%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SYN045^4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 11:55:42 EDT 2024

% Result   : Theorem 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYN045^4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 17:55:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TH0_THM_EQU_NAR problem
% 0.13/0.35  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824
% 0.13/0.37  % (29936)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.13/0.37  % (29933)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.13/0.37  % (29937)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.13/0.37  % (29938)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.13/0.37  % (29939)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.13/0.37  % (29936)Instruction limit reached!
% 0.13/0.37  % (29936)------------------------------
% 0.13/0.37  % (29936)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (29936)Termination reason: Unknown
% 0.13/0.37  % (29937)Instruction limit reached!
% 0.13/0.37  % (29937)------------------------------
% 0.13/0.37  % (29937)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (29936)Termination phase: shuffling
% 0.13/0.37  
% 0.13/0.37  % (29936)Memory used [KB]: 1023
% 0.13/0.37  % (29936)Time elapsed: 0.003 s
% 0.13/0.37  % (29936)Instructions burned: 2 (million)
% 0.13/0.37  % (29936)------------------------------
% 0.13/0.37  % (29936)------------------------------
% 0.13/0.37  % (29937)Termination reason: Unknown
% 0.13/0.37  % (29937)Termination phase: Property scanning
% 0.13/0.37  
% 0.13/0.37  % (29937)Memory used [KB]: 1023
% 0.13/0.37  % (29937)Time elapsed: 0.003 s
% 0.13/0.37  % (29937)Instructions burned: 2 (million)
% 0.13/0.37  % (29937)------------------------------
% 0.13/0.37  % (29937)------------------------------
% 0.13/0.37  % (29940)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.13/0.37  % (29938)Refutation not found, incomplete strategy
% 0.13/0.37  % (29938)------------------------------
% 0.13/0.37  % (29938)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (29938)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.37  
% 0.13/0.37  
% 0.13/0.37  % (29938)Memory used [KB]: 5500
% 0.13/0.37  % (29938)Time elapsed: 0.005 s
% 0.13/0.37  % (29938)Instructions burned: 5 (million)
% 0.13/0.37  % (29938)------------------------------
% 0.13/0.37  % (29938)------------------------------
% 0.13/0.37  % (29940)Instruction limit reached!
% 0.13/0.37  % (29940)------------------------------
% 0.13/0.37  % (29940)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37  % (29940)Termination reason: Unknown
% 0.13/0.37  % (29940)Termination phase: Function definition elimination
% 0.13/0.37  
% 0.13/0.37  % (29940)Memory used [KB]: 1023
% 0.13/0.37  % (29940)Time elapsed: 0.004 s
% 0.13/0.37  % (29940)Instructions burned: 4 (million)
% 0.13/0.37  % (29940)------------------------------
% 0.13/0.37  % (29940)------------------------------
% 0.13/0.37  % (29934)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 Vampire---4 for (2999ds/4Mi)
% 0.13/0.38  % (29935)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 Vampire---4 for (2999ds/27Mi)
% 0.13/0.38  % (29934)Instruction limit reached!
% 0.13/0.38  % (29934)------------------------------
% 0.13/0.38  % (29934)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38  % (29934)Termination reason: Unknown
% 0.13/0.38  % (29934)Termination phase: Property scanning
% 0.13/0.38  
% 0.13/0.38  % (29934)Memory used [KB]: 1023
% 0.13/0.38  % (29934)Time elapsed: 0.004 s
% 0.13/0.38  % (29934)Instructions burned: 5 (million)
% 0.13/0.38  % (29934)------------------------------
% 0.13/0.38  % (29934)------------------------------
% 0.13/0.38  % (29939)Instruction limit reached!
% 0.13/0.38  % (29939)------------------------------
% 0.13/0.38  % (29939)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38  % (29939)Termination reason: Unknown
% 0.13/0.38  % (29939)Termination phase: Saturation
% 0.13/0.38  
% 0.13/0.38  % (29939)Memory used [KB]: 5628
% 0.13/0.38  % (29939)Time elapsed: 0.011 s
% 0.13/0.38  % (29939)Instructions burned: 19 (million)
% 0.13/0.38  % (29939)------------------------------
% 0.13/0.38  % (29939)------------------------------
% 0.13/0.38  % (29941)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 Vampire---4 for (2999ds/37Mi)
% 0.13/0.39  % (29942)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 Vampire---4 for (2999ds/15Mi)
% 0.13/0.39  % (29943)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.13/0.39  % (29943)Instruction limit reached!
% 0.13/0.39  % (29943)------------------------------
% 0.13/0.39  % (29943)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (29943)Termination reason: Unknown
% 0.13/0.39  % (29943)Termination phase: Function definition elimination
% 0.13/0.39  
% 0.13/0.39  % (29943)Memory used [KB]: 1023
% 0.13/0.39  % (29943)Time elapsed: 0.004 s
% 0.13/0.39  % (29943)Instructions burned: 5 (million)
% 0.13/0.39  % (29943)------------------------------
% 0.13/0.39  % (29943)------------------------------
% 0.13/0.39  % (29935)Instruction limit reached!
% 0.13/0.39  % (29935)------------------------------
% 0.13/0.39  % (29935)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (29935)Termination reason: Unknown
% 0.13/0.39  % (29935)Termination phase: Saturation
% 0.13/0.39  
% 0.13/0.39  % (29935)Memory used [KB]: 5756
% 0.13/0.39  % (29935)Time elapsed: 0.016 s
% 0.13/0.39  % (29935)Instructions burned: 28 (million)
% 0.13/0.39  % (29935)------------------------------
% 0.13/0.39  % (29935)------------------------------
% 0.13/0.39  % (29946)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.13/0.39  % (29944)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 Vampire---4 for (2999ds/1041Mi)
% 0.13/0.39  % (29945)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.13/0.39  % (29942)Instruction limit reached!
% 0.13/0.39  % (29942)------------------------------
% 0.13/0.39  % (29942)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39  % (29942)Termination reason: Unknown
% 0.13/0.39  % (29942)Termination phase: Saturation
% 0.13/0.39  
% 0.13/0.39  % (29942)Memory used [KB]: 5628
% 0.13/0.39  % (29942)Time elapsed: 0.009 s
% 0.13/0.39  % (29942)Instructions burned: 15 (million)
% 0.13/0.39  % (29942)------------------------------
% 0.13/0.39  % (29942)------------------------------
% 0.13/0.40  % (29945)Instruction limit reached!
% 0.13/0.40  % (29945)------------------------------
% 0.13/0.40  % (29945)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40  % (29945)Termination reason: Unknown
% 0.13/0.40  % (29945)Termination phase: Saturation
% 0.13/0.40  
% 0.13/0.40  % (29945)Memory used [KB]: 1023
% 0.13/0.40  % (29945)Time elapsed: 0.006 s
% 0.13/0.40  % (29945)Instructions burned: 9 (million)
% 0.13/0.40  % (29945)------------------------------
% 0.13/0.40  % (29945)------------------------------
% 0.13/0.40  % (29946)Instruction limit reached!
% 0.13/0.40  % (29946)------------------------------
% 0.13/0.40  % (29946)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40  % (29946)Termination reason: Unknown
% 0.13/0.40  % (29946)Termination phase: Saturation
% 0.13/0.40  
% 0.13/0.40  % (29946)Memory used [KB]: 5884
% 0.21/0.40  % (29946)Time elapsed: 0.033 s
% 0.21/0.40  % (29946)Instructions burned: 17 (million)
% 0.21/0.40  % (29946)------------------------------
% 0.21/0.40  % (29946)------------------------------
% 0.21/0.40  % (29947)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 Vampire---4 for (2999ds/3Mi)
% 0.21/0.40  % (29948)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 Vampire---4 for (2999ds/3Mi)
% 0.21/0.40  % (29941)Instruction limit reached!
% 0.21/0.40  % (29941)------------------------------
% 0.21/0.40  % (29941)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40  % (29941)Termination reason: Unknown
% 0.21/0.40  % (29941)Termination phase: Saturation
% 0.21/0.40  
% 0.21/0.40  % (29941)Memory used [KB]: 5628
% 0.21/0.40  % (29941)Time elapsed: 0.022 s
% 0.21/0.40  % (29941)Instructions burned: 37 (million)
% 0.21/0.40  % (29941)------------------------------
% 0.21/0.40  % (29941)------------------------------
% 0.21/0.41  % (29947)Instruction limit reached!
