TSTP Solution File: SYN367^7 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN367^7 : TPTP v8.2.0. Released v5.5.0.
% 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 : n011.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 : Tue May 21 08:22:04 EDT 2024
% Result : Theorem 2.21s 0.63s
% Output : Refutation 2.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN367^7 : TPTP v8.2.0. Released v5.5.0.
% 0.12/0.14 % 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
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 14:28:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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/benchmark/theBenchmark.p
% 0.15/0.38 % (28495)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (28493)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 theBenchmark for (2999ds/27Mi)
% 0.15/0.38 % (28494)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (28492)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 theBenchmark for (2999ds/4Mi)
% 0.15/0.38 % (28491)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (28496)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.15/0.38 % (28497)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (28498)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.38 % (28494)Instruction limit reached!
% 0.15/0.38 % (28494)------------------------------
% 0.15/0.38 % (28494)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28494)Termination reason: Unknown
% 0.15/0.38 % (28495)Instruction limit reached!
% 0.15/0.38 % (28495)------------------------------
% 0.15/0.38 % (28495)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28495)Termination reason: Unknown
% 0.15/0.38 % (28495)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (28495)Memory used [KB]: 1023
% 0.15/0.38 % (28495)Time elapsed: 0.004 s
% 0.15/0.38 % (28495)Instructions burned: 3 (million)
% 0.15/0.38 % (28495)------------------------------
% 0.15/0.38 % (28495)------------------------------
% 0.15/0.38 % (28494)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (28494)Memory used [KB]: 1023
% 0.15/0.38 % (28494)Time elapsed: 0.004 s
% 0.15/0.38 % (28494)Instructions burned: 3 (million)
% 0.15/0.38 % (28494)------------------------------
% 0.15/0.38 % (28494)------------------------------
% 0.15/0.38 % (28498)Instruction limit reached!
% 0.15/0.38 % (28498)------------------------------
% 0.15/0.38 % (28498)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28498)Termination reason: Unknown
% 0.15/0.38 % (28498)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (28498)Memory used [KB]: 1023
% 0.15/0.38 % (28498)Time elapsed: 0.004 s
% 0.15/0.38 % (28498)Instructions burned: 3 (million)
% 0.15/0.38 % (28498)------------------------------
% 0.15/0.38 % (28498)------------------------------
% 0.15/0.38 % (28492)Instruction limit reached!
% 0.15/0.38 % (28492)------------------------------
% 0.15/0.38 % (28492)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (28492)Termination reason: Unknown
% 0.15/0.38 % (28492)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (28492)Memory used [KB]: 1023
% 0.15/0.38 % (28492)Time elapsed: 0.004 s
% 0.15/0.38 % (28492)Instructions burned: 5 (million)
% 0.15/0.38 % (28492)------------------------------
% 0.15/0.38 % (28492)------------------------------
% 0.15/0.39 % (28497)Instruction limit reached!
% 0.15/0.39 % (28497)------------------------------
% 0.15/0.39 % (28497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28497)Termination reason: Unknown
% 0.15/0.39 % (28497)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (28497)Memory used [KB]: 5628
% 0.15/0.39 % (28497)Time elapsed: 0.011 s
% 0.15/0.39 % (28497)Instructions burned: 18 (million)
% 0.15/0.39 % (28497)------------------------------
% 0.15/0.39 % (28497)------------------------------
% 0.15/0.40 % (28493)Instruction limit reached!
% 0.15/0.40 % (28493)------------------------------
% 0.15/0.40 % (28493)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (28493)Termination reason: Unknown
% 0.15/0.40 % (28493)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (28493)Memory used [KB]: 5756
% 0.15/0.40 % (28493)Time elapsed: 0.016 s
% 0.15/0.40 % (28493)Instructions burned: 27 (million)
% 0.15/0.40 % (28493)------------------------------
% 0.15/0.40 % (28493)------------------------------
% 0.15/0.40 % (28499)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 theBenchmark for (2999ds/37Mi)
% 0.15/0.40 % (28500)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 theBenchmark for (2999ds/15Mi)
% 0.15/0.40 % (28501)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.40 % (28502)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 theBenchmark for (2999ds/1041Mi)
% 0.15/0.40 % (28501)Instruction limit reached!
% 0.15/0.40 % (28501)------------------------------
% 0.15/0.40 % (28501)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (28501)Termination reason: Unknown
% 0.15/0.40 % (28501)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (28501)Memory used [KB]: 1023
% 0.15/0.40 % (28501)Time elapsed: 0.004 s
% 0.15/0.40 % (28501)Instructions burned: 4 (million)
% 0.15/0.40 % (28501)------------------------------
% 0.15/0.40 % (28501)------------------------------
% 0.15/0.40 % (28503)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.41 % (28500)Instruction limit reached!
% 0.15/0.41 % (28500)------------------------------
% 0.15/0.41 % (28500)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (28500)Termination reason: Unknown
% 0.15/0.41 % (28500)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (28500)Memory used [KB]: 5628
% 0.15/0.41 % (28500)Time elapsed: 0.010 s
% 0.15/0.41 % (28500)Instructions burned: 16 (million)
% 0.15/0.41 % (28500)------------------------------
% 0.15/0.41 % (28500)------------------------------
% 0.22/0.41 % (28503)Instruction limit reached!
% 0.22/0.41 % (28503)------------------------------
% 0.22/0.41 % (28503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (28503)Termination reason: Unknown
% 0.22/0.41 % (28503)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (28503)Memory used [KB]: 1023
% 0.22/0.41 % (28503)Time elapsed: 0.006 s
% 0.22/0.41 % (28503)Instructions burned: 7 (million)
% 0.22/0.41 % (28503)------------------------------
% 0.22/0.41 % (28503)------------------------------
% 0.22/0.41 % (28504)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42 % (28505)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 theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (28499)Instruction limit reached!
% 0.22/0.42 % (28499)------------------------------
% 0.22/0.42 % (28499)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (28505)Instruction limit reached!
% 0.22/0.42 % (28505)------------------------------
% 0.22/0.42 % (28505)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (28499)Termination reason: Unknown
% 0.22/0.42 % (28499)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (28499)Memory used [KB]: 5756
% 0.22/0.42 % (28499)Time elapsed: 0.022 s
% 0.22/0.42 % (28499)Instructions burned: 37 (million)
% 0.22/0.42 % (28499)------------------------------
% 0.22/0.42 % (28499)------------------------------
% 0.22/0.42 % (28505)Termination reason: Unknown
% 0.22/0.42 % (28505)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (28505)Memory used [KB]: 1023
% 0.22/0.42 % (28505)Time elapsed: 0.004 s
% 0.22/0.42 % (28505)Instructions burned: 4 (million)
% 0.22/0.42 % (28505)------------------------------
% 0.22/0.42 % (28505)------------------------------
% 0.22/0.42 % (28504)Instruction limit reached!
