876080)
0.22/0.44	ipcrm: permission denied for id (72908849)
0.22/0.44	ipcrm: permission denied for id (73039927)
0.22/0.45	ipcrm: permission denied for id (73072697)
0.22/0.45	ipcrm: permission denied for id (73105466)
0.22/0.46	ipcrm: permission denied for id (74252353)
0.22/0.46	ipcrm: permission denied for id (74383427)
0.22/0.46	ipcrm: permission denied for id (74416196)
0.22/0.47	ipcrm: permission denied for id (74514505)
0.22/0.48	ipcrm: permission denied for id (74678353)
0.22/0.48	ipcrm: permission denied for id (74776661)
0.22/0.48	ipcrm: permission denied for id (74809430)
0.22/0.49	ipcrm: permission denied for id (74874969)
0.22/0.49	ipcrm: permission denied for id (74907738)
0.22/0.49	ipcrm: permission denied for id (74973276)
0.22/0.49	ipcrm: permission denied for id (75006045)
0.22/0.50	ipcrm: permission denied for id (75071585)
0.22/0.50	ipcrm: permission denied for id (75104354)
0.22/0.50	ipcrm: permission denied for id (75137124)
0.22/0.50	ipcrm: permission denied for id (75169894)
0.22/0.51	ipcrm: permission denied for id (75268202)
0.22/0.51	ipcrm: permission denied for id (75300971)
0.22/0.51	ipcrm: permission denied for id (75432047)
0.22/0.51	ipcrm: permission denied for id (75464816)
0.22/0.52	ipcrm: permission denied for id (75497586)
0.22/0.52	ipcrm: permission denied for id (75595892)
0.35/0.52	ipcrm: permission denied for id (75661430)
0.35/0.52	ipcrm: permission denied for id (75792504)
0.35/0.53	ipcrm: permission denied for id (75825274)
0.35/0.53	ipcrm: permission denied for id (75890811)
0.35/0.53	ipcrm: permission denied for id (75923580)
0.35/0.53	ipcrm: permission denied for id (75989118)
0.35/0.53	ipcrm: permission denied for id (76021887)
0.39/0.55	% (2650)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_2233 for (2398ds/4Mi)
0.39/0.55	% (2649)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_2233 for (2398ds/183Mi)
0.39/0.55	% (2653)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_2233 for (2398ds/2Mi)
0.39/0.55	% (2656)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_2233 for (2398ds/18Mi)
0.39/0.55	% (2654)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_2233 for (2398ds/2Mi)
0.39/0.55	% (2652)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_2233 for (2398ds/27Mi)
0.39/0.55	% (2655)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_2233 for (2398ds/275Mi)
0.39/0.55	% (2654)Instruction limit reached!
0.39/0.55	% (2654)------------------------------
0.39/0.55	% (2654)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.55	% (2654)Termination reason: Unknown
0.39/0.55	% (2654)Termination phase: shuffling
0.39/0.55	
0.39/0.55	% (2654)Memory used [KB]: 1023
0.39/0.55	% (2654)Time elapsed: 0.003 s
0.39/0.55	% (2654)Instructions burned: 2 (million)
0.39/0.55	% (2654)------------------------------
0.39/0.55	% (2654)------------------------------
0.39/0.55	% (2653)Instruction limit reached!
0.39/0.55	% (2653)------------------------------
0.39/0.55	% (2653)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.55	% (2653)Termination reason: Unknown
0.39/0.55	% (2653)Termination phase: Preprocessing 3
0.39/0.55	
0.39/0.55	% (2653)Memory used [KB]: 1023
0.39/0.55	% (2653)Time elapsed: 0.004 s
0.39/0.55	% (2653)Instructions burned: 3 (million)
0.39/0.55	% (2653)------------------------------
0.39/0.55	% (2653)------------------------------
0.39/0.56	% (2650)Instruction limit reached!
0.39/0.56	% (2650)------------------------------
0.39/0.56	% (2650)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.56	% (2650)Termination reason: Unknown
0.39/0.56	% (2650)Termination phase: Property scanning
0.39/0.56	
0.39/0.56	% (2650)Memory used [KB]: 1023
0.39/0.56	% (2650)Time elapsed: 0.005 s
0.39/0.56	% (2650)Instructions burned: 5 (million)
0.39/0.56	% (2650)------------------------------
0.39/0.56	% (2650)------------------------------
0.39/0.56	% (2655)Refutation not found, incomplete strategy
0.39/0.56	% (2655)------------------------------
0.39/0.56	% (2655)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.56	% (2655)Termination reason: Refutation not found, incomplete strategy
0.39/0.56	
0.39/0.56	
0.39/0.56	% (2655)Memory used [KB]: 5628
0.39/0.56	% (2655)Time elapsed: 0.008 s
0.39/0.56	% (2655)Instructions burned: 7 (million)
0.39/0.56	% (2655)------------------------------
0.39/0.56	% (2655)------------------------------
0.39/0.56	% (2656)Instruction limit reached!