% 0.21/0.41  % (29947)------------------------------
% 0.21/0.41  % (29947)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (29947)Termination reason: Unknown
% 0.21/0.41  % (29947)Termination phase: Function definition elimination
% 0.21/0.41  
% 0.21/0.41  % (29947)Memory used [KB]: 1023
% 0.21/0.41  % (29947)Time elapsed: 0.004 s
% 0.21/0.41  % (29947)Instructions burned: 4 (million)
% 0.21/0.41  % (29947)------------------------------
% 0.21/0.41  % (29947)------------------------------
% 0.21/0.41  % (29948)Instruction limit reached!
% 0.21/0.41  % (29948)------------------------------
% 0.21/0.41  % (29948)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (29948)Termination reason: Unknown
% 0.21/0.41  % (29948)Termination phase: Function definition elimination
% 0.21/0.41  
% 0.21/0.41  % (29948)Memory used [KB]: 1023
% 0.21/0.41  % (29948)Time elapsed: 0.004 s
% 0.21/0.41  % (29948)Instructions burned: 4 (million)
% 0.21/0.41  % (29948)------------------------------
% 0.21/0.41  % (29948)------------------------------
% 0.21/0.41  % (29949)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.21/0.41  % (29951)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.21/0.41  % (29950)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.41  % (29949)Instruction limit reached!
% 0.21/0.41  % (29949)------------------------------
% 0.21/0.41  % (29949)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (29949)Termination reason: Unknown
% 0.21/0.41  % (29949)Termination phase: Saturation
% 0.21/0.41  
% 0.21/0.41  % (29949)Memory used [KB]: 5500
% 0.21/0.41  % (29949)Time elapsed: 0.005 s
% 0.21/0.41  % (29949)Instructions burned: 7 (million)
% 0.21/0.41  % (29949)------------------------------
% 0.21/0.41  % (29949)------------------------------
% 0.21/0.41  % (29951)Instruction limit reached!
% 0.21/0.41  % (29951)------------------------------
% 0.21/0.41  % (29951)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (29950)Instruction limit reached!
% 0.21/0.41  % (29950)------------------------------
% 0.21/0.41  % (29950)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41  % (29950)Termination reason: Unknown
% 0.21/0.41  % (29950)Termination phase: Property scanning
% 0.21/0.41  
% 0.21/0.41  % (29950)Memory used [KB]: 1023
% 0.21/0.41  % (29950)Time elapsed: 0.003 s
% 0.21/0.41  % (29950)Instructions burned: 3 (million)
% 0.21/0.41  % (29950)------------------------------
% 0.21/0.41  % (29950)------------------------------
% 0.21/0.41  % (29951)Termination reason: Unknown
% 0.21/0.41  % (29951)Termination phase: Function definition elimination
% 0.21/0.41  
% 0.21/0.41  % (29951)Memory used [KB]: 1023
% 0.21/0.41  % (29951)Time elapsed: 0.003 s
% 0.21/0.41  % (29951)Instructions burned: 4 (million)
% 0.21/0.41  % (29951)------------------------------
% 0.21/0.41  % (29951)------------------------------
% 0.21/0.42  % (29952)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.42  % (29953)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.21/0.42  % (29957)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.21/0.42  % (29954)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.21/0.42  % (29957)Instruction limit reached!
% 0.21/0.42  % (29957)------------------------------
% 0.21/0.42  % (29957)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (29957)Termination reason: Unknown
% 0.21/0.42  % (29957)Termination phase: Property scanning
% 0.21/0.42  
% 0.21/0.42  % (29957)Memory used [KB]: 1023
% 0.21/0.42  % (29957)Time elapsed: 0.003 s
% 0.21/0.42  % (29957)Instructions burned: 6 (million)
% 0.21/0.42  % (29957)------------------------------
% 0.21/0.42  % (29957)------------------------------
% 0.21/0.42  % (29954)Instruction limit reached!
% 0.21/0.42  % (29954)------------------------------
% 0.21/0.42  % (29954)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (29954)Termination reason: Unknown
% 0.21/0.42  % (29954)Termination phase: Saturation
% 0.21/0.42  
% 0.21/0.42  % (29954)Memory used [KB]: 5500
% 0.21/0.42  % (29954)Time elapsed: 0.005 s
% 0.21/0.42  % (29954)Instructions burned: 6 (million)
% 0.21/0.42  % (29954)------------------------------
% 0.21/0.42  % (29954)------------------------------
% 0.21/0.42  % (29953)Refutation not found, incomplete strategy
% 0.21/0.42  % (29953)------------------------------
% 0.21/0.42  % (29953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42  % (29953)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42  
% 0.21/0.42  
% 0.21/0.42  % (29953)Memory used [KB]: 5500
% 0.21/0.42  % (29953)Time elapsed: 0.006 s
% 0.21/0.42  % (29953)Instructions burned: 5 (million)
% 0.21/0.42  % (29953)------------------------------
% 0.21/0.42  % (29953)------------------------------
% 0.21/0.43  % (29955)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 Vampire---4 for (2999ds/902Mi)
% 0.21/0.43  % (29955)Refutation not found, incomplete strategy
% 0.21/0.43  % (29955)------------------------------
% 0.21/0.43  % (29955)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (29955)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  % (29955)Memory used [KB]: 5500
% 0.21/0.43  % (29958)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 Vampire---4 for (2999ds/6Mi)
% 0.21/0.43  % (29955)Time elapsed: 0.005 s
% 0.21/0.43  % (29955)Instructions burned: 4 (million)
% 0.21/0.43  % (29955)------------------------------
% 0.21/0.43  % (29955)------------------------------
% 0.21/0.43  % (29952)Instruction limit reached!
% 0.21/0.43  % (29952)------------------------------
% 0.21/0.43  % (29952)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (29952)Termination reason: Unknown
% 0.21/0.43  % (29958)Refutation not found, incomplete strategy
% 0.21/0.43  % (29958)------------------------------
% 0.21/0.43  % (29958)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43  % (29958)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  % (29958)Memory used [KB]: 5500
% 0.21/0.43  % (29958)Time elapsed: 0.003 s
% 0.21/0.43  % (29958)Instructions burned: 3 (million)
% 0.21/0.43  % (29958)------------------------------
% 0.21/0.43  % (29958)------------------------------
% 0.21/0.43  % (29952)Termination phase: Saturation
% 0.21/0.43  
% 0.21/0.43  % (29952)Memory used [KB]: 5628
% 0.21/0.43  % (29952)Time elapsed: 0.014 s
% 0.21/0.43  % (29952)Instructions burned: 19 (million)
% 0.21/0.43  % (29952)------------------------------
% 0.21/0.43  % (29952)------------------------------
% 0.21/0.43  % (29956)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 Vampire---4 for (2999ds/21Mi)
% 0.21/0.44  % (29959)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.21/0.44  % (29963)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2999ds/17Mi)
% 0.21/0.44  % (29960)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 Vampire---4 for (2999ds/779Mi)
% 0.21/0.44  % (29963)Instruction limit reached!
% 0.21/0.44  % (29963)------------------------------
% 0.21/0.44  % (29963)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44  % (29963)Termination reason: Unknown
% 0.21/0.44  % (29963)Termination phase: Saturation
% 0.21/0.44  
% 0.21/0.44  % (29963)Memory used [KB]: 5628
% 0.21/0.44  % (29963)Time elapsed: 0.006 s
% 0.21/0.44  % (29963)Instructions burned: 18 (million)
% 0.21/0.44  % (29963)------------------------------
% 0.21/0.44  % (29963)------------------------------
% 0.21/0.44  % (29961)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 Vampire---4 for (2999ds/19Mi)
% 0.21/0.45  % (29962)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2999ds/879Mi)
% 0.21/0.45  % (29961)Refutation not found, incomplete strategy
% 0.21/0.45  % (29961)------------------------------
% 0.21/0.45  % (29961)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (29961)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  % (29961)Memory used [KB]: 5500
% 0.21/0.45  % (29961)Time elapsed: 0.004 s
% 0.21/0.45  % (29961)Instructions burned: 4 (million)
% 0.21/0.45  % (29961)------------------------------
% 0.21/0.45  % (29961)------------------------------
% 0.21/0.45  % (29964)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.45  % (29956)Instruction limit reached!