% 0.22/0.42 % (28504)------------------------------
% 0.22/0.42 % (28504)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (28504)Termination reason: Unknown
% 0.22/0.42 % (28504)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (28504)Memory used [KB]: 5884
% 0.22/0.42 % (28504)Time elapsed: 0.012 s
% 0.22/0.42 % (28504)Instructions burned: 16 (million)
% 0.22/0.42 % (28504)------------------------------
% 0.22/0.42 % (28504)------------------------------
% 0.22/0.42 % (28506)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 theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (28506)Instruction limit reached!
% 0.22/0.42 % (28506)------------------------------
% 0.22/0.42 % (28506)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (28506)Termination reason: Unknown
% 0.22/0.42 % (28506)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (28506)Memory used [KB]: 1023
% 0.22/0.42 % (28506)Time elapsed: 0.004 s
% 0.22/0.42 % (28506)Instructions burned: 4 (million)
% 0.22/0.42 % (28506)------------------------------
% 0.22/0.42 % (28506)------------------------------
% 0.22/0.43 % (28511)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.43 % (28512)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.43 % (28508)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.43 % (28511)Instruction limit reached!
% 0.22/0.43 % (28511)------------------------------
% 0.22/0.43 % (28511)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (28511)Termination reason: Unknown
% 0.22/0.43 % (28511)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (28511)Memory used [KB]: 1023
% 0.22/0.43 % (28511)Time elapsed: 0.004 s
% 0.22/0.43 % (28511)Instructions burned: 4 (million)
% 0.22/0.43 % (28512)Instruction limit reached!
% 0.22/0.43 % (28512)------------------------------
% 0.22/0.43 % (28512)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (28512)Termination reason: Unknown
% 0.22/0.43 % (28512)Termination phase: shuffling
% 0.22/0.43
% 0.22/0.43 % (28512)Memory used [KB]: 1023
% 0.22/0.43 % (28512)Time elapsed: 0.004 s
% 0.22/0.43 % (28512)Instructions burned: 4 (million)
% 0.22/0.43 % (28512)------------------------------
% 0.22/0.43 % (28512)------------------------------
% 0.22/0.43 % (28511)------------------------------
% 0.22/0.43 % (28511)------------------------------
% 0.22/0.43 % (28513)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.44 % (28514)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.44 % (28508)Instruction limit reached!
% 0.22/0.44 % (28508)------------------------------
% 0.22/0.44 % (28508)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (28508)Termination reason: Unknown
% 0.22/0.44 % (28508)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (28508)Memory used [KB]: 1023
% 0.22/0.44 % (28508)Time elapsed: 0.009 s
% 0.22/0.44 % (28508)Instructions burned: 7 (million)
% 0.22/0.44 % (28508)------------------------------
% 0.22/0.44 % (28508)------------------------------
% 0.22/0.45 % (28513)Instruction limit reached!
% 0.22/0.45 % (28513)------------------------------
% 0.22/0.45 % (28513)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (28513)Termination reason: Unknown
% 0.22/0.45 % (28513)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (28513)Memory used [KB]: 5628
% 0.22/0.45 % (28513)Time elapsed: 0.014 s
% 0.22/0.45 % (28513)Instructions burned: 19 (million)
% 0.22/0.45 % (28513)------------------------------
% 0.22/0.45 % (28513)------------------------------
% 0.22/0.45 % (28516)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 theBenchmark for (2999ds/902Mi)
% 0.22/0.45 % (28515)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45 % (28515)Instruction limit reached!
% 0.22/0.45 % (28515)------------------------------
% 0.22/0.45 % (28515)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (28515)Termination reason: Unknown
% 0.22/0.45 % (28515)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (28515)Memory used [KB]: 1023
% 0.22/0.45 % (28515)Time elapsed: 0.005 s
% 0.22/0.45 % (28515)Instructions burned: 6 (million)
% 0.22/0.45 % (28515)------------------------------
% 0.22/0.45 % (28515)------------------------------
% 0.22/0.45 % (28514)Refutation not found, incomplete strategy
% 0.22/0.45 % (28514)------------------------------
% 0.22/0.45 % (28514)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (28514)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 % (28514)Memory used [KB]: 5756
% 0.22/0.45 % (28514)Time elapsed: 0.020 s
% 0.22/0.45 % (28514)Instructions burned: 28 (million)
% 0.22/0.45 % (28514)------------------------------
% 0.22/0.45 % (28514)------------------------------
% 0.22/0.45 % (28516)Refutation not found, incomplete strategy
% 0.22/0.45 % (28516)------------------------------
% 0.22/0.45 % (28516)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (28516)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45
% 0.22/0.45 % (28516)Memory used [KB]: 5628
% 0.22/0.45 % (28516)Time elapsed: 0.008 s
% 0.22/0.45 % (28516)Instructions burned: 11 (million)
% 0.22/0.45 % (28516)------------------------------
% 0.22/0.45 % (28516)------------------------------
% 0.22/0.46 % (28517)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 theBenchmark for (2999ds/21Mi)
% 0.22/0.46 % (28518)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.46 % (28518)Instruction limit reached!
% 0.22/0.46 % (28518)------------------------------
% 0.22/0.46 % (28518)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (28518)Termination reason: Unknown
% 0.22/0.46 % (28518)Termination phase: Property scanning
% 0.22/0.46
% 0.22/0.46 % (28518)Memory used [KB]: 1023
% 0.22/0.46 % (28518)Time elapsed: 0.005 s
% 0.22/0.46 % (28518)Instructions burned: 6 (million)
% 0.22/0.46 % (28518)------------------------------
% 0.22/0.46 % (28518)------------------------------
% 0.22/0.47 % (28520)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.47 % (28521)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 theBenchmark for (2999ds/779Mi)
% 0.22/0.47 % (28519)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 theBenchmark for (2999ds/6Mi)
% 0.22/0.47 % (28517)Instruction limit reached!
% 0.22/0.47 % (28517)------------------------------
% 0.22/0.47 % (28517)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (28517)Termination reason: Unknown
% 0.22/0.47 % (28517)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (28517)Memory used [KB]: 5756
% 0.22/0.47 % (28517)Time elapsed: 0.014 s
% 0.22/0.47 % (28517)Instructions burned: 21 (million)
% 0.22/0.47 % (28517)------------------------------
% 0.22/0.47 % (28517)------------------------------
% 0.22/0.48 % (28519)Instruction limit reached!
% 0.22/0.48 % (28519)------------------------------
% 0.22/0.48 % (28519)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (28519)Termination reason: Unknown
% 0.22/0.48 % (28519)Termination phase: Property scanning
% 0.22/0.48
% 0.22/0.48 % (28519)Memory used [KB]: 1023
% 0.22/0.48 % (28519)Time elapsed: 0.007 s
% 0.22/0.48 % (28519)Instructions burned: 7 (million)
% 0.22/0.48 % (28519)------------------------------
% 0.22/0.48 % (28519)------------------------------
% 0.22/0.49 % (28523)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.22/0.49 % (28491)Instruction limit reached!