0.39/0.56	% (2656)------------------------------
0.39/0.56	% (2656)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.56	% (2656)Termination reason: Unknown
0.39/0.56	% (2656)Termination phase: Saturation
0.39/0.56	
0.39/0.56	% (2656)Memory used [KB]: 5628
0.39/0.56	% (2656)Time elapsed: 0.013 s
0.39/0.56	% (2656)Instructions burned: 18 (million)
0.39/0.56	% (2656)------------------------------
0.39/0.56	% (2656)------------------------------
0.39/0.57	% (2669)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_2233 for (2398ds/3Mi)
0.39/0.57	% (2669)Instruction limit reached!
0.39/0.57	% (2669)------------------------------
0.39/0.57	% (2669)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.57	% (2669)Termination reason: Unknown
0.39/0.57	% (2669)Termination phase: Property scanning
0.39/0.57	
0.39/0.57	% (2669)Memory used [KB]: 1023
0.39/0.57	% (2669)Time elapsed: 0.003 s
0.39/0.57	% (2669)Instructions burned: 3 (million)
0.39/0.57	% (2669)------------------------------
0.39/0.57	% (2669)------------------------------
0.39/0.57	% (2652)Instruction limit reached!
0.39/0.57	% (2652)------------------------------
0.39/0.57	% (2652)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.57	% (2652)Termination reason: Unknown
0.39/0.57	% (2652)Termination phase: Saturation
0.39/0.57	
0.39/0.57	% (2652)Memory used [KB]: 5500
0.39/0.57	% (2652)Time elapsed: 0.017 s
0.39/0.57	% (2652)Instructions burned: 27 (million)
0.39/0.57	% (2652)------------------------------
0.39/0.57	% (2652)------------------------------
0.39/0.57	% (2671)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_2233 for (2398ds/37Mi)
0.39/0.57	% (2672)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_2233 for (2398ds/15Mi)
0.39/0.58	% (2681)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_2233 for (2398ds/7Mi)
0.39/0.58	% (2676)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_2233 for (2398ds/3Mi)
0.39/0.58	% (2681)Instruction limit reached!
0.39/0.58	% (2681)------------------------------
0.39/0.58	% (2681)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.58	% (2681)Termination reason: Unknown
0.39/0.58	% (2681)Termination phase: Saturation
0.39/0.58	
0.39/0.58	% (2681)Memory used [KB]: 1023
0.39/0.58	% (2681)Time elapsed: 0.004 s
0.39/0.58	% (2681)Instructions burned: 7 (million)
0.39/0.58	% (2681)------------------------------
0.39/0.58	% (2681)------------------------------
0.39/0.58	% (2678)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_2233 for (2398ds/1041Mi)
0.39/0.58	% (2676)Instruction limit reached!
0.39/0.58	% (2676)------------------------------
0.39/0.58	% (2676)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.58	% (2676)Termination reason: Unknown
0.39/0.58	% (2676)Termination phase: Function definition elimination
0.39/0.58	
0.39/0.58	% (2676)Memory used [KB]: 1023
0.39/0.58	% (2676)Time elapsed: 0.005 s
0.39/0.58	% (2676)Instructions burned: 4 (million)
0.39/0.58	% (2676)------------------------------
0.39/0.58	% (2676)------------------------------
0.39/0.58	% (2672)Instruction limit reached!
0.39/0.58	% (2672)------------------------------
0.39/0.58	% (2672)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.58	% (2672)Termination reason: Unknown
0.39/0.58	% (2672)Termination phase: Saturation
0.39/0.58	
0.39/0.58	% (2672)Memory used [KB]: 5756
0.39/0.58	% (2672)Time elapsed: 0.034 s
0.39/0.58	% (2672)Instructions burned: 16 (million)
0.39/0.58	% (2672)------------------------------
0.39/0.58	% (2672)------------------------------
0.39/0.58	% (2682)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_2233 for (2398ds/16Mi)
0.39/0.59	% (2687)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_2233 for (2398ds/3Mi)
0.39/0.59	% (2687)Instruction limit reached!
0.39/0.59	% (2687)------------------------------
0.39/0.59	% (2687)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.59	% (2687)Termination reason: Unknown
0.39/0.59	% (2687)Termination phase: Function definition elimination
0.39/0.59	
0.39/0.59	% (2687)Memory used [KB]: 1023
0.39/0.59	% (2687)Time elapsed: 0.003 s
0.39/0.59	% (2687)Instructions burned: 4 (million)
0.39/0.59	% (2687)------------------------------
0.39/0.59	% (2687)------------------------------
0.39/0.59	% (2671)Instruction limit reached!
0.39/0.59	% (2671)------------------------------
0.39/0.59	% (2671)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.59	% (2671)Termination reason: Unknown
0.39/0.59	% (2671)Termination phase: Saturation
0.39/0.59	
0.39/0.59	% (2671)Memory used [KB]: 5628
0.39/0.59	% (2671)Time elapsed: 0.023 s
0.39/0.59	% (2671)Instructions burned: 37 (million)
0.39/0.59	% (2671)------------------------------
0.39/0.59	% (2671)------------------------------
0.39/0.59	% (2682)Instruction limit reached!