% 0.21/0.45  % (29956)------------------------------
% 0.21/0.45  % (29956)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (29956)Termination reason: Unknown
% 0.21/0.45  % (29956)Termination phase: Saturation
% 0.21/0.45  
% 0.21/0.45  % (29956)Memory used [KB]: 5628
% 0.21/0.45  % (29956)Time elapsed: 0.020 s
% 0.21/0.45  % (29956)Instructions burned: 21 (million)
% 0.21/0.45  % (29956)------------------------------
% 0.21/0.45  % (29956)------------------------------
% 0.21/0.45  % (29964)Instruction limit reached!
% 0.21/0.45  % (29964)------------------------------
% 0.21/0.45  % (29964)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45  % (29964)Termination reason: Unknown
% 0.21/0.45  % (29964)Termination phase: Property scanning
% 0.21/0.45  
% 0.21/0.45  % (29964)Memory used [KB]: 1023
% 0.21/0.45  % (29964)Time elapsed: 0.002 s
% 0.21/0.45  % (29964)Instructions burned: 3 (million)
% 0.21/0.45  % (29964)------------------------------
% 0.21/0.45  % (29964)------------------------------
% 0.21/0.45  % (29944)First to succeed.
% 0.21/0.46  % (29966)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on Vampire---4 for (2999ds/127Mi)
% 0.21/0.46  % (29965)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on Vampire---4 for (2999ds/30Mi)
% 0.21/0.46  % (29944)Refutation found. Thanks to Tanya!
% 0.21/0.46  % SZS status Theorem for Vampire---4
% 0.21/0.46  % SZS output start Proof for Vampire---4
% 0.21/0.46  thf(func_def_0, type, irel: $i > $i > $o).
% 0.21/0.46  thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_9, type, itrue: $i > $o).
% 0.21/0.46  thf(func_def_10, type, ifalse: $i > $o).
% 0.21/0.46  thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.46  thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.21/0.46  thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.21/0.46  thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.21/0.46  thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.21/0.46  thf(func_def_21, type, p: $i > $o).
% 0.21/0.46  thf(func_def_22, type, q: $i > $o).
% 0.21/0.46  thf(func_def_23, type, r: $i > $o).
% 0.21/0.46  thf(func_def_37, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.46  thf(f714,plain,(
% 0.21/0.46    $false),
% 0.21/0.46    inference(avatar_sat_refutation,[],[f130,f154,f204,f332,f361,f434,f455,f536,f589,f597,f619,f713])).
% 0.21/0.46  thf(f713,plain,(
% 0.21/0.46    ~spl0_2 | ~spl0_4 | ~spl0_6),
% 0.21/0.46    inference(avatar_contradiction_clause,[],[f712])).
% 0.21/0.46  thf(f712,plain,(
% 0.21/0.46    $false | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 0.21/0.46    inference(trivial_inequality_removal,[],[f711])).
% 0.21/0.46  thf(f711,plain,(
% 0.21/0.46    ($false = $true) | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 0.21/0.46    inference(forward_demodulation,[],[f708,f699])).
% 0.21/0.46  thf(f699,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK4) = $false) | (~spl0_4 | ~spl0_6)),
% 0.21/0.46    inference(not_proxy_clausification,[],[f654])).
% 0.21/0.46  thf(f654,plain,(
% 0.21/0.46    ((~ (irel @ sK2 @ sK4)) = $true) | (~spl0_4 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f653])).
% 0.21/0.46  thf(f653,plain,(
% 0.21/0.46    ($true = ((irel @ sK2 @ sK4) => $false)) | (~spl0_4 | ~spl0_6)),
% 0.21/0.46    inference(superposition,[],[f602,f642])).
% 0.21/0.46  thf(f642,plain,(
% 0.21/0.46    ((p @ sK4) = $false) | ~spl0_6),
% 0.21/0.46    inference(boolean_simplification,[],[f641])).
% 0.21/0.46  thf(f641,plain,(
% 0.21/0.46    (($true => (p @ sK4)) = $false) | ~spl0_6),
% 0.21/0.46    inference(backward_demodulation,[],[f636,f640])).
% 0.21/0.46  thf(f640,plain,(
% 0.21/0.46    ($true = (irel @ sK3 @ sK4)) | ~spl0_6),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f636])).
% 0.21/0.46  thf(f636,plain,(
% 0.21/0.46    ($false = ((irel @ sK3 @ sK4) => (p @ sK4))) | ~spl0_6),
% 0.21/0.46    inference(beta_eta_normalization,[],[f635])).
% 0.21/0.46  thf(f635,plain,(
% 0.21/0.46    ($false = ((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))) @ sK4)) | ~spl0_6),
% 0.21/0.46    inference(sigma_clausification,[],[f631])).
% 0.21/0.46  thf(f631,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))))) | ~spl0_6),
% 0.21/0.46    inference(boolean_simplification,[],[f630])).
% 0.21/0.46  thf(f630,plain,(
% 0.21/0.46    ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | $false)) | ~spl0_6),
% 0.21/0.46    inference(backward_demodulation,[],[f203,f628])).
% 0.21/0.46  thf(f628,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))))) | ~spl0_6),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f203])).
% 0.21/0.46  thf(f203,plain,(
% 0.21/0.46    ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0)))))) | ~spl0_6),
% 0.21/0.46    inference(avatar_component_clause,[],[f202])).
% 0.21/0.46  thf(f202,plain,(
% 0.21/0.46    spl0_6 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))))))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.21/0.46  thf(f602,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (p @ X1)) = $true)) ) | ~spl0_4),
% 0.21/0.46    inference(beta_eta_normalization,[],[f600])).
% 0.21/0.46  thf(f600,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))) @ X1))) ) | ~spl0_4),
% 0.21/0.46    inference(pi_clausification,[],[f153])).
% 0.21/0.46  thf(f153,plain,(
% 0.21/0.46    ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | ~spl0_4),
% 0.21/0.46    inference(avatar_component_clause,[],[f152])).
% 0.21/0.46  thf(f152,plain,(
% 0.21/0.46    spl0_4 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.21/0.46  thf(f708,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK4) = $true) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f706])).
% 0.21/0.46  thf(f706,plain,(
% 0.21/0.46    (($true => (irel @ sK2 @ sK4)) = $true) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(superposition,[],[f685,f640])).
% 0.21/0.46  thf(f685,plain,(
% 0.21/0.46    ( ! [X0 : $i] : ((((irel @ sK3 @ X0) => (irel @ sK2 @ X0)) = $true)) ) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f678])).
% 0.21/0.46  thf(f678,plain,(
% 0.21/0.46    ( ! [X0 : $i] : (($true = (((irel @ sK3 @ X0) & $true) => (irel @ sK2 @ X0)))) ) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(superposition,[],[f108,f669])).
% 0.21/0.46  thf(f669,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK3) = $true) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(not_proxy_clausification,[],[f662])).
% 0.21/0.46  thf(f662,plain,(
% 0.21/0.46    ($false = (~ (irel @ sK2 @ sK3))) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f661])).
% 0.21/0.46  thf(f661,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => $false)) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f660])).
% 0.21/0.46  thf(f660,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0)))) & $false))) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(forward_demodulation,[],[f659,f628])).
% 0.21/0.46  thf(f659,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))))))) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f658])).
% 0.21/0.46  thf(f658,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) & (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))))))) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f657])).
% 0.21/0.46  thf(f657,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) & ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0)))))))) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(forward_demodulation,[],[f656,f631])).
% 0.21/0.46  thf(f656,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0)))))))) | ~spl0_2),
% 0.21/0.46    inference(beta_eta_normalization,[],[f655])).
% 0.21/0.46  thf(f655,plain,(
% 0.21/0.46    ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))) @ sK3)) | ~spl0_2),
% 0.21/0.46    inference(sigma_clausification,[],[f624])).
% 0.21/0.46  thf(f624,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))) = $false) | ~spl0_2),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f129])).
% 0.21/0.46  thf(f129,plain,(
% 0.21/0.46    ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))))) | ~spl0_2),
% 0.21/0.46    inference(avatar_component_clause,[],[f128])).
% 0.21/0.46  thf(f128,plain,(
% 0.21/0.46    spl0_2 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.21/0.46  thf(f108,plain,(
% 0.21/0.46    ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((irel @ X3 @ X2) & (irel @ X1 @ X3)) => (irel @ X1 @ X2)) = $true)) )),
% 0.21/0.46    inference(beta_eta_normalization,[],[f107])).