% 0.22/0.49 % (28491)------------------------------
% 0.22/0.49 % (28491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.49 % (28491)Termination reason: Unknown
% 0.22/0.49 % (28491)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (28491)Memory used [KB]: 6524
% 0.22/0.49 % (28491)Time elapsed: 0.110 s
% 0.22/0.49 % (28491)Instructions burned: 184 (million)
% 0.22/0.49 % (28491)------------------------------
% 0.22/0.49 % (28491)------------------------------
% 0.22/0.49 % (28524)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.22/0.50 % (28524)Instruction limit reached!
% 0.22/0.50 % (28524)------------------------------
% 0.22/0.50 % (28524)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (28524)Termination reason: Unknown
% 0.22/0.50 % (28524)Termination phase: Saturation
% 0.22/0.50
% 0.22/0.50 % (28524)Memory used [KB]: 5628
% 0.22/0.50 % (28524)Time elapsed: 0.008 s
% 0.22/0.50 % (28524)Instructions burned: 18 (million)
% 0.22/0.50 % (28524)------------------------------
% 0.22/0.50 % (28524)------------------------------
% 0.22/0.50 % (28522)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 theBenchmark for (2998ds/19Mi)
% 0.22/0.50 % (28525)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.50 % (28525)Instruction limit reached!
% 0.22/0.50 % (28525)------------------------------
% 0.22/0.50 % (28525)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.50 % (28525)Termination reason: Unknown
% 0.22/0.50 % (28525)Termination phase: shuffling
% 0.22/0.50
% 0.22/0.50 % (28525)Memory used [KB]: 1023
% 0.22/0.50 % (28525)Time elapsed: 0.004 s
% 0.22/0.50 % (28525)Instructions burned: 4 (million)
% 0.22/0.50 % (28525)------------------------------
% 0.22/0.50 % (28525)------------------------------
% 0.22/0.51 % (28526)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.51 % (28522)Instruction limit reached!
% 0.22/0.51 % (28522)------------------------------
% 0.22/0.51 % (28522)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.51 % (28522)Termination reason: Unknown
% 0.22/0.51 % (28522)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (28522)Memory used [KB]: 5628
% 0.22/0.51 % (28522)Time elapsed: 0.018 s
% 0.22/0.51 % (28522)Instructions burned: 19 (million)
% 0.22/0.52 % (28522)------------------------------
% 0.22/0.52 % (28522)------------------------------
% 0.22/0.52 % (28527)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.22/0.52 % (28526)Instruction limit reached!
% 0.22/0.52 % (28526)------------------------------
% 0.22/0.52 % (28526)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (28526)Termination reason: Unknown
% 0.22/0.52 % (28526)Termination phase: Saturation
% 0.22/0.52
% 0.22/0.52 % (28526)Memory used [KB]: 5756
% 0.22/0.52 % (28526)Time elapsed: 0.011 s
% 0.22/0.52 % (28526)Instructions burned: 31 (million)
% 0.22/0.52 % (28526)------------------------------
% 0.22/0.52 % (28526)------------------------------
% 0.22/0.52 % (28496)Refutation not found, incomplete strategy
% 0.22/0.52 % (28496)------------------------------
% 0.22/0.52 % (28496)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.52 % (28496)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.52
% 0.22/0.52
% 0.22/0.52 % (28496)Memory used [KB]: 6396
% 0.22/0.52 % (28496)Time elapsed: 0.142 s
% 0.22/0.52 % (28496)Instructions burned: 253 (million)
% 0.22/0.52 % (28496)------------------------------
% 0.22/0.52 % (28496)------------------------------
% 0.22/0.53 % (28529)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.53 % (28529)Instruction limit reached!
% 0.22/0.53 % (28529)------------------------------
% 0.22/0.53 % (28529)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (28529)Termination reason: Unknown
% 0.22/0.53 % (28529)Termination phase: shuffling
% 0.22/0.53
% 0.22/0.53 % (28529)Memory used [KB]: 1023
% 0.22/0.53 % (28529)Time elapsed: 0.002 s
% 0.22/0.53 % (28529)Instructions burned: 3 (million)
% 0.22/0.53 % (28529)------------------------------
% 0.22/0.53 % (28529)------------------------------
% 0.22/0.53 % (28531)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 0.22/0.53 % (28528)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 0.22/0.53 % (28531)Refutation not found, incomplete strategy
% 0.22/0.53 % (28531)------------------------------
% 0.22/0.53 % (28531)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.53 % (28531)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.53
% 0.22/0.53
% 0.22/0.53 % (28531)Memory used [KB]: 5628
% 0.22/0.53 % (28531)Time elapsed: 0.006 s
% 0.22/0.53 % (28531)Instructions burned: 16 (million)
% 0.22/0.53 % (28531)------------------------------
% 0.22/0.53 % (28531)------------------------------
% 0.22/0.54 % (28533)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 0.22/0.54 % (28534)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2998ds/107Mi)
% 0.22/0.56 % (28527)Instruction limit reached!
% 0.22/0.56 % (28527)------------------------------
% 0.22/0.56 % (28527)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.56 % (28527)Termination reason: Unknown
% 0.22/0.56 % (28527)Termination phase: Saturation
% 0.22/0.56
% 0.22/0.56 % (28527)Memory used [KB]: 6012
% 0.22/0.56 % (28527)Time elapsed: 0.047 s
% 0.22/0.56 % (28527)Instructions burned: 129 (million)
% 0.22/0.56 % (28527)------------------------------
% 0.22/0.56 % (28527)------------------------------
% 0.22/0.57 % (28533)Instruction limit reached!
% 0.22/0.57 % (28533)------------------------------
% 0.22/0.57 % (28533)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.57 % (28533)Termination reason: Unknown
% 0.22/0.57 % (28533)Termination phase: Saturation
% 0.22/0.57
% 0.22/0.57 % (28533)Memory used [KB]: 6012
% 0.22/0.57 % (28533)Time elapsed: 0.031 s
% 0.22/0.57 % (28533)Instructions burned: 86 (million)
% 0.22/0.57 % (28533)------------------------------
% 0.22/0.57 % (28533)------------------------------
% 0.22/0.57 % (28535)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2998ds/39Mi)
% 0.22/0.58 % (28536)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2998ds/448Mi)
% 0.22/0.58 % (28534)Instruction limit reached!
% 0.22/0.58 % (28534)------------------------------
% 0.22/0.58 % (28534)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.58 % (28534)Termination reason: Unknown
% 0.22/0.58 % (28534)Termination phase: Saturation
% 0.22/0.58
% 0.22/0.58 % (28534)Memory used [KB]: 6012
% 0.22/0.58 % (28534)Time elapsed: 0.038 s
% 0.22/0.58 % (28534)Instructions burned: 107 (million)
% 0.22/0.58 % (28534)------------------------------
% 0.22/0.58 % (28534)------------------------------
% 0.22/0.58 % (28535)Instruction limit reached!