0.39/0.59	% (2682)------------------------------
0.39/0.59	% (2682)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.59	% (2682)Termination reason: Unknown
0.39/0.59	% (2682)Termination phase: Saturation
0.39/0.59	
0.39/0.59	% (2682)Memory used [KB]: 5884
0.39/0.59	% (2682)Time elapsed: 0.013 s
0.39/0.59	% (2682)Instructions burned: 17 (million)
0.39/0.59	% (2682)------------------------------
0.39/0.59	% (2682)------------------------------
0.39/0.60	% (2692)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_2233 for (2398ds/3Mi)
0.39/0.60	% (2700)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_2233 for (2397ds/3Mi)
0.39/0.60	% (2694)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_2233 for (2397ds/7Mi)
0.39/0.60	% (2700)Instruction limit reached!
0.39/0.60	% (2700)------------------------------
0.39/0.60	% (2700)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.60	% (2700)Termination reason: Unknown
0.39/0.60	% (2700)Termination phase: Property scanning
0.39/0.60	
0.39/0.60	% (2700)Memory used [KB]: 1023
0.39/0.60	% (2700)Time elapsed: 0.003 s
0.39/0.60	% (2700)Instructions burned: 4 (million)
0.39/0.60	% (2700)------------------------------
0.39/0.60	% (2700)------------------------------
0.39/0.60	% (2692)Instruction limit reached!
0.39/0.60	% (2692)------------------------------
0.39/0.60	% (2692)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.60	% (2692)Termination reason: Unknown
0.39/0.60	% (2692)Termination phase: Property scanning
0.39/0.60	
0.39/0.60	% (2692)Memory used [KB]: 1023
0.39/0.60	% (2692)Time elapsed: 0.004 s
0.39/0.60	% (2692)Instructions burned: 3 (million)
0.39/0.60	% (2692)------------------------------
0.39/0.60	% (2692)------------------------------
0.39/0.60	% (2694)Instruction limit reached!
0.39/0.60	% (2694)------------------------------
0.39/0.60	% (2694)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.60	% (2694)Termination reason: Unknown
0.39/0.60	% (2694)Termination phase: Saturation
0.39/0.60	
0.39/0.60	% (2694)Memory used [KB]: 5500
0.39/0.60	% (2694)Time elapsed: 0.006 s
0.39/0.60	% (2694)Instructions burned: 7 (million)
0.39/0.60	% (2694)------------------------------
0.39/0.60	% (2694)------------------------------
0.39/0.61	% (2703)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_2233 for (2397ds/4Mi)
0.39/0.61	% (2707)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_2233 for (2397ds/710Mi)
0.39/0.61	% (2703)Instruction limit reached!
0.39/0.61	% (2703)------------------------------
0.39/0.61	% (2703)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.61	% (2703)Termination reason: Unknown
0.39/0.61	% (2703)Termination phase: Property scanning
0.39/0.61	
0.39/0.61	% (2703)Memory used [KB]: 1023
0.39/0.61	% (2703)Time elapsed: 0.005 s
0.39/0.61	% (2703)Instructions burned: 6 (million)
0.39/0.61	% (2703)------------------------------
0.39/0.61	% (2703)------------------------------
0.39/0.61	% (2706)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_2233 for (2397ds/18Mi)
0.39/0.61	% (2678)First to succeed.
0.39/0.61	% (2708)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_2233 for (2397ds/6Mi)
0.39/0.62	% (2709)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_2233 for (2397ds/902Mi)
0.39/0.62	% (2708)Instruction limit reached!
0.39/0.62	% (2708)------------------------------
0.39/0.62	% (2708)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.62	% (2708)Termination reason: Unknown
0.39/0.62	% (2708)Termination phase: Saturation
0.39/0.62	
0.39/0.62	% (2708)Memory used [KB]: 5500
0.39/0.62	% (2708)Time elapsed: 0.006 s
0.39/0.62	% (2708)Instructions burned: 7 (million)
0.39/0.62	% (2708)------------------------------
0.39/0.62	% (2708)------------------------------
0.39/0.62	% (2709)Refutation not found, incomplete strategy
0.39/0.62	% (2709)------------------------------
0.39/0.62	% (2709)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.62	% (2709)Termination reason: Refutation not found, incomplete strategy
0.39/0.62	
0.39/0.62	
0.39/0.62	% (2709)Memory used [KB]: 5628
0.39/0.62	% (2709)Time elapsed: 0.007 s
0.39/0.62	% (2709)Instructions burned: 7 (million)
0.39/0.62	% (2709)------------------------------
0.39/0.62	% (2709)------------------------------
0.39/0.62	% (2706)Instruction limit reached!
0.39/0.62	% (2706)------------------------------
0.39/0.62	% (2706)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.62	% (2706)Termination reason: Unknown
0.39/0.62	% (2706)Termination phase: Saturation
0.39/0.62	
0.39/0.62	% (2706)Memory used [KB]: 5628
0.39/0.62	% (2706)Time elapsed: 0.014 s
0.39/0.62	% (2706)Instructions burned: 18 (million)
0.39/0.62	% (2706)------------------------------
0.39/0.62	% (2706)------------------------------
0.39/0.63	% (2678)Refutation found. Thanks to Tanya!
0.39/0.63	% SZS status Theorem for E---3.1_2233
0.39/0.63	% SZS output start Proof for E---3.1_2233
0.39/0.63	thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
0.39/0.63	thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
0.39/0.63	thf(func_def_2, type, cZERO: ($i > $o) > $o).