% 0.21/0.46  thf(f107,plain,(
% 0.21/0.46    ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((irel @ Y0 @ X2) & (irel @ X1 @ Y0)) => (irel @ X1 @ X2))) @ X3) = $true)) )),
% 0.21/0.46    inference(pi_clausification,[],[f106])).
% 0.21/0.46  thf(f106,plain,(
% 0.21/0.46    ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((irel @ Y0 @ X2) & (irel @ X1 @ Y0)) => (irel @ X1 @ X2)))))) )),
% 0.21/0.46    inference(beta_eta_normalization,[],[f105])).
% 0.21/0.46  thf(f105,plain,(
% 0.21/0.46    ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((irel @ Y1 @ Y0) & (irel @ X1 @ Y1)) => (irel @ X1 @ Y0))))) @ X2))) )),
% 0.21/0.46    inference(pi_clausification,[],[f104])).
% 0.21/0.46  thf(f104,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((irel @ Y1 @ Y0) & (irel @ X1 @ Y1)) => (irel @ X1 @ Y0)))))))) )),
% 0.21/0.46    inference(beta_eta_normalization,[],[f103])).
% 0.21/0.46  thf(f103,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((irel @ Y2 @ Y1) & (irel @ Y0 @ Y2)) => (irel @ Y0 @ Y1))))))) @ X1))) )),
% 0.21/0.46    inference(pi_clausification,[],[f84])).
% 0.21/0.46  thf(f84,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((irel @ Y2 @ Y1) & (irel @ Y0 @ Y2)) => (irel @ Y0 @ Y1)))))))) = $true)),
% 0.21/0.46    inference(cnf_transformation,[],[f42])).
% 0.21/0.46  thf(f42,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((irel @ Y2 @ Y1) & (irel @ Y0 @ Y2)) => (irel @ Y0 @ Y1)))))))) = $true)),
% 0.21/0.46    inference(fool_elimination,[],[f41])).
% 0.21/0.46  thf(f41,plain,(
% 0.21/0.46    ! [X0,X1,X2] : (((irel @ X2 @ X0) & (irel @ X0 @ X1)) => (irel @ X2 @ X1))),
% 0.21/0.46    inference(rectify,[],[f2])).
% 0.21/0.46  thf(f2,axiom,(
% 0.21/0.46    ! [X1,X2,X0] : (((irel @ X0 @ X1) & (irel @ X1 @ X2)) => (irel @ X0 @ X2))),
% 0.21/0.46    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',trans_axiom)).
% 0.21/0.46  thf(f619,plain,(
% 0.21/0.46    ~spl0_1 | ~spl0_4),
% 0.21/0.46    inference(avatar_contradiction_clause,[],[f618])).
% 0.21/0.46  thf(f618,plain,(
% 0.21/0.46    $false | (~spl0_1 | ~spl0_4)),
% 0.21/0.46    inference(trivial_inequality_removal,[],[f617])).
% 0.21/0.46  thf(f617,plain,(
% 0.21/0.46    ($false = $true) | (~spl0_1 | ~spl0_4)),
% 0.21/0.46    inference(boolean_simplification,[],[f616])).
% 0.21/0.46  thf(f616,plain,(
% 0.21/0.46    ((~ $true) = $true) | (~spl0_1 | ~spl0_4)),
% 0.21/0.46    inference(forward_demodulation,[],[f613,f576])).
% 0.21/0.46  thf(f576,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK9) = $true) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f572])).
% 0.21/0.46  thf(f572,plain,(
% 0.21/0.46    ($true = ($true => (irel @ sK2 @ sK9))) | ~spl0_1),
% 0.21/0.46    inference(superposition,[],[f385,f517])).
% 0.21/0.46  thf(f517,plain,(
% 0.21/0.46    ($true = (irel @ sK7 @ sK9)) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f511])).
% 0.21/0.46  thf(f511,plain,(
% 0.21/0.46    ($false = ((irel @ sK7 @ sK9) => (p @ sK9))) | ~spl0_1),
% 0.21/0.46    inference(beta_eta_normalization,[],[f509])).
% 0.21/0.46  thf(f509,plain,(
% 0.21/0.46    ($false = ((^[Y0 : $i]: ((irel @ sK7 @ Y0) => (p @ Y0))) @ sK9)) | ~spl0_1),
% 0.21/0.46    inference(sigma_clausification,[],[f399])).
% 0.21/0.46  thf(f399,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (p @ Y0))))) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f376])).
% 0.21/0.46  thf(f376,plain,(
% 0.21/0.46    ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => ((q @ Y0) & (r @ Y0))))))) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f375])).
% 0.21/0.46  thf(f375,plain,(
% 0.21/0.46    (($true => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => ((q @ Y0) & (r @ Y0))))))) = $false) | ~spl0_1),
% 0.21/0.46    inference(backward_demodulation,[],[f369,f374])).
% 0.21/0.46  thf(f374,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK7) = $true) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f369])).
% 0.21/0.46  thf(f369,plain,(
% 0.21/0.46    (((irel @ sK2 @ sK7) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => ((q @ Y0) & (r @ Y0))))))) = $false) | ~spl0_1),
% 0.21/0.46    inference(beta_eta_normalization,[],[f368])).
% 0.21/0.46  thf(f368,plain,(
% 0.21/0.46    (((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))) @ sK7) = $false) | ~spl0_1),
% 0.21/0.46    inference(sigma_clausification,[],[f364])).
% 0.21/0.46  thf(f364,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f126])).
% 0.21/0.46  thf(f126,plain,(
% 0.21/0.46    ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1))))))))))) | ~spl0_1),
% 0.21/0.46    inference(avatar_component_clause,[],[f125])).
% 0.21/0.46  thf(f125,plain,(
% 0.21/0.46    spl0_1 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.46  thf(f385,plain,(
% 0.21/0.46    ( ! [X0 : $i] : (($true = ((irel @ sK7 @ X0) => (irel @ sK2 @ X0)))) ) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f381])).
% 0.21/0.46  thf(f381,plain,(
% 0.21/0.46    ( ! [X0 : $i] : (((((irel @ sK7 @ X0) & $true) => (irel @ sK2 @ X0)) = $true)) ) | ~spl0_1),
% 0.21/0.46    inference(superposition,[],[f108,f374])).
% 0.21/0.46  thf(f613,plain,(
% 0.21/0.46    ((~ (irel @ sK2 @ sK9)) = $true) | (~spl0_1 | ~spl0_4)),
% 0.21/0.46    inference(boolean_simplification,[],[f610])).
% 0.21/0.46  thf(f610,plain,(
% 0.21/0.46    (((irel @ sK2 @ sK9) => $false) = $true) | (~spl0_1 | ~spl0_4)),
% 0.21/0.46    inference(superposition,[],[f602,f519])).
% 0.21/0.46  thf(f519,plain,(
% 0.21/0.46    ((p @ sK9) = $false) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f518])).
% 0.21/0.46  thf(f518,plain,(
% 0.21/0.46    (($true => (p @ sK9)) = $false) | ~spl0_1),
% 0.21/0.46    inference(backward_demodulation,[],[f511,f517])).
% 0.21/0.46  thf(f597,plain,(
% 0.21/0.46    ~spl0_1 | ~spl0_7 | ~spl0_10),
% 0.21/0.46    inference(avatar_contradiction_clause,[],[f596])).
% 0.21/0.46  thf(f596,plain,(
% 0.21/0.46    $false | (~spl0_1 | ~spl0_7 | ~spl0_10)),
% 0.21/0.46    inference(trivial_inequality_removal,[],[f595])).
% 0.21/0.46  thf(f595,plain,(
% 0.21/0.46    ($false = $true) | (~spl0_1 | ~spl0_7 | ~spl0_10)),
% 0.21/0.46    inference(boolean_simplification,[],[f594])).
% 0.21/0.46  thf(f594,plain,(
% 0.21/0.46    ((~ $true) = $true) | (~spl0_1 | ~spl0_7 | ~spl0_10)),
% 0.21/0.46    inference(forward_demodulation,[],[f593,f574])).
% 0.21/0.46  thf(f574,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK8) = $true) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f571])).