% 0.22/0.58 % (28535)------------------------------
% 0.22/0.58 % (28535)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.58 % (28535)Termination reason: Unknown
% 0.22/0.58 % (28535)Termination phase: Saturation
% 0.22/0.58
% 0.22/0.58 % (28535)Memory used [KB]: 5884
% 0.22/0.58 % (28535)Time elapsed: 0.014 s
% 0.22/0.58 % (28535)Instructions burned: 40 (million)
% 0.22/0.58 % (28535)------------------------------
% 0.22/0.58 % (28535)------------------------------
% 0.22/0.59 % (28528)Instruction limit reached!
% 0.22/0.59 % (28528)------------------------------
% 0.22/0.59 % (28528)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.59 % (28528)Termination reason: Unknown
% 0.22/0.59 % (28528)Termination phase: Saturation
% 0.22/0.59
% 0.22/0.59 % (28528)Memory used [KB]: 5884
% 0.22/0.59 % (28528)Time elapsed: 0.055 s
% 0.22/0.59 % (28528)Instructions burned: 100 (million)
% 0.22/0.59 % (28528)------------------------------
% 0.22/0.59 % (28528)------------------------------
% 0.22/0.59 % (28537)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2997ds/46Mi)
% 0.22/0.59 % (28538)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2997ds/98Mi)
% 1.98/0.61 % (28537)Instruction limit reached!
% 1.98/0.61 % (28537)------------------------------
% 1.98/0.61 % (28537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.61 % (28537)Termination reason: Unknown
% 1.98/0.61 % (28537)Termination phase: Saturation
% 1.98/0.61
% 1.98/0.61 % (28537)Memory used [KB]: 5756
% 1.98/0.61 % (28537)Time elapsed: 0.019 s
% 1.98/0.61 % (28537)Instructions burned: 48 (million)
% 1.98/0.61 % (28537)------------------------------
% 1.98/0.61 % (28537)------------------------------
% 1.98/0.61 % (28539)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2997ds/507Mi)
% 1.98/0.61 % (28520)Instruction limit reached!
% 1.98/0.61 % (28520)------------------------------
% 1.98/0.61 % (28520)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.61 % (28520)Termination reason: Unknown
% 1.98/0.61 % (28520)Termination phase: Saturation
% 1.98/0.61
% 1.98/0.61 % (28520)Memory used [KB]: 6524
% 1.98/0.61 % (28520)Time elapsed: 0.141 s
% 1.98/0.61 % (28520)Instructions burned: 377 (million)
% 1.98/0.61 % (28520)------------------------------
% 1.98/0.61 % (28520)------------------------------
% 1.98/0.61 % (28539)Refutation not found, incomplete strategy
% 1.98/0.61 % (28539)------------------------------
% 1.98/0.61 % (28539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.98/0.61 % (28539)Termination reason: Refutation not found, incomplete strategy
% 1.98/0.61
% 1.98/0.61
% 1.98/0.61 % (28539)Memory used [KB]: 5628
% 1.98/0.61 % (28539)Time elapsed: 0.029 s
% 1.98/0.61 % (28539)Instructions burned: 16 (million)
% 1.98/0.61 % (28539)------------------------------
% 1.98/0.61 % (28539)------------------------------
% 1.98/0.62 % (28540)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2997ds/149Mi)
% 2.12/0.62 % (28541)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 2.12/0.63 % (28502)First to succeed.
% 2.12/0.63 % (28538)Instruction limit reached!
% 2.12/0.63 % (28538)------------------------------
% 2.12/0.63 % (28538)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.12/0.63 % (28538)Termination reason: Unknown
% 2.12/0.63 % (28538)Termination phase: Saturation
% 2.12/0.63
% 2.12/0.63 % (28538)Memory used [KB]: 1407
% 2.12/0.63 % (28538)Time elapsed: 0.035 s
% 2.12/0.63 % (28538)Instructions burned: 98 (million)
% 2.12/0.63 % (28538)------------------------------
% 2.12/0.63 % (28538)------------------------------
% 2.12/0.63 % (28542)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2997ds/6Mi)
% 2.12/0.63 % (28542)Instruction limit reached!
% 2.12/0.63 % (28542)------------------------------
% 2.12/0.63 % (28542)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.12/0.63 % (28542)Termination reason: Unknown
% 2.12/0.63 % (28541)Instruction limit reached!
% 2.12/0.63 % (28541)------------------------------
% 2.12/0.63 % (28541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.12/0.63 % (28541)Termination reason: Unknown
% 2.21/0.63 % (28541)Termination phase: Saturation
% 2.21/0.63
% 2.21/0.63 % (28542)Termination phase: Property scanning
% 2.21/0.63
% 2.21/0.63 % (28542)Memory used [KB]: 1023
% 2.21/0.63 % (28542)Time elapsed: 0.005 s
% 2.21/0.63 % (28542)Instructions burned: 6 (million)
% 2.21/0.63 % (28542)------------------------------
% 2.21/0.63 % (28542)------------------------------
% 2.21/0.63 % (28541)Memory used [KB]: 5756
% 2.21/0.63 % (28541)Time elapsed: 0.013 s
% 2.21/0.63 % (28541)Instructions burned: 39 (million)
% 2.21/0.63 % (28541)------------------------------
% 2.21/0.63 % (28541)------------------------------
% 2.21/0.63 % (28502)Refutation found. Thanks to Tanya!
% 2.21/0.63 % SZS status Theorem for theBenchmark
% 2.21/0.63 % SZS output start Proof for theBenchmark
% 2.21/0.63 thf(type_def_5, type, mu: $tType).
% 2.21/0.63 thf(func_def_0, type, mu: $tType).
% 2.21/0.63 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 2.21/0.63 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_8, type, mtrue: $i > $o).
% 2.21/0.63 thf(func_def_9, type, mfalse: $i > $o).
% 2.21/0.63 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 2.21/0.63 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 2.21/0.63 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 2.21/0.63 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 2.21/0.63 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 2.21/0.63 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 2.21/0.63 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 2.21/0.63 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 2.21/0.63 thf(func_def_37, type, p: $i > $o).
% 2.21/0.63 thf(func_def_38, type, big_r: mu > $i > $o).
% 2.21/0.63 thf(func_def_39, type, big_q: mu > $i > $o).
% 2.21/0.63 thf(func_def_56, type, ph1: !>[X0: $tType]:(X0)).
% 2.21/0.63 thf(func_def_57, type, sK2: $i > mu).
% 2.21/0.63 thf(func_def_61, type, sK6: mu).
% 2.21/0.63 thf(func_def_63, type, sK8: mu).