0.39/0.63	thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
0.39/0.63	thf(func_def_19, type, sK2: (($i > $o) > $o) > $o).
0.39/0.63	thf(func_def_20, type, sK3: ($i > $o) > $o).
0.39/0.63	thf(func_def_21, type, sK4: (($i > $o) > $o) > $o).
0.39/0.63	thf(func_def_22, type, sK5: ($i > $o) > $o).
0.39/0.63	thf(func_def_23, type, sK6: (($i > $o) > $o) > $o).
0.39/0.63	thf(f183,plain,(
0.39/0.63	  $false),
0.39/0.63	  inference(avatar_sat_refutation,[],[f55,f71,f176,f179])).
0.39/0.63	thf(f179,plain,(
0.39/0.63	  spl0_4 | ~spl0_1),
0.39/0.63	  inference(avatar_split_clause,[],[f178,f50,f98])).
0.39/0.63	thf(f98,plain,(
0.39/0.63	  spl0_4 <=> ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $false)),
0.39/0.63	  introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
0.39/0.63	thf(f50,plain,(
0.39/0.63	  spl0_1 <=> ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) = $false)),
0.39/0.63	  introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
0.39/0.63	thf(f178,plain,(
0.39/0.63	  ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $false) | ~spl0_1),
0.39/0.63	  inference(boolean_simplification,[],[f177])).
0.39/0.63	thf(f177,plain,(
0.39/0.63	  ($false = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & $true)) | ~spl0_1),
0.39/0.63	  inference(forward_demodulation,[],[f88,f106])).
0.39/0.63	thf(f106,plain,(
0.39/0.63	  ($true = (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) | ~spl0_1),
0.39/0.63	  inference(boolean_simplification,[],[f105])).
0.39/0.63	thf(f105,plain,(
0.39/0.63	  ($true = ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))) | ~spl0_1),
0.39/0.63	  inference(forward_demodulation,[],[f104,f89])).
0.39/0.63	thf(f89,plain,(
0.39/0.63	  ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5))))) | ~spl0_1),
0.39/0.63	  inference(binary_proxy_clausification,[],[f86])).
0.39/0.63	thf(f86,plain,(
0.39/0.63	  ($true = ((sK2 @ sK5) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))))) | ~spl0_1),
0.39/0.63	  inference(binary_proxy_clausification,[],[f77])).
0.39/0.63	thf(f77,plain,(
0.39/0.63	  ((((sK2 @ sK5) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))) = $false) | ~spl0_1),
0.39/0.63	  inference(beta_eta_normalization,[],[f76])).
0.39/0.63	thf(f76,plain,(
0.39/0.63	  (((^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) @ sK5) = $false) | ~spl0_1),
0.39/0.63	  inference(sigma_clausification,[],[f51])).
0.39/0.63	thf(f51,plain,(
0.39/0.63	  ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) = $false) | ~spl0_1),
0.39/0.63	  inference(avatar_component_clause,[],[f50])).
0.39/0.63	thf(f104,plain,(
0.39/0.63	  ($true = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))) | ~spl0_1),
0.39/0.63	  inference(boolean_simplification,[],[f103])).
0.39/0.63	thf(f103,plain,(
0.39/0.63	  ($true = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5)))) => ($true => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))))) | ~spl0_1),
0.39/0.63	  inference(superposition,[],[f75,f92])).
0.39/0.63	thf(f92,plain,(
0.39/0.63	  ($true = (sK2 @ sK5)) | ~spl0_1),
0.39/0.63	  inference(boolean_simplification,[],[f91])).
0.39/0.63	thf(f91,plain,(
0.39/0.63	  ($true = ((sK2 @ sK5) & $true)) | ~spl0_1),
0.39/0.63	  inference(backward_demodulation,[],[f86,f89])).
0.39/0.63	thf(f75,plain,(
0.39/0.63	  ( ! [X1 : ($i > $o) > $o] : (($true = ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ X1)))) => ((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))))) )),
0.39/0.63	  inference(beta_eta_normalization,[],[f74])).
0.39/0.63	thf(f74,plain,(
0.39/0.63	  ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) @ X1))) )),
0.39/0.63	  inference(pi_clausification,[],[f34])).
0.39/0.63	thf(f34,plain,(
0.39/0.63	  ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))))),
0.39/0.63	  inference(boolean_simplification,[],[f33])).
0.39/0.63	thf(f33,plain,(
0.39/0.63	  ($true = ($true & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))))))),
0.39/0.63	  inference(backward_demodulation,[],[f28,f32])).
0.39/0.63	thf(f32,plain,(
0.39/0.63	  ($true = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
0.39/0.63	  inference(binary_proxy_clausification,[],[f28])).
0.39/0.63	thf(f28,plain,(
0.39/0.63	  ($true = ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))))))),
0.39/0.63	  inference(binary_proxy_clausification,[],[f26])).
0.39/0.63	thf(f26,plain,(
0.39/0.63	  ((((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))) => ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => ((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0))))) = $false)),
0.39/0.63	  inference(beta_eta_normalization,[],[f25])).