% 0.21/0.46  thf(f571,plain,(
% 0.21/0.46    ($true = ($true => (irel @ sK2 @ sK8))) | ~spl0_1),
% 0.21/0.46    inference(superposition,[],[f385,f416])).
% 0.21/0.46  thf(f416,plain,(
% 0.21/0.46    ($true = (irel @ sK7 @ sK8)) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f410])).
% 0.21/0.46  thf(f410,plain,(
% 0.21/0.46    (((irel @ sK7 @ sK8) => ((q @ sK8) & (r @ sK8))) = $false) | ~spl0_1),
% 0.21/0.46    inference(beta_eta_normalization,[],[f409])).
% 0.21/0.46  thf(f409,plain,(
% 0.21/0.46    (((^[Y0 : $i]: ((irel @ sK7 @ Y0) => ((q @ Y0) & (r @ Y0)))) @ sK8) = $false) | ~spl0_1),
% 0.21/0.46    inference(sigma_clausification,[],[f402])).
% 0.21/0.46  thf(f402,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => ((q @ Y0) & (r @ Y0))))) = $false) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f401])).
% 0.21/0.46  thf(f401,plain,(
% 0.21/0.46    ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => ((q @ Y0) & (r @ Y0))))))) | ~spl0_1),
% 0.21/0.46    inference(backward_demodulation,[],[f376,f399])).
% 0.21/0.46  thf(f593,plain,(
% 0.21/0.46    ($true = (~ (irel @ sK2 @ sK8))) | (~spl0_7 | ~spl0_10)),
% 0.21/0.46    inference(boolean_simplification,[],[f592])).
% 0.21/0.46  thf(f592,plain,(
% 0.21/0.46    ($true = ((irel @ sK2 @ sK8) => $false)) | (~spl0_7 | ~spl0_10)),
% 0.21/0.46    inference(superposition,[],[f548,f430])).
% 0.21/0.46  thf(f430,plain,(
% 0.21/0.46    ($false = (r @ sK8)) | ~spl0_7),
% 0.21/0.46    inference(avatar_component_clause,[],[f429])).
% 0.21/0.46  thf(f429,plain,(
% 0.21/0.46    spl0_7 <=> ($false = (r @ sK8))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.21/0.46  thf(f548,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (r @ X1)) = $true)) ) | ~spl0_10),
% 0.21/0.46    inference(beta_eta_normalization,[],[f546])).
% 0.21/0.46  thf(f546,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))) @ X1))) ) | ~spl0_10),
% 0.21/0.46    inference(pi_clausification,[],[f535])).
% 0.21/0.46  thf(f535,plain,(
% 0.21/0.46    ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) | ~spl0_10),
% 0.21/0.46    inference(avatar_component_clause,[],[f534])).
% 0.21/0.46  thf(f534,plain,(
% 0.21/0.46    spl0_10 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.21/0.46  thf(f589,plain,(
% 0.21/0.46    ~spl0_1 | ~spl0_8 | ~spl0_9),
% 0.21/0.46    inference(avatar_contradiction_clause,[],[f588])).
% 0.21/0.46  thf(f588,plain,(
% 0.21/0.46    $false | (~spl0_1 | ~spl0_8 | ~spl0_9)),
% 0.21/0.46    inference(trivial_inequality_removal,[],[f587])).
% 0.21/0.46  thf(f587,plain,(
% 0.21/0.46    ($false = $true) | (~spl0_1 | ~spl0_8 | ~spl0_9)),
% 0.21/0.46    inference(boolean_simplification,[],[f586])).
% 0.21/0.46  thf(f586,plain,(
% 0.21/0.46    ((~ $true) = $true) | (~spl0_1 | ~spl0_8 | ~spl0_9)),
% 0.21/0.46    inference(forward_demodulation,[],[f504,f574])).
% 0.21/0.46  thf(f504,plain,(
% 0.21/0.46    ($true = (~ (irel @ sK2 @ sK8))) | (~spl0_8 | ~spl0_9)),
% 0.21/0.46    inference(boolean_simplification,[],[f497])).
% 0.21/0.46  thf(f497,plain,(
% 0.21/0.46    ($true = ((irel @ sK2 @ sK8) => $false)) | (~spl0_8 | ~spl0_9)),
% 0.21/0.46    inference(superposition,[],[f489,f433])).
% 0.21/0.46  thf(f433,plain,(
% 0.21/0.46    ($false = (q @ sK8)) | ~spl0_8),
% 0.21/0.46    inference(avatar_component_clause,[],[f432])).
% 0.21/0.46  thf(f432,plain,(
% 0.21/0.46    spl0_8 <=> ($false = (q @ sK8))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.21/0.46  thf(f489,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => (q @ X1)))) ) | ~spl0_9),
% 0.21/0.46    inference(beta_eta_normalization,[],[f487])).
% 0.21/0.46  thf(f487,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))) @ X1) = $true)) ) | ~spl0_9),
% 0.21/0.46    inference(pi_clausification,[],[f454])).
% 0.21/0.46  thf(f454,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) = $true) | ~spl0_9),
% 0.21/0.46    inference(avatar_component_clause,[],[f453])).
% 0.21/0.46  thf(f453,plain,(
% 0.21/0.46    spl0_9 <=> ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) = $true)),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.21/0.46  thf(f536,plain,(
% 0.21/0.46    spl0_10 | spl0_4 | ~spl0_1),
% 0.21/0.46    inference(avatar_split_clause,[],[f526,f125,f152,f534])).
% 0.21/0.46  thf(f526,plain,(
% 0.21/0.46    ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f440])).
% 0.21/0.46  thf(f440,plain,(
% 0.21/0.46    (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))) = $true) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f391])).
% 0.21/0.46  thf(f391,plain,(
% 0.21/0.46    ($true = (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0))))))) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f388])).
% 0.21/0.46  thf(f388,plain,(
% 0.21/0.46    ($true = ($true => (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (r @ Y0)))))))) | ~spl0_1),
% 0.21/0.46    inference(superposition,[],[f378,f102])).
% 0.21/0.46  thf(f102,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (((irel @ X1 @ X1) = $true)) )),
% 0.21/0.46    inference(beta_eta_normalization,[],[f101])).
% 0.21/0.46  thf(f101,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (irel @ Y0 @ Y0)) @ X1))) )),
% 0.21/0.46    inference(pi_clausification,[],[f85])).
% 0.21/0.46  thf(f85,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: (irel @ Y0 @ Y0))) = $true)),
% 0.21/0.46    inference(cnf_transformation,[],[f46])).
% 0.21/0.46  thf(f46,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: (irel @ Y0 @ Y0))) = $true)),
% 0.21/0.46    inference(fool_elimination,[],[f45])).
% 0.21/0.46  thf(f45,plain,(
% 0.21/0.46    ! [X0] : (irel @ X0 @ X0)),
% 0.21/0.46    inference(rectify,[],[f1])).
% 0.21/0.46  thf(f1,axiom,(
% 0.21/0.46    ! [X0] : (irel @ X0 @ X0)),
% 0.21/0.46    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',refl_axiom)).
% 0.21/0.46  thf(f378,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (q @ Y0))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (r @ Y0))))))) = $true)) ) | ~spl0_1),
% 0.21/0.46    inference(beta_eta_normalization,[],[f377])).
% 0.21/0.46  thf(f377,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.21/0.46    inference(pi_clausification,[],[f370])).
% 0.21/0.46  thf(f370,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))) = $true) | ~spl0_1),
% 0.21/0.46    inference(not_proxy_clausification,[],[f367])).
% 0.21/0.46  thf(f367,plain,(
% 0.21/0.46    ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) = $false) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f366])).
% 0.21/0.46  thf(f366,plain,(
% 0.21/0.46    (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) | $false) = $false) | ~spl0_1),
% 0.21/0.46    inference(backward_demodulation,[],[f126,f364])).
% 0.21/0.46  thf(f455,plain,(
% 0.21/0.46    spl0_9 | spl0_4 | ~spl0_1),
% 0.21/0.46    inference(avatar_split_clause,[],[f449,f125,f152,f453])).
% 0.21/0.46  thf(f449,plain,(
% 0.21/0.46    ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))) = $true) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f445])).
% 0.21/0.46  thf(f445,plain,(
% 0.21/0.46    ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0)))))) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f444])).
% 0.21/0.46  thf(f444,plain,(
% 0.21/0.46    ((((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (q @ Y0))))) & $true) = $true) | ~spl0_1),
% 0.21/0.46    inference(backward_demodulation,[],[f391,f440])).