% 2.21/0.63 thf(f3263,plain,(
% 2.21/0.63 $false),
% 2.21/0.63 inference(avatar_sat_refutation,[],[f1190,f2149,f3262])).
% 2.21/0.63 thf(f3262,plain,(
% 2.21/0.63 ~spl0_6),
% 2.21/0.63 inference(avatar_contradiction_clause,[],[f3261])).
% 2.21/0.63 thf(f3261,plain,(
% 2.21/0.63 $false | ~spl0_6),
% 2.21/0.63 inference(trivial_inequality_removal,[],[f3260])).
% 2.21/0.63 thf(f3260,plain,(
% 2.21/0.63 ($false = $true) | ~spl0_6),
% 2.21/0.63 inference(boolean_simplification,[],[f3259])).
% 2.21/0.63 thf(f3259,plain,(
% 2.21/0.63 ((~ $true) = $true) | ~spl0_6),
% 2.21/0.63 inference(backward_demodulation,[],[f3182,f3258])).
% 2.21/0.63 thf(f3258,plain,(
% 2.21/0.63 ((rel_s4 @ sK4 @ sK11) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f3214])).
% 2.21/0.63 thf(f3214,plain,(
% 2.21/0.63 ($true = ($true => (rel_s4 @ sK4 @ sK11)))),
% 2.21/0.63 inference(superposition,[],[f287,f3188])).
% 2.21/0.63 thf(f3188,plain,(
% 2.21/0.63 ($true = (rel_s4 @ sK5 @ sK11))),
% 2.21/0.63 inference(not_proxy_clausification,[],[f3172])).
% 2.21/0.63 thf(f3172,plain,(
% 2.21/0.63 ($false = (~ (rel_s4 @ sK5 @ sK11)))),
% 2.21/0.63 inference(boolean_simplification,[],[f3171])).
% 2.21/0.63 thf(f3171,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK5 @ sK11)) | $false))),
% 2.21/0.63 inference(backward_demodulation,[],[f3163,f3169])).
% 2.21/0.63 thf(f3169,plain,(
% 2.21/0.63 ($false = (p @ sK11))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f3163])).
% 2.21/0.63 thf(f3163,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK5 @ sK11)) | (p @ sK11)))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f3159])).
% 2.21/0.63 thf(f3159,plain,(
% 2.21/0.63 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))) @ sK11))),
% 2.21/0.63 inference(sigma_clausification,[],[f2991])).
% 2.21/0.63 thf(f2991,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))),
% 2.21/0.63 inference(not_proxy_clausification,[],[f1884])).
% 2.21/0.63 thf(f1884,plain,(
% 2.21/0.63 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f1883])).
% 2.21/0.63 thf(f1883,plain,(
% 2.21/0.63 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f1881])).
% 2.21/0.63 thf(f1881,plain,(
% 2.21/0.63 (((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f1871,f166])).
% 2.21/0.63 thf(f166,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f165])).
% 2.21/0.63 thf(f165,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 2.21/0.63 inference(pi_clausification,[],[f164])).
% 2.21/0.63 thf(f164,plain,(
% 2.21/0.63 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f159])).
% 2.21/0.63 thf(f159,plain,(
% 2.21/0.63 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 2.21/0.63 inference(definition_unfolding,[],[f123,f147])).
% 2.21/0.63 thf(f147,plain,(
% 2.21/0.63 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 2.21/0.63 inference(cnf_transformation,[],[f90])).
% 2.21/0.63 thf(f90,plain,(
% 2.21/0.63 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 2.21/0.63 inference(fool_elimination,[],[f89])).
% 2.21/0.63 thf(f89,plain,(
% 2.21/0.63 ((^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))) = mreflexive)),
% 2.21/0.63 inference(rectify,[],[f18])).
% 2.21/0.63 thf(f18,axiom,(
% 2.21/0.63 ((^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))) = mreflexive)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 2.21/0.63 thf(f123,plain,(
% 2.21/0.63 ((mreflexive @ rel_s4) = $true)),
% 2.21/0.63 inference(cnf_transformation,[],[f63])).
% 2.21/0.63 thf(f63,plain,(
% 2.21/0.63 ((mreflexive @ rel_s4) = $true)),
% 2.21/0.63 inference(fool_elimination,[],[f62])).
% 2.21/0.63 thf(f62,plain,(
% 2.21/0.63 (mreflexive @ rel_s4)),
% 2.21/0.63 inference(rectify,[],[f34])).
% 2.21/0.63 thf(f34,axiom,(
% 2.21/0.63 (mreflexive @ rel_s4)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 2.21/0.63 thf(f1871,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK5 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0)))))))) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f1870])).
% 2.21/0.63 thf(f1870,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1))) )),
% 2.21/0.63 inference(pi_clausification,[],[f1826])).
% 2.21/0.63 thf(f1826,plain,(
% 2.21/0.63 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) = $true)),
% 2.21/0.63 inference(not_proxy_clausification,[],[f891])).
% 2.21/0.63 thf(f891,plain,(
% 2.21/0.63 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f868])).
% 2.21/0.63 thf(f868,plain,(
% 2.21/0.63 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 2.21/0.63 inference(not_proxy_clausification,[],[f683])).
% 2.21/0.63 thf(f683,plain,(
% 2.21/0.63 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f682])).
% 2.21/0.63 thf(f682,plain,(
% 2.21/0.63 (($true => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(forward_demodulation,[],[f679,f370])).
% 2.21/0.63 thf(f370,plain,(
% 2.21/0.63 ((exists_in_world @ sK6 @ sK5) = $true)),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f359])).
% 2.21/0.63 thf(f359,plain,(
% 2.21/0.63 ($false = ((exists_in_world @ sK6 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_q @ sK6 @ Y0))))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f358])).
% 2.21/0.63 thf(f358,plain,(
% 2.21/0.63 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1)))))) @ sK6))),
% 2.21/0.63 inference(sigma_clausification,[],[f273])).
% 2.21/0.63 thf(f273,plain,(
% 2.21/0.63 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1))))))))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f272])).
% 2.21/0.63 thf(f272,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1)))))))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f271])).
% 2.21/0.63 thf(f271,plain,(
% 2.21/0.63 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))))))) @ sK5))),
% 2.21/0.63 inference(sigma_clausification,[],[f270])).
% 2.21/0.63 thf(f270,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2)))))))))))),
% 2.21/0.63 inference(boolean_simplification,[],[f269])).
% 2.21/0.63 thf(f269,plain,(
% 2.21/0.63 ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))))))))))),
% 2.21/0.63 inference(backward_demodulation,[],[f259,f268])).
% 2.21/0.63 thf(f268,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2)))))))))))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f259])).
% 2.21/0.63 thf(f259,plain,(
% 2.21/0.63 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))))))))))),
% 2.21/0.63 inference(boolean_simplification,[],[f258])).