0.39/0.63	thf(f25,plain,(
0.39/0.63	  ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4)))) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7)))))))))))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y2 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => ((Y0 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))))) => (Y0 @ Y1)))))) @ sK2))),
0.39/0.63	  inference(sigma_clausification,[],[f22])).
0.39/0.63	thf(f22,plain,(
0.39/0.63	  ($false = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4)))) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7)))))))))))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y2 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => ((Y0 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))))) => (Y0 @ Y1))))))))),
0.39/0.63	  inference(not_proxy_clausification,[],[f21])).
0.39/0.63	thf(f21,plain,(
0.39/0.63	  ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))) => ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))))))))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ Y4)))) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7)))))))))))))) => (Y3 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y2 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y0 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => ((Y0 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1)))))) => (Y0 @ Y1)))))))))),
0.39/0.63	  inference(beta_eta_normalization,[],[f20])).
0.39/0.63	thf(f20,plain,(
0.39/0.63	  ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ (^[Y2 : $i]: (Y1 @ Y2)))))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ Y1) => ((Y0 @ Y1) => (Y0 @ ((^[Y2 : ($i > $o) > $o]: ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))) @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5)))))) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))))))))) @ Y4)))))) => (Y3 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))))))))) @ Y2))))) & (Y0 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((Y5 @ Y7) & (~ (Y6 = Y7))))))))))) @ Y3))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ (^[Y4 : $i]: (Y3 @ Y4))))))) => (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ (^[Y4 : $i]: (Y3 @ Y4)))))))))) & (Y0 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => ((Y0 @ Y1) & ((^[Y2 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ ((^[Y5 : ($i > $o) > $o]: ((^[Y6 : $i > $o]: (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (Y5 @ (^[Y8 : $i]: ((Y6 @ Y8) & (~ (Y7 = Y8))))))))))) @ Y4))))) & (Y3 @ (^[Y4 : $i > $o]: (~ (?? @ $i @ (^[Y5 : $i]: (Y4 @ Y5))))))) => (Y3 @ Y2))))) @ Y1))) => (Y0 @ Y1)))))))))),
0.39/0.63	  inference(definition_unfolding,[],[f17,f18,f19,f15,f15,f18,f18,f15,f15,f15,f15,f18,f18,f18,f19])).
0.39/0.63	thf(f15,plain,(
0.39/0.63	  (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
0.39/0.63	  inference(cnf_transformation,[],[f8])).
0.39/0.63	thf(f8,plain,(
0.39/0.63	  (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
0.39/0.63	  inference(fool_elimination,[],[f7])).
0.39/0.63	thf(f7,plain,(
0.39/0.63	  ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3)))) & (X1 @ X2)))) = cSUCC)),
0.39/0.63	  inference(rectify,[],[f2])).
0.39/0.63	thf(f2,axiom,(
0.39/0.63	  ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3)))) & (X0 @ X1)))) = cSUCC)),
0.39/0.63	  file('/export/starexec/sandbox/tmp/tmp.guXwhKhjpX/E---3.1_2233.p',cSUCC_def)).
0.39/0.63	thf(f19,plain,(
0.39/0.63	  (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
0.39/0.63	  inference(definition_unfolding,[],[f16,f15,f18])).
0.39/0.63	thf(f16,plain,(
0.39/0.63	  (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
0.39/0.63	  inference(cnf_transformation,[],[f14])).
0.39/0.63	thf(f14,plain,(
0.39/0.63	  (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
0.39/0.63	  inference(fool_elimination,[],[f13])).
0.39/0.63	thf(f13,plain,(
0.39/0.63	  (cNAT = (^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))))),
0.39/0.63	  inference(rectify,[],[f3])).
0.39/0.63	thf(f3,axiom,(
0.39/0.63	  (cNAT = (^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))))),
0.39/0.63	  file('/export/starexec/sandbox/tmp/tmp.guXwhKhjpX/E---3.1_2233.p',cNAT_def)).
0.39/0.63	thf(f18,plain,(
0.39/0.63	  (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
0.39/0.63	  inference(cnf_transformation,[],[f12])).
0.39/0.63	thf(f12,plain,(
0.39/0.63	  (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
0.39/0.63	  inference(fool_elimination,[],[f11])).
0.39/0.63	thf(f11,plain,(
0.39/0.63	  ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
0.39/0.63	  inference(rectify,[],[f1])).
0.39/0.63	thf(f1,axiom,(
0.39/0.63	  ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
0.39/0.63	  file('/export/starexec/sandbox/tmp/tmp.guXwhKhjpX/E---3.1_2233.p',cZERO_def)).
0.39/0.63	thf(f17,plain,(
0.39/0.63	  ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (cSUCC @ Y4))))) & (Y3 @ cZERO)) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (cSUCC @ Y4)))))) => (Y3 @ (cSUCC @ Y2))))) & (Y0 @ (cSUCC @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3))))) & (Y2 @ cZERO)) => (Y2 @ cZERO))))) & (Y0 @ cZERO)) => ((Y0 @ Y1) & (cNAT @ Y1))) => (Y0 @ Y1)))))))))),
0.39/0.63	  inference(cnf_transformation,[],[f10])).