% 0.21/0.46  thf(f434,plain,(
% 0.21/0.46    spl0_7 | spl0_8 | ~spl0_1),
% 0.21/0.46    inference(avatar_split_clause,[],[f425,f125,f432,f429])).
% 0.21/0.46  thf(f425,plain,(
% 0.21/0.46    ($false = (q @ sK8)) | ($false = (r @ sK8)) | ~spl0_1),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f418])).
% 0.21/0.46  thf(f418,plain,(
% 0.21/0.46    (((q @ sK8) & (r @ sK8)) = $false) | ~spl0_1),
% 0.21/0.46    inference(boolean_simplification,[],[f417])).
% 0.21/0.46  thf(f417,plain,(
% 0.21/0.46    (($true => ((q @ sK8) & (r @ sK8))) = $false) | ~spl0_1),
% 0.21/0.46    inference(backward_demodulation,[],[f410,f416])).
% 0.21/0.46  thf(f361,plain,(
% 0.21/0.46    ~spl0_2 | ~spl0_3 | ~spl0_6),
% 0.21/0.46    inference(avatar_contradiction_clause,[],[f360])).
% 0.21/0.46  thf(f360,plain,(
% 0.21/0.46    $false | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.46    inference(trivial_inequality_removal,[],[f359])).
% 0.21/0.46  thf(f359,plain,(
% 0.21/0.46    ($false = $true) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f358])).
% 0.21/0.46  thf(f358,plain,(
% 0.21/0.46    ((~ $true) = $true) | (~spl0_2 | ~spl0_3 | ~spl0_6)),
% 0.21/0.46    inference(backward_demodulation,[],[f349,f355])).
% 0.21/0.46  thf(f355,plain,(
% 0.21/0.46    ($true = (irel @ sK2 @ sK6)) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f350])).
% 0.21/0.46  thf(f350,plain,(
% 0.21/0.46    ($true = ($true => (irel @ sK2 @ sK6))) | (~spl0_2 | ~spl0_6)),
% 0.21/0.46    inference(superposition,[],[f189,f344])).
% 0.21/0.46  thf(f344,plain,(
% 0.21/0.46    ((irel @ sK3 @ sK6) = $true) | ~spl0_6),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f342])).
% 0.21/0.46  thf(f342,plain,(
% 0.21/0.46    ($false = ((irel @ sK3 @ sK6) => (r @ sK6))) | ~spl0_6),
% 0.21/0.46    inference(beta_eta_normalization,[],[f341])).
% 0.21/0.46  thf(f341,plain,(
% 0.21/0.46    ($false = ((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))) @ sK6)) | ~spl0_6),
% 0.21/0.46    inference(sigma_clausification,[],[f340])).
% 0.21/0.46  thf(f340,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))))) | ~spl0_6),
% 0.21/0.46    inference(boolean_simplification,[],[f337])).
% 0.21/0.46  thf(f337,plain,(
% 0.21/0.46    ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0)))))) | ~spl0_6),
% 0.21/0.46    inference(backward_demodulation,[],[f203,f336])).
% 0.21/0.46  thf(f336,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))))) | ~spl0_6),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f203])).
% 0.21/0.46  thf(f189,plain,(
% 0.21/0.46    ( ! [X0 : $i] : ((((irel @ sK3 @ X0) => (irel @ sK2 @ X0)) = $true)) ) | ~spl0_2),
% 0.21/0.46    inference(boolean_simplification,[],[f186])).
% 0.21/0.46  thf(f186,plain,(
% 0.21/0.46    ( ! [X0 : $i] : (($true = (((irel @ sK3 @ X0) & $true) => (irel @ sK2 @ X0)))) ) | ~spl0_2),
% 0.21/0.46    inference(superposition,[],[f108,f174])).
% 0.21/0.46  thf(f174,plain,(
% 0.21/0.46    ((irel @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f166])).
% 0.21/0.46  thf(f166,plain,(
% 0.21/0.46    ($false = ((irel @ sK2 @ sK3) => (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0)))))))) | ~spl0_2),
% 0.21/0.46    inference(beta_eta_normalization,[],[f165])).
% 0.21/0.46  thf(f165,plain,(
% 0.21/0.46    ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))) @ sK3)) | ~spl0_2),
% 0.21/0.46    inference(sigma_clausification,[],[f133])).
% 0.21/0.46  thf(f133,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))) = $false) | ~spl0_2),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f129])).
% 0.21/0.46  thf(f349,plain,(
% 0.21/0.46    ($true = (~ (irel @ sK2 @ sK6))) | (~spl0_3 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f348])).
% 0.21/0.46  thf(f348,plain,(
% 0.21/0.46    ($true = ((irel @ sK2 @ sK6) => $false)) | (~spl0_3 | ~spl0_6)),
% 0.21/0.46    inference(boolean_simplification,[],[f347])).
% 0.21/0.46  thf(f347,plain,(
% 0.21/0.46    (((irel @ sK2 @ sK6) => ((q @ sK6) & $false)) = $true) | (~spl0_3 | ~spl0_6)),
% 0.21/0.46    inference(superposition,[],[f159,f346])).
% 0.21/0.46  thf(f346,plain,(
% 0.21/0.46    ((r @ sK6) = $false) | ~spl0_6),
% 0.21/0.46    inference(boolean_simplification,[],[f345])).
% 0.21/0.46  thf(f345,plain,(
% 0.21/0.46    ($false = ($true => (r @ sK6))) | ~spl0_6),
% 0.21/0.46    inference(backward_demodulation,[],[f342,f344])).
% 0.21/0.46  thf(f159,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => ((q @ X1) & (r @ X1))))) ) | ~spl0_3),
% 0.21/0.46    inference(beta_eta_normalization,[],[f157])).
% 0.21/0.46  thf(f157,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (r @ Y0)))) @ X1) = $true)) ) | ~spl0_3),
% 0.21/0.46    inference(pi_clausification,[],[f150])).
% 0.21/0.46  thf(f150,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (r @ Y0))))) = $true) | ~spl0_3),
% 0.21/0.46    inference(avatar_component_clause,[],[f149])).
% 0.21/0.46  thf(f149,plain,(
% 0.21/0.46    spl0_3 <=> ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (r @ Y0))))) = $true)),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.21/0.46  thf(f332,plain,(
% 0.21/0.46    ~spl0_2 | ~spl0_5),
% 0.21/0.46    inference(avatar_contradiction_clause,[],[f331])).
% 0.21/0.46  thf(f331,plain,(
% 0.21/0.46    $false | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(trivial_inequality_removal,[],[f330])).
% 0.21/0.46  thf(f330,plain,(
% 0.21/0.46    ($false = $true) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(boolean_simplification,[],[f329])).
% 0.21/0.46  thf(f329,plain,(
% 0.21/0.46    ((~ $true) = $true) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(forward_demodulation,[],[f307,f280])).
% 0.21/0.46  thf(f280,plain,(
% 0.21/0.46    ((irel @ sK3 @ sK5) = $true) | ~spl0_5),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f272])).
% 0.21/0.46  thf(f272,plain,(
% 0.21/0.46    ($false = ((irel @ sK3 @ sK5) => (q @ sK5))) | ~spl0_5),
% 0.21/0.46    inference(beta_eta_normalization,[],[f271])).
% 0.21/0.46  thf(f271,plain,(
% 0.21/0.46    (((^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))) @ sK5) = $false) | ~spl0_5),
% 0.21/0.46    inference(sigma_clausification,[],[f213])).
% 0.21/0.46  thf(f213,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0)))) = $false) | ~spl0_5),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.46  thf(f200,plain,(
% 0.21/0.46    ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0)))))) | ~spl0_5),
% 0.21/0.46    inference(avatar_component_clause,[],[f199])).
% 0.21/0.46  thf(f199,plain,(
% 0.21/0.46    spl0_5 <=> ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))))),
% 0.21/0.46    introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.21/0.46  thf(f307,plain,(
% 0.21/0.46    ($true = (~ (irel @ sK3 @ sK5))) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(boolean_simplification,[],[f306])).
% 0.21/0.46  thf(f306,plain,(
% 0.21/0.46    (((irel @ sK3 @ sK5) => $false) = $true) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(boolean_simplification,[],[f303])).