% 2.21/0.63 thf(f258,plain,(
% 2.21/0.63 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))))))))) | $false))),
% 2.21/0.63 inference(backward_demodulation,[],[f212,f256])).
% 2.21/0.63 thf(f256,plain,(
% 2.21/0.63 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (p @ Y2))))))))))))))))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f212])).
% 2.21/0.63 thf(f212,plain,(
% 2.21/0.63 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (p @ Y2)))))))))))))))))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f211])).
% 2.21/0.63 thf(f211,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK3 @ sK4)) | (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (p @ Y2))))))))))))))))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f210])).
% 2.21/0.63 thf(f210,plain,(
% 2.21/0.63 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_r @ Y2 @ Y3)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_q @ Y2 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_r @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4))))))))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_q @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (p @ Y3)))))))))))))))))) @ sK4))),
% 2.21/0.63 inference(sigma_clausification,[],[f209])).
% 2.21/0.63 thf(f209,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_r @ Y2 @ Y3)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_q @ Y2 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_r @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4))))))))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_q @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (p @ Y3))))))))))))))))))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f208])).
% 2.21/0.63 thf(f208,plain,(
% 2.21/0.63 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_r @ Y3 @ Y4)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_q @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_r @ Y3 @ Y4))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5))))))))))) | (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_q @ Y3 @ Y4))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (p @ Y4)))))))))))))))))))) @ sK3))),
% 2.21/0.63 inference(sigma_clausification,[],[f205])).
% 2.21/0.63 thf(f205,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_r @ Y3 @ Y4)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_q @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_r @ Y3 @ Y4))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5))))))))))) | (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_q @ Y3 @ Y4))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (p @ Y4))))))))))))))))))))))),
% 2.21/0.63 inference(not_proxy_clausification,[],[f163])).
% 2.21/0.63 thf(f163,plain,(
% 2.21/0.63 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_r @ Y3 @ Y4)))))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_q @ Y3 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => ((~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_r @ Y3 @ Y4))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5))))))))))) | (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_q @ Y3 @ Y4))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (p @ Y4)))))))))))))))))))))) = $true)),
% 2.21/0.63 inference(beta_eta_normalization,[],[f160])).
% 2.21/0.63 thf(f160,plain,(
% 2.21/0.63 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y2 @ Y3) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ p) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_q @ Y0))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ p))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_r @ Y0))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_q @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_r @ Y0)))))))))) = $true)),
% 2.21/0.63 inference(definition_unfolding,[],[f142,f136,f139,f151,f139,f122,f116,f150,f139,f139,f150,f139,f134,f139,f139,f116,f139,f122,f139,f139,f122,f139])).
% 2.21/0.63 thf(f134,plain,(
% 2.21/0.63 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f49])).
% 2.21/0.63 thf(f49,plain,(
% 2.21/0.63 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 2.21/0.63 inference(fool_elimination,[],[f48])).
% 2.21/0.63 thf(f48,plain,(
% 2.21/0.63 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 2.21/0.63 inference(rectify,[],[f2])).
% 2.21/0.63 thf(f2,axiom,(
% 2.21/0.63 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 2.21/0.63 thf(f150,plain,(
% 2.21/0.63 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 2.21/0.63 inference(definition_unfolding,[],[f135,f134,f116,f134,f134])).
% 2.21/0.63 thf(f135,plain,(
% 2.21/0.63 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f47])).
% 2.21/0.63 thf(f47,plain,(
% 2.21/0.63 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 2.21/0.63 inference(fool_elimination,[],[f46])).
% 2.21/0.63 thf(f46,plain,(
% 2.21/0.63 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 2.21/0.63 inference(rectify,[],[f8])).
% 2.21/0.63 thf(f8,axiom,(
% 2.21/0.63 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 2.21/0.63 thf(f116,plain,(
% 2.21/0.63 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f88])).
% 2.21/0.63 thf(f88,plain,(
% 2.21/0.63 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 2.21/0.63 inference(fool_elimination,[],[f87])).
% 2.21/0.63 thf(f87,plain,(
% 2.21/0.63 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 2.21/0.63 inference(rectify,[],[f3])).
% 2.21/0.63 thf(f3,axiom,(
% 2.21/0.63 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 2.21/0.63 thf(f122,plain,(
% 2.21/0.63 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f65])).
% 2.21/0.63 thf(f65,plain,(
% 2.21/0.63 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 2.21/0.63 inference(fool_elimination,[],[f64])).
% 2.21/0.63 thf(f64,plain,(
% 2.21/0.63 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 2.21/0.63 inference(rectify,[],[f15])).
% 2.21/0.63 thf(f15,axiom,(
% 2.21/0.63 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 2.21/0.63 thf(f151,plain,(
% 2.21/0.63 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 2.21/0.63 inference(definition_unfolding,[],[f124,f116,f134])).
% 2.21/0.63 thf(f124,plain,(
% 2.21/0.63 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 2.21/0.63 inference(cnf_transformation,[],[f104])).
% 2.21/0.63 thf(f104,plain,(
% 2.21/0.63 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 2.21/0.63 inference(fool_elimination,[],[f103])).
% 2.21/0.63 thf(f103,plain,(
% 2.21/0.63 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 2.21/0.63 inference(rectify,[],[f9])).
% 2.21/0.63 thf(f9,axiom,(
% 2.21/0.63 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 2.21/0.63 thf(f139,plain,(
% 2.21/0.63 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f92])).
% 2.21/0.63 thf(f92,plain,(
% 2.21/0.63 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 2.21/0.63 inference(fool_elimination,[],[f91])).
% 2.21/0.63 thf(f91,plain,(
% 2.21/0.63 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 2.21/0.63 inference(rectify,[],[f32])).
% 2.21/0.63 thf(f32,axiom,(
% 2.21/0.63 ((^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))) = mbox_s4)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 2.21/0.63 thf(f136,plain,(
% 2.21/0.63 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 2.21/0.63 inference(cnf_transformation,[],[f51])).
% 2.21/0.63 thf(f51,plain,(
% 2.21/0.63 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 2.21/0.63 inference(fool_elimination,[],[f50])).
% 2.21/0.63 thf(f50,plain,(
% 2.21/0.63 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 2.21/0.63 inference(rectify,[],[f28])).
% 2.21/0.63 thf(f28,axiom,(
% 2.21/0.63 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 2.21/0.63 thf(f142,plain,(
% 2.21/0.63 ((~ (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ Y0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ Y0))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_q @ Y0))))) @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_r @ Y0)))))))))) = $true)),
% 2.21/0.63 inference(cnf_transformation,[],[f43])).
% 2.21/0.63 thf(f43,plain,(
% 2.21/0.63 ((~ (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ Y0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ Y0))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_q @ Y0))))) @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_r @ Y0)))))))))) = $true)),
% 2.21/0.63 inference(fool_elimination,[],[f42])).