0.39/0.63	thf(f10,plain,(
0.39/0.63	  ($true = (~ (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((cNAT @ Y1) => ((Y0 @ Y1) => (Y0 @ (cSUCC @ Y1))))))) => (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: (((Y0 @ Y2) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (cSUCC @ Y4))))) & (Y3 @ cZERO)) => (Y3 @ Y2))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y3 : (($i > $o) > $o) > $o]: (((Y3 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y4 : ($i > $o) > $o]: ((Y3 @ Y4) => (Y3 @ (cSUCC @ Y4)))))) => (Y3 @ (cSUCC @ Y2))))) & (Y0 @ (cSUCC @ Y2)))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3))))) & (Y2 @ cZERO)) => (Y2 @ cZERO))))) & (Y0 @ cZERO)) => ((Y0 @ Y1) & (cNAT @ Y1))) => (Y0 @ Y1)))))))))),
0.39/0.63	  inference(fool_elimination,[],[f9])).
0.39/0.63	thf(f9,plain,(
0.39/0.63	  ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X2 : ($i > $o) > $o] : ((((X0 @ cZERO) & ! [X3 : (($i > $o) > $o) > $o] : (((X3 @ cZERO) & ! [X4 : ($i > $o) > $o] : ((X3 @ X4) => (X3 @ (cSUCC @ X4)))) => (X3 @ cZERO)) & ! [X5 : ($i > $o) > $o] : ((! [X6 : (($i > $o) > $o) > $o] : (((X6 @ cZERO) & ! [X7 : ($i > $o) > $o] : ((X6 @ X7) => (X6 @ (cSUCC @ X7)))) => (X6 @ X5)) & (X0 @ X5)) => ((X0 @ (cSUCC @ X5)) & ! [X8 : (($i > $o) > $o) > $o] : ((! [X9 : ($i > $o) > $o] : ((X8 @ X9) => (X8 @ (cSUCC @ X9))) & (X8 @ cZERO)) => (X8 @ (cSUCC @ X5)))))) => ((cNAT @ X2) & (X0 @ X2))) => (X0 @ X2)))),
0.39/0.63	  inference(rectify,[],[f5])).
0.39/0.63	thf(f5,negated_conjecture,(
0.39/0.63	  ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X4 : ($i > $o) > $o] : ((((X0 @ cZERO) & ! [X5 : (($i > $o) > $o) > $o] : (((X5 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X5 @ X1) => (X5 @ (cSUCC @ X1)))) => (X5 @ cZERO)) & ! [X1 : ($i > $o) > $o] : ((! [X5 : (($i > $o) > $o) > $o] : (((X5 @ cZERO) & ! [X6 : ($i > $o) > $o] : ((X5 @ X6) => (X5 @ (cSUCC @ X6)))) => (X5 @ X1)) & (X0 @ X1)) => ((X0 @ (cSUCC @ X1)) & ! [X5 : (($i > $o) > $o) > $o] : ((! [X6 : ($i > $o) > $o] : ((X5 @ X6) => (X5 @ (cSUCC @ X6))) & (X5 @ cZERO)) => (X5 @ (cSUCC @ X1)))))) => ((cNAT @ X4) & (X0 @ X4))) => (X0 @ X4)))),
0.39/0.63	  inference(negated_conjecture,[],[f4])).
0.39/0.63	thf(f4,conjecture,(
0.39/0.63	  ! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) & (X0 @ cZERO)) => ! [X4 : ($i > $o) > $o] : ((((X0 @ cZERO) & ! [X5 : (($i > $o) > $o) > $o] : (((X5 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X5 @ X1) => (X5 @ (cSUCC @ X1)))) => (X5 @ cZERO)) & ! [X1 : ($i > $o) > $o] : ((! [X5 : (($i > $o) > $o) > $o] : (((X5 @ cZERO) & ! [X6 : ($i > $o) > $o] : ((X5 @ X6) => (X5 @ (cSUCC @ X6)))) => (X5 @ X1)) & (X0 @ X1)) => ((X0 @ (cSUCC @ X1)) & ! [X5 : (($i > $o) > $o) > $o] : ((! [X6 : ($i > $o) > $o] : ((X5 @ X6) => (X5 @ (cSUCC @ X6))) & (X5 @ cZERO)) => (X5 @ (cSUCC @ X1)))))) => ((cNAT @ X4) & (X0 @ X4))) => (X0 @ X4)))),
0.39/0.63	  file('/export/starexec/sandbox/tmp/tmp.guXwhKhjpX/E---3.1_2233.p',cX6102_C)).
0.39/0.63	thf(f88,plain,(
0.39/0.63	  (((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) = $false) | ~spl0_1),
0.39/0.63	  inference(boolean_simplification,[],[f87])).
0.39/0.63	thf(f87,plain,(
0.39/0.63	  (($true => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))) = $false) | ~spl0_1),
0.39/0.63	  inference(backward_demodulation,[],[f77,f86])).
0.39/0.63	thf(f176,plain,(
0.39/0.63	  ~spl0_1 | ~spl0_4),
0.39/0.63	  inference(avatar_contradiction_clause,[],[f175])).
0.39/0.63	thf(f175,plain,(
0.39/0.63	  $false | (~spl0_1 | ~spl0_4)),
0.39/0.63	  inference(trivial_inequality_removal,[],[f174])).