% 0.21/0.46  thf(f303,plain,(
% 0.21/0.46    ($true = ((irel @ sK3 @ sK5) => ($false & (r @ sK5)))) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(superposition,[],[f292,f279])).
% 0.21/0.46  thf(f279,plain,(
% 0.21/0.46    ((q @ sK5) = $false) | ~spl0_5),
% 0.21/0.46    inference(binary_proxy_clausification,[],[f272])).
% 0.21/0.46  thf(f292,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((irel @ sK3 @ X1) => ((q @ X1) & (r @ X1))) = $true)) ) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(beta_eta_normalization,[],[f288])).
% 0.21/0.46  thf(f288,plain,(
% 0.21/0.46    ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK3 @ Y0) => ((q @ Y0) & (r @ Y0)))) @ X1))) ) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(pi_clausification,[],[f218])).
% 0.21/0.46  thf(f218,plain,(
% 0.21/0.46    ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => ((q @ Y0) & (r @ Y0))))) = $true) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(boolean_simplification,[],[f217])).
% 0.21/0.46  thf(f217,plain,(
% 0.21/0.46    (($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => ((q @ Y0) & (r @ Y0)))))) = $true) | (~spl0_2 | ~spl0_5)),
% 0.21/0.46    inference(backward_demodulation,[],[f188,f216])).
% 0.21/0.46  thf(f216,plain,(
% 0.21/0.46    ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0))))) | ~spl0_5),
% 0.21/0.46    inference(boolean_simplification,[],[f215])).
% 0.21/0.46  thf(f215,plain,(
% 0.21/0.46    ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | $false)) | ~spl0_5),
% 0.21/0.46    inference(backward_demodulation,[],[f200,f213])).
% 0.21/0.46  thf(f188,plain,(
% 0.21/0.46    ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => ((q @ Y0) & (r @ Y0))))))) | ~spl0_2),
% 0.21/0.46    inference(boolean_simplification,[],[f184])).
% 0.21/0.46  thf(f184,plain,(
% 0.21/0.46    ($true = ($true => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => ((q @ Y0) & (r @ Y0)))))))) | ~spl0_2),
% 0.21/0.46    inference(superposition,[],[f141,f174])).
% 0.21/0.46  thf(f141,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((q @ Y0) & (r @ Y0))))))) = $true)) ) | ~spl0_2),
% 0.21/0.46    inference(beta_eta_normalization,[],[f140])).
% 0.21/0.46  thf(f140,plain,(
% 0.21/0.46    ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))) @ X1) = $true)) ) | ~spl0_2),
% 0.21/0.46    inference(pi_clausification,[],[f137])).
% 0.21/0.46  thf(f137,plain,(
% 0.21/0.46    ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | ~spl0_2),
% 0.21/0.46    inference(not_proxy_clausification,[],[f136])).
% 0.21/0.46  thf(f136,plain,(
% 0.21/0.46    ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1))))))))))) | ~spl0_2),
% 0.21/0.47    inference(boolean_simplification,[],[f135])).
% 0.21/0.47  thf(f135,plain,(
% 0.21/0.47    ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | $false)) | ~spl0_2),
% 0.21/0.47    inference(backward_demodulation,[],[f129,f133])).
% 0.21/0.47  thf(f204,plain,(
% 0.21/0.47    spl0_5 | spl0_6 | ~spl0_2),
% 0.21/0.47    inference(avatar_split_clause,[],[f197,f128,f202,f199])).
% 0.21/0.47  thf(f197,plain,(
% 0.21/0.47    ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0)))))) | ~spl0_2),
% 0.21/0.47    inference(binary_proxy_clausification,[],[f173])).
% 0.21/0.47  thf(f173,plain,(
% 0.21/0.47    ($false = (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (q @ Y0))))) & ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (r @ Y0))))))) | ~spl0_2),
% 0.21/0.47    inference(binary_proxy_clausification,[],[f166])).
% 0.21/0.47  thf(f154,plain,(
% 0.21/0.47    spl0_3 | spl0_4 | ~spl0_2),
% 0.21/0.47    inference(avatar_split_clause,[],[f145,f128,f152,f149])).
% 0.21/0.47  thf(f145,plain,(
% 0.21/0.47    ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (r @ Y0))))) = $true) | ~spl0_2),
% 0.21/0.47    inference(binary_proxy_clausification,[],[f144])).
% 0.21/0.47  thf(f144,plain,(
% 0.21/0.47    (((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (r @ Y0)))))) = $true) | ~spl0_2),
% 0.21/0.47    inference(boolean_simplification,[],[f143])).
% 0.21/0.47  thf(f143,plain,(
% 0.21/0.47    (($true => ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((q @ Y0) & (r @ Y0))))))) = $true) | ~spl0_2),
% 0.21/0.47    inference(superposition,[],[f141,f102])).
% 0.21/0.47  thf(f130,plain,(
% 0.21/0.47    spl0_1 | spl0_2),
% 0.21/0.47    inference(avatar_split_clause,[],[f123,f128,f125])).
% 0.21/0.47  thf(f123,plain,(
% 0.21/0.47    ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))))),
% 0.21/0.47    inference(binary_proxy_clausification,[],[f122])).
% 0.21/0.47  thf(f122,plain,(
% 0.21/0.47    ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (q @ Y1))))) & ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (r @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((q @ Y1) & (r @ Y1))))))))))) = $false)),
% 0.21/0.47    inference(beta_eta_normalization,[],[f121])).
% 0.21/0.47  thf(f121,plain,(
% 0.21/0.47    ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((q @ Y2) & (r @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) & ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) & ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((q @ Y2) & (r @ Y2)))))))))))) @ sK2))),
% 0.21/0.47    inference(sigma_clausification,[],[f118])).
% 0.21/0.47  thf(f118,plain,(
% 0.21/0.47    ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((q @ Y2) & (r @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) & ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) & ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((q @ Y2) & (r @ Y2))))))))))))))),
% 0.21/0.47    inference(not_proxy_clausification,[],[f100])).
% 0.21/0.47  thf(f100,plain,(
% 0.21/0.47    ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((q @ Y2) & (r @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) & ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (q @ Y2))))) & ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (r @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => ((q @ Y2) & (r @ Y2)))))))))))))) = $true)),
% 0.21/0.47    inference(beta_eta_normalization,[],[f99])).
% 0.21/0.47  thf(f99,plain,(
% 0.21/0.47    ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ q) @ ((^[Y0 : $i > $o]: (Y0)) @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p) @ ((^[Y0 : $i > $o]: (Y0)) @ r)))))) = $true)),
% 0.21/0.47    inference(definition_unfolding,[],[f70,f69,f97,f94,f89,f93,f89,f89,f93,f94,f89,f89,f94,f89,f89])).
% 0.21/0.47  thf(f93,plain,(
% 0.21/0.47    (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ Y0 @ Y1)))))),
% 0.21/0.47    inference(definition_unfolding,[],[f80,f76])).
% 0.21/0.47  thf(f76,plain,(
% 0.21/0.47    (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f26])).
% 0.21/0.47  thf(f26,plain,(
% 0.21/0.47    (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.21/0.47    inference(fool_elimination,[],[f25])).
% 0.21/0.47  thf(f25,plain,(
% 0.21/0.47    (mand = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 0.21/0.47    inference(rectify,[],[f5])).
% 0.21/0.47  thf(f5,axiom,(
% 0.21/0.47    (mand = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) & (X0 @ X3))))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',mand)).
% 0.21/0.47  thf(f80,plain,(
% 0.21/0.47    (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.21/0.47    inference(cnf_transformation,[],[f54])).
% 0.21/0.47  thf(f54,plain,(
% 0.21/0.47    (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.21/0.47    inference(fool_elimination,[],[f53])).
% 0.21/0.47  thf(f53,plain,(
% 0.21/0.47    ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ X0 @ X1)) = iand)),
% 0.21/0.47    inference(rectify,[],[f12])).
% 0.21/0.47  thf(f12,axiom,(
% 0.21/0.47    ((^[X5 : $i > $o, X7 : $i > $o] : (mand @ X5 @ X7)) = iand)),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',iand)).
% 0.21/0.47  thf(f89,plain,(
% 0.21/0.47    (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.21/0.47    inference(cnf_transformation,[],[f67])).
% 0.21/0.47  thf(f67,plain,(
% 0.21/0.47    (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.21/0.47    inference(fool_elimination,[],[f66])).