% 2.21/0.63 thf(f42,plain,(
% 2.21/0.63 ~(mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ X0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ X0))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (big_q @ X1))))) @ (mbox_s4 @ (mforall_ind @ (^[X2 : mu] : (mbox_s4 @ (big_r @ X2)))))))))),
% 2.21/0.63 inference(rectify,[],[f38])).
% 2.21/0.63 thf(f38,negated_conjecture,(
% 2.21/0.63 ~(mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ X0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ X0))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mbox_s4 @ (big_q @ X0))))) @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mbox_s4 @ (big_r @ X0)))))))))),
% 2.21/0.63 inference(negated_conjecture,[],[f37])).
% 2.21/0.63 thf(f37,conjecture,(
% 2.21/0.63 (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ X0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ X0))))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mbox_s4 @ (big_q @ X0))))) @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mbox_s4 @ (big_r @ X0)))))))))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2118)).
% 2.21/0.63 thf(f679,plain,(
% 2.21/0.63 (((exists_in_world @ sK6 @ sK5) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f678])).
% 2.21/0.63 thf(f678,plain,(
% 2.21/0.63 (((exists_in_world @ sK6 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | $false)) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f677])).
% 2.21/0.63 thf(f677,plain,(
% 2.21/0.63 (((exists_in_world @ sK6 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ $true))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f676])).
% 2.21/0.63 thf(f676,plain,(
% 2.21/0.63 (((exists_in_world @ sK6 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ($true | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f669])).
% 2.21/0.63 thf(f669,plain,(
% 2.21/0.63 (((exists_in_world @ sK6 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ sK6 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ $false) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f663,f369])).
% 2.21/0.63 thf(f369,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_q @ sK6 @ Y0)))))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f359])).
% 2.21/0.63 thf(f663,plain,(
% 2.21/0.63 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_r @ X1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_q @ X1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f661])).
% 2.21/0.63 thf(f661,plain,(
% 2.21/0.63 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (p @ Y1)))))))))) @ X1))) )),
% 2.21/0.63 inference(pi_clausification,[],[f482])).
% 2.21/0.63 thf(f482,plain,(
% 2.21/0.63 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f481])).
% 2.21/0.63 thf(f481,plain,(
% 2.21/0.63 ($true = ($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (p @ Y1)))))))))))))),
% 2.21/0.63 inference(boolean_simplification,[],[f479])).
% 2.21/0.63 thf(f479,plain,(
% 2.21/0.63 (((~ $true) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK5) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK5 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f470,f277])).
% 2.21/0.63 thf(f277,plain,(
% 2.21/0.63 ((rel_s4 @ sK4 @ sK5) = $true)),
% 2.21/0.63 inference(not_proxy_clausification,[],[f276])).
% 2.21/0.63 thf(f276,plain,(
% 2.21/0.63 ($false = (~ (rel_s4 @ sK4 @ sK5)))),
% 2.21/0.63 inference(boolean_simplification,[],[f275])).
% 2.21/0.63 thf(f275,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | $false))),
% 2.21/0.63 inference(backward_demodulation,[],[f272,f273])).
% 2.21/0.63 thf(f470,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (p @ Y1)))))))))))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f469])).
% 2.21/0.63 thf(f469,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (p @ Y2))))))))))))) @ X1))) )),
% 2.21/0.63 inference(pi_clausification,[],[f460])).
% 2.21/0.63 thf(f460,plain,(
% 2.21/0.63 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_q @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (p @ Y2)))))))))))))))),
% 2.21/0.63 inference(not_proxy_clausification,[],[f256])).
% 2.21/0.63 thf(f287,plain,(
% 2.21/0.63 ( ! [X0 : $i] : ((((rel_s4 @ sK5 @ X0) => (rel_s4 @ sK4 @ X0)) = $true)) )),
% 2.21/0.63 inference(boolean_simplification,[],[f283])).
% 2.21/0.63 thf(f283,plain,(
% 2.21/0.63 ( ! [X0 : $i] : (($true = (((rel_s4 @ sK5 @ X0) & $true) => (rel_s4 @ sK4 @ X0)))) )),
% 2.21/0.63 inference(superposition,[],[f195,f277])).
% 2.21/0.63 thf(f195,plain,(
% 2.21/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s4 @ X1 @ X2) & (rel_s4 @ X3 @ X1)) => (rel_s4 @ X3 @ X2)) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f194])).
% 2.21/0.63 thf(f194,plain,(
% 2.21/0.63 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s4 @ X1 @ X2) & (rel_s4 @ Y0 @ X1)) => (rel_s4 @ Y0 @ X2))) @ X3) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f193])).
% 2.21/0.63 thf(f193,plain,(
% 2.21/0.63 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ X1 @ X2) & (rel_s4 @ Y0 @ X1)) => (rel_s4 @ Y0 @ X2)))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f192])).
% 2.21/0.63 thf(f192,plain,(
% 2.21/0.63 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y1 @ X1)) => (rel_s4 @ Y1 @ Y0))))) @ X2) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f191])).
% 2.21/0.63 thf(f191,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y1 @ X1)) => (rel_s4 @ Y1 @ Y0)))))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f190])).
% 2.21/0.63 thf(f190,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y1) & (rel_s4 @ Y2 @ Y0)) => (rel_s4 @ Y2 @ Y1))))))) @ X1) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f162])).
% 2.21/0.63 thf(f162,plain,(
% 2.21/0.63 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y1) & (rel_s4 @ Y2 @ Y0)) => (rel_s4 @ Y2 @ Y1)))))))) = $true)),
% 2.21/0.63 inference(beta_eta_normalization,[],[f161])).
% 2.21/0.63 thf(f161,plain,(
% 2.21/0.63 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) @ rel_s4) = $true)),
% 2.21/0.63 inference(definition_unfolding,[],[f146,f128])).
% 2.21/0.63 thf(f128,plain,(
% 2.21/0.63 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f61])).
% 2.21/0.63 thf(f61,plain,(
% 2.21/0.63 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 2.21/0.63 inference(fool_elimination,[],[f60])).
% 2.21/0.63 thf(f60,plain,(
% 2.21/0.63 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X3 @ X2)) => (X0 @ X1 @ X2)))) = mtransitive)),
% 2.21/0.63 inference(rectify,[],[f21])).
% 2.21/0.63 thf(f21,axiom,(
% 2.21/0.63 ((^[X5 : $i > $i > $o] : (! [X8,X10,X9] : (((X5 @ X8 @ X9) & (X5 @ X9 @ X10)) => (X5 @ X8 @ X10)))) = mtransitive)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 2.21/0.63 thf(f146,plain,(
% 2.21/0.63 ((mtransitive @ rel_s4) = $true)),
% 2.21/0.63 inference(cnf_transformation,[],[f111])).
% 2.21/0.63 thf(f111,plain,(
% 2.21/0.63 ((mtransitive @ rel_s4) = $true)),
% 2.21/0.63 inference(fool_elimination,[],[f110])).