0.39/0.63	thf(f174,plain,(
0.39/0.63	  ($true = $false) | (~spl0_1 | ~spl0_4)),
0.39/0.63	  inference(forward_demodulation,[],[f173,f134])).
0.39/0.63	thf(f134,plain,(
0.39/0.63	  ((sK6 @ sK5) = $false) | ~spl0_4),
0.39/0.63	  inference(not_proxy_clausification,[],[f133])).
0.39/0.63	thf(f133,plain,(
0.39/0.63	  ($true = (~ (sK6 @ sK5))) | ~spl0_4),
0.39/0.63	  inference(boolean_simplification,[],[f126])).
0.39/0.63	thf(f126,plain,(
0.39/0.63	  ($true = ((sK6 @ sK5) => $false)) | ~spl0_4),
0.39/0.63	  inference(superposition,[],[f124,f118])).
0.39/0.63	thf(f118,plain,(
0.39/0.63	  ($false = (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) | ~spl0_4),
0.39/0.63	  inference(boolean_simplification,[],[f117])).
0.39/0.63	thf(f117,plain,(
0.39/0.63	  (($true => (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) = $false) | ~spl0_4),
0.39/0.63	  inference(backward_demodulation,[],[f108,f116])).
0.39/0.63	thf(f116,plain,(
0.39/0.63	  ($true = ((sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))))) | ~spl0_4),
0.39/0.63	  inference(binary_proxy_clausification,[],[f108])).
0.39/0.63	thf(f108,plain,(
0.39/0.63	  ((((sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) => (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK5 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))) = $false) | ~spl0_4),
0.39/0.63	  inference(beta_eta_normalization,[],[f107])).
0.39/0.63	thf(f107,plain,(
0.39/0.63	  ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ sK6)) | ~spl0_4),
0.39/0.63	  inference(sigma_clausification,[],[f99])).
0.39/0.63	thf(f99,plain,(
0.39/0.63	  ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK5 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $false) | ~spl0_4),
0.39/0.63	  inference(avatar_component_clause,[],[f98])).
0.39/0.63	thf(f124,plain,(
0.39/0.63	  ( ! [X1 : ($i > $o) > $o] : (($true = ((sK6 @ X1) => (sK6 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))))) ) | ~spl0_4),
0.39/0.63	  inference(beta_eta_normalization,[],[f123])).
0.39/0.63	thf(f123,plain,(
0.39/0.63	  ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ X1))) ) | ~spl0_4),
0.39/0.63	  inference(pi_clausification,[],[f122])).
0.39/0.63	thf(f122,plain,(
0.39/0.63	  ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) | ~spl0_4),
0.39/0.63	  inference(boolean_simplification,[],[f121])).
0.39/0.63	thf(f121,plain,(
0.39/0.63	  ($true = ($true & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK6 @ Y0) => (sK6 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))))) | ~spl0_4),
0.39/0.63	  inference(backward_demodulation,[],[f116,f120])).
0.39/0.63	thf(f120,plain,(
0.39/0.63	  ($true = (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl0_4),
0.39/0.63	  inference(binary_proxy_clausification,[],[f116])).
0.39/0.63	thf(f173,plain,(
0.39/0.63	  ($true = (sK6 @ sK5)) | (~spl0_1 | ~spl0_4)),
0.39/0.63	  inference(boolean_simplification,[],[f172])).
0.39/0.63	thf(f172,plain,(
0.39/0.63	  ($true = ($true => (sK6 @ sK5))) | (~spl0_1 | ~spl0_4)),
0.39/0.63	  inference(forward_demodulation,[],[f154,f120])).
0.39/0.63	thf(f154,plain,(
0.39/0.63	  ($true = ((sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) => (sK6 @ sK5))) | (~spl0_1 | ~spl0_4)),
0.39/0.63	  inference(boolean_simplification,[],[f153])).
0.39/0.63	thf(f153,plain,(
0.39/0.63	  ($true = (($true & (sK6 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK6 @ sK5))) | (~spl0_1 | ~spl0_4)),
0.39/0.63	  inference(superposition,[],[f142,f122])).
0.39/0.63	thf(f142,plain,(
0.39/0.63	  ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK5)))) ) | ~spl0_1),
0.39/0.63	  inference(beta_eta_normalization,[],[f139])).
0.39/0.63	thf(f139,plain,(
0.39/0.63	  ( ! [X1 : (($i > $o) > $o) > $o] : (($true = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK5))) @ X1))) ) | ~spl0_1),
0.39/0.63	  inference(pi_clausification,[],[f89])).
0.39/0.63	thf(f71,plain,(
0.39/0.63	  ~spl0_2),
0.39/0.63	  inference(avatar_contradiction_clause,[],[f70])).
0.39/0.63	thf(f70,plain,(
0.39/0.63	  $false | ~spl0_2),
0.39/0.63	  inference(trivial_inequality_removal,[],[f69])).
0.39/0.63	thf(f69,plain,(
0.39/0.63	  ($true = $false) | ~spl0_2),
0.39/0.63	  inference(boolean_simplification,[],[f68])).
0.39/0.63	thf(f68,plain,(
0.39/0.63	  ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK4 @ Y0) => (sK4 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & $false)) | ~spl0_2),
0.39/0.63	  inference(forward_demodulation,[],[f61,f60])).