% 0.21/0.47  thf(f66,plain,(
% 0.21/0.47    (iatom = (^[X0 : $i > $o] : (X0)))),
% 0.21/0.47    inference(rectify,[],[f8])).
% 0.21/0.47  thf(f8,axiom,(
% 0.21/0.47    (iatom = (^[X5 : $i > $o] : (X5)))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',iatom)).
% 0.21/0.47  thf(f94,plain,(
% 0.21/0.47    (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.21/0.47    inference(definition_unfolding,[],[f75,f81,f72,f72])).
% 0.21/0.47  thf(f72,plain,(
% 0.21/0.47    (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f40])).
% 0.21/0.47  thf(f40,plain,(
% 0.21/0.47    (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.21/0.47    inference(fool_elimination,[],[f39])).
% 0.21/0.47  thf(f39,plain,(
% 0.21/0.47    (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))))),
% 0.21/0.47    inference(rectify,[],[f7])).
% 0.21/0.47  thf(f7,axiom,(
% 0.21/0.47    (mbox_s4 = (^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',mbox_s4)).
% 0.21/0.47  thf(f81,plain,(
% 0.21/0.47    (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f56])).
% 0.21/0.47  thf(f56,plain,(
% 0.21/0.47    (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.47    inference(fool_elimination,[],[f55])).
% 0.21/0.47  thf(f55,plain,(
% 0.21/0.47    (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.21/0.47    inference(rectify,[],[f4])).
% 0.21/0.47  thf(f4,axiom,(
% 0.21/0.47    (mor = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',mor)).
% 0.21/0.47  thf(f75,plain,(
% 0.21/0.47    (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f58])).
% 0.21/0.47  thf(f58,plain,(
% 0.21/0.47    (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.21/0.47    inference(fool_elimination,[],[f57])).
% 0.21/0.47  thf(f57,plain,(
% 0.21/0.47    ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = ior)),
% 0.21/0.47    inference(rectify,[],[f13])).
% 0.21/0.47  thf(f13,axiom,(
% 0.21/0.47    ((^[X5 : $i > $o, X7 : $i > $o] : (mor @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = ior)),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',ior)).
% 0.21/0.47  thf(f97,plain,(
% 0.21/0.47    (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) & (Y5 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 0.21/0.47    inference(definition_unfolding,[],[f87,f93,f95,f95])).
% 0.21/0.47  thf(f95,plain,(
% 0.21/0.47    (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.21/0.47    inference(definition_unfolding,[],[f73,f90,f72,f72])).
% 0.21/0.47  thf(f90,plain,(
% 0.21/0.47    (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.47    inference(definition_unfolding,[],[f79,f81,f68])).
% 0.21/0.47  thf(f68,plain,(
% 0.21/0.47    (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f28])).
% 0.21/0.47  thf(f28,plain,(
% 0.21/0.47    (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.47    inference(fool_elimination,[],[f27])).
% 0.21/0.47  thf(f27,plain,(
% 0.21/0.47    ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.47    inference(rectify,[],[f3])).
% 0.21/0.47  thf(f3,axiom,(
% 0.21/0.47    ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',mnot)).
% 0.21/0.47  thf(f79,plain,(
% 0.21/0.47    (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.47    inference(cnf_transformation,[],[f65])).
% 0.21/0.47  thf(f65,plain,(
% 0.21/0.47    (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.47    inference(fool_elimination,[],[f64])).
% 0.21/0.47  thf(f64,plain,(
% 0.21/0.47    ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.47    inference(rectify,[],[f6])).
% 0.21/0.47  thf(f6,axiom,(
% 0.21/0.47    ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',mimplies)).
% 0.21/0.47  thf(f73,plain,(
% 0.21/0.47    (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f48])).
% 0.21/0.47  thf(f48,plain,(
% 0.21/0.47    (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.21/0.47    inference(fool_elimination,[],[f47])).
% 0.21/0.47  thf(f47,plain,(
% 0.21/0.47    (iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.21/0.47    inference(rectify,[],[f14])).
% 0.21/0.47  thf(f14,axiom,(
% 0.21/0.47    (iimplies = (^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',iimplies)).
% 0.21/0.47  thf(f87,plain,(
% 0.21/0.47    (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f52])).
% 0.21/0.47  thf(f52,plain,(
% 0.21/0.47    (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.21/0.47    inference(fool_elimination,[],[f51])).
% 0.21/0.47  thf(f51,plain,(
% 0.21/0.47    (iequiv = (^[X0 : $i > $o, X1 : $i > $o] : (iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0))))),
% 0.21/0.47    inference(rectify,[],[f16])).
% 0.21/0.47  thf(f16,axiom,(
% 0.21/0.47    (iequiv = (^[X5 : $i > $o, X7 : $i > $o] : (iand @ (iimplies @ X5 @ X7) @ (iimplies @ X7 @ X5))))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',iequiv)).
% 0.21/0.47  thf(f69,plain,(
% 0.21/0.47    (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.47    inference(cnf_transformation,[],[f32])).
% 0.21/0.47  thf(f32,plain,(
% 0.21/0.47    (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.47    inference(fool_elimination,[],[f31])).
% 0.21/0.47  thf(f31,plain,(
% 0.21/0.47    ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.21/0.47    inference(rectify,[],[f18])).
% 0.21/0.47  thf(f18,axiom,(
% 0.21/0.47    ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',ivalid)).
% 0.21/0.47  thf(f70,plain,(
% 0.21/0.47    ($true = (~ (ivalid @ (iequiv @ (ior @ (iatom @ p) @ (iand @ (iatom @ q) @ (iatom @ r))) @ (iand @ (ior @ (iatom @ p) @ (iatom @ q)) @ (ior @ (iatom @ p) @ (iatom @ r)))))))),
% 0.21/0.47    inference(cnf_transformation,[],[f36])).
% 0.21/0.47  thf(f36,plain,(
% 0.21/0.47    ($true = (~ (ivalid @ (iequiv @ (ior @ (iatom @ p) @ (iand @ (iatom @ q) @ (iatom @ r))) @ (iand @ (ior @ (iatom @ p) @ (iatom @ q)) @ (ior @ (iatom @ p) @ (iatom @ r)))))))),
% 0.21/0.47    inference(fool_elimination,[],[f35])).
% 0.21/0.47  thf(f35,plain,(
% 0.21/0.47    ~(ivalid @ (iequiv @ (ior @ (iatom @ p) @ (iand @ (iatom @ q) @ (iatom @ r))) @ (iand @ (ior @ (iatom @ p) @ (iatom @ q)) @ (ior @ (iatom @ p) @ (iatom @ r)))))),
% 0.21/0.47    inference(rectify,[],[f23])).
% 0.21/0.47  thf(f23,negated_conjecture,(
% 0.21/0.47    ~(ivalid @ (iequiv @ (ior @ (iatom @ p) @ (iand @ (iatom @ q) @ (iatom @ r))) @ (iand @ (ior @ (iatom @ p) @ (iatom @ q)) @ (ior @ (iatom @ p) @ (iatom @ r)))))),
% 0.21/0.47    inference(negated_conjecture,[],[f22])).
% 0.21/0.47  thf(f22,conjecture,(
% 0.21/0.47    (ivalid @ (iequiv @ (ior @ (iatom @ p) @ (iand @ (iatom @ q) @ (iatom @ r))) @ (iand @ (ior @ (iatom @ p) @ (iatom @ q)) @ (ior @ (iatom @ p) @ (iatom @ r)))))),
% 0.21/0.47    file('/export/starexec/sandbox/tmp/tmp.TsvtjasgJv/Vampire---4.8_29824',pel13)).
% 0.21/0.47  % SZS output end Proof for Vampire---4
% 0.21/0.47  % (29944)------------------------------
% 0.21/0.47  % (29944)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47  % (29944)Termination reason: Refutation
% 0.21/0.47  
% 0.21/0.47  % (29944)Memory used [KB]: 6012
% 0.21/0.47  % (29944)Time elapsed: 0.097 s
% 0.21/0.47  % (29944)Instructions burned: 100 (million)
% 0.21/0.47  % (29944)------------------------------
% 0.21/0.47  % (29944)------------------------------
% 0.21/0.47  % (29932)Success in time 0.108 s
% 0.21/0.47  % Vampire---4.8 exiting
%------------------------------------------------------------------------------