0.39/0.63	thf(f60,plain,(
0.39/0.63	  ((sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ~spl0_2),
0.39/0.63	  inference(binary_proxy_clausification,[],[f59])).
0.39/0.63	thf(f59,plain,(
0.39/0.63	  ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK4 @ Y0) => (sK4 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $false) | ~spl0_2),
0.39/0.63	  inference(beta_eta_normalization,[],[f58])).
0.39/0.63	thf(f58,plain,(
0.39/0.63	  (((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))) @ sK4) = $false) | ~spl0_2),
0.39/0.63	  inference(sigma_clausification,[],[f54])).
0.39/0.63	thf(f54,plain,(
0.39/0.63	  ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) = $false) | ~spl0_2),
0.39/0.63	  inference(avatar_component_clause,[],[f53])).
0.39/0.63	thf(f53,plain,(
0.39/0.63	  spl0_2 <=> ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) = $false)),
0.39/0.63	  introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
0.39/0.63	thf(f61,plain,(
0.39/0.63	  ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK4 @ Y0) => (sK4 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK4 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl0_2),
0.39/0.63	  inference(binary_proxy_clausification,[],[f59])).
0.39/0.63	thf(f55,plain,(
0.39/0.63	  spl0_1 | spl0_2),
0.39/0.63	  inference(avatar_split_clause,[],[f48,f53,f50])).
0.39/0.63	thf(f48,plain,(
0.39/0.63	  ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))))) = $false) | ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) = $false)),
0.39/0.63	  inference(binary_proxy_clausification,[],[f45])).
0.39/0.63	thf(f45,plain,(
0.39/0.63	  (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) = $false)),
0.39/0.63	  inference(boolean_simplification,[],[f44])).
0.39/0.63	thf(f44,plain,(
0.39/0.63	  ($false = (~ (~ ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))))))),
0.39/0.63	  inference(boolean_simplification,[],[f43])).
0.39/0.63	thf(f43,plain,(
0.39/0.63	  ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => $false)) = $false)),
0.39/0.63	  inference(boolean_simplification,[],[f42])).
0.39/0.63	thf(f42,plain,(
0.39/0.63	  ((~ (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ($false & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3))))))) = $false)),
0.39/0.63	  inference(boolean_simplification,[],[f41])).
0.39/0.63	thf(f41,plain,(
0.39/0.63	  ($false = ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ($false & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => $false))),
0.39/0.63	  inference(backward_demodulation,[],[f38,f39])).
0.39/0.63	thf(f39,plain,(
0.39/0.63	  ((sK2 @ sK3) = $false)),
0.39/0.63	  inference(binary_proxy_clausification,[],[f38])).
0.39/0.63	thf(f38,plain,(
0.39/0.63	  ($false = ((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) => ((sK2 @ sK3) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => (sK2 @ sK3)))),
0.39/0.63	  inference(boolean_simplification,[],[f37])).
0.39/0.63	thf(f37,plain,(
0.39/0.63	  ((((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) & $true) => ((sK2 @ sK3) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => (sK2 @ sK3)) = $false)),
0.39/0.63	  inference(forward_demodulation,[],[f36,f32])).
0.39/0.63	thf(f36,plain,(
0.39/0.63	  ($false = (((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5)))))))))))))) => (Y1 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y0 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => ((sK2 @ sK3) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK3)))))) => (sK2 @ sK3)))),
0.39/0.63	  inference(beta_eta_normalization,[],[f35])).
0.39/0.63	thf(f35,plain,(
0.39/0.63	  (((^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => ((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0))) @ sK3) = $false)),
0.39/0.63	  inference(sigma_clausification,[],[f30])).
0.39/0.63	thf(f30,plain,(
0.39/0.63	  ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => ((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0)))) = $false)),
0.39/0.63	  inference(boolean_simplification,[],[f29])).
0.39/0.63	thf(f29,plain,(
0.39/0.63	  (($true => (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: (((((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: (((sK2 @ Y1) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))))) & (Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3))))) => (Y2 @ Y1))))) => ((!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ (^[Y3 : $i > $o]: (~ (?? @ $i @ Y3)))) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6)))))))))))))) => (Y2 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y1 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (sK2 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4)))))))))))))) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2)))))))) & (sK2 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => ((sK2 @ Y0) & (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ (^[Y5 : $i]: ((Y3 @ Y5) & (~ (Y4 = Y5))))))))))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ Y2))))) => (Y1 @ Y0)))))) => (sK2 @ Y0))))) = $false)),
0.39/0.63	  inference(backward_demodulation,[],[f26,f28])).
0.39/0.63	% SZS output end Proof for E---3.1_2233
0.39/0.63	% (2678)------------------------------
0.39/0.63	% (2678)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.39/0.63	% (2678)Termination reason: Refutation
0.39/0.63	
0.39/0.63	% (2678)Memory used [KB]: 6140
0.39/0.63	% (2678)Time elapsed: 0.068 s
0.39/0.63	% (2678)Instructions burned: 55 (million)
0.39/0.63	% (2678)------------------------------
0.39/0.63	% (2678)------------------------------
0.39/0.63	% (2483)Success in time 0.256 s
0.39/0.63	EOF