% 2.21/0.63 thf(f110,plain,(
% 2.21/0.63 (mtransitive @ rel_s4)),
% 2.21/0.63 inference(rectify,[],[f35])).
% 2.21/0.63 thf(f35,axiom,(
% 2.21/0.63 (mtransitive @ rel_s4)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 2.21/0.63 thf(f3182,plain,(
% 2.21/0.63 ((~ (rel_s4 @ sK4 @ sK11)) = $true) | ~spl0_6),
% 2.21/0.63 inference(boolean_simplification,[],[f3181])).
% 2.21/0.63 thf(f3181,plain,(
% 2.21/0.63 (((~ (rel_s4 @ sK4 @ sK11)) | $false) = $true) | ~spl0_6),
% 2.21/0.63 inference(superposition,[],[f1535,f3169])).
% 2.21/0.63 thf(f1535,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | (p @ X1)) = $true)) ) | ~spl0_6),
% 2.21/0.63 inference(beta_eta_normalization,[],[f1534])).
% 2.21/0.63 thf(f1534,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))) @ X1) = $true)) ) | ~spl0_6),
% 2.21/0.63 inference(pi_clausification,[],[f1514])).
% 2.21/0.63 thf(f1514,plain,(
% 2.21/0.63 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))) | ~spl0_6),
% 2.21/0.63 inference(not_proxy_clausification,[],[f1467])).
% 2.21/0.63 thf(f1467,plain,(
% 2.21/0.63 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) | ~spl0_6),
% 2.21/0.63 inference(boolean_simplification,[],[f1466])).
% 2.21/0.63 thf(f1466,plain,(
% 2.21/0.63 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))) | ~spl0_6),
% 2.21/0.63 inference(backward_demodulation,[],[f1447,f1461])).
% 2.21/0.63 thf(f1461,plain,(
% 2.21/0.63 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0)))))) | ~spl0_6),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f1447])).
% 2.21/0.63 thf(f1447,plain,(
% 2.21/0.63 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))) | ~spl0_6),
% 2.21/0.63 inference(not_proxy_clausification,[],[f1189])).
% 2.21/0.63 thf(f1189,plain,(
% 2.21/0.63 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))) = $true) | ~spl0_6),
% 2.21/0.63 inference(avatar_component_clause,[],[f1188])).
% 2.21/0.63 thf(f1188,plain,(
% 2.21/0.63 spl0_6 <=> ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))) = $true)),
% 2.21/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 2.21/0.63 thf(f2149,plain,(
% 2.21/0.63 ~spl0_5),
% 2.21/0.63 inference(avatar_contradiction_clause,[],[f2148])).
% 2.21/0.63 thf(f2148,plain,(
% 2.21/0.63 $false | ~spl0_5),
% 2.21/0.63 inference(trivial_inequality_removal,[],[f2147])).
% 2.21/0.63 thf(f2147,plain,(
% 2.21/0.63 ($false = $true) | ~spl0_5),
% 2.21/0.63 inference(boolean_simplification,[],[f2146])).
% 2.21/0.63 thf(f2146,plain,(
% 2.21/0.63 ((~ $true) = $true) | ~spl0_5),
% 2.21/0.63 inference(boolean_simplification,[],[f2142])).
% 2.21/0.63 thf(f2142,plain,(
% 2.21/0.63 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | $true)) = $true) | ~spl0_5),
% 2.21/0.63 inference(backward_demodulation,[],[f1751,f2118])).
% 2.21/0.63 thf(f2118,plain,(
% 2.21/0.63 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_5),
% 2.21/0.63 inference(boolean_simplification,[],[f2117])).
% 2.21/0.63 thf(f2117,plain,(
% 2.21/0.63 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_5),
% 2.21/0.63 inference(boolean_simplification,[],[f2113])).
% 2.21/0.63 thf(f2113,plain,(
% 2.21/0.63 (((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_5),
% 2.21/0.63 inference(superposition,[],[f2070,f398])).
% 2.21/0.63 thf(f398,plain,(
% 2.21/0.63 ((rel_s4 @ sK4 @ sK7) = $true)),
% 2.21/0.63 inference(not_proxy_clausification,[],[f395])).
% 2.21/0.63 thf(f395,plain,(
% 2.21/0.63 ($false = (~ (rel_s4 @ sK4 @ sK7)))),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f384])).
% 2.21/0.63 thf(f384,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK4 @ sK7)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1)))))))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f383])).
% 2.21/0.63 thf(f383,plain,(
% 2.21/0.63 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_r @ Y1 @ Y2))))))))) @ sK7))),
% 2.21/0.63 inference(sigma_clausification,[],[f268])).
% 2.21/0.63 thf(f2070,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0)))))) = $true)) ) | ~spl0_5),
% 2.21/0.63 inference(beta_eta_normalization,[],[f2069])).
% 2.21/0.63 thf(f2069,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1) = $true)) ) | ~spl0_5),
% 2.21/0.63 inference(pi_clausification,[],[f2063])).
% 2.21/0.63 thf(f2063,plain,(
% 2.21/0.63 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) = $true) | ~spl0_5),
% 2.21/0.63 inference(not_proxy_clausification,[],[f1664])).
% 2.21/0.63 thf(f1664,plain,(
% 2.21/0.63 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_5),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f1656])).
% 2.21/0.63 thf(f1656,plain,(
% 2.21/0.63 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | ~spl0_5),
% 2.21/0.63 inference(not_proxy_clausification,[],[f1186])).
% 2.21/0.63 thf(f1186,plain,(
% 2.21/0.63 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true) | ~spl0_5),
% 2.21/0.63 inference(avatar_component_clause,[],[f1185])).
% 2.21/0.63 thf(f1185,plain,(
% 2.21/0.63 spl0_5 <=> ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 2.21/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 2.21/0.63 thf(f1751,plain,(
% 2.21/0.63 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f1750])).
% 2.21/0.63 thf(f1750,plain,(
% 2.21/0.63 (($false | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f1749])).
% 2.21/0.63 thf(f1749,plain,(
% 2.21/0.63 (((~ $true) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f1748])).
% 2.21/0.63 thf(f1748,plain,(
% 2.21/0.63 (((~ ($true | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f1747])).
% 2.21/0.63 thf(f1747,plain,(
% 2.21/0.63 (((~ ((~ $false) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))))) = $true)),
% 2.21/0.63 inference(forward_demodulation,[],[f1745,f422])).
% 2.21/0.63 thf(f422,plain,(
% 2.21/0.63 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_r @ sK8 @ Y0)))))),
% 2.21/0.63 inference(boolean_simplification,[],[f421])).
% 2.21/0.63 thf(f421,plain,(
% 2.21/0.63 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_r @ sK8 @ Y0))))))),
% 2.21/0.63 inference(backward_demodulation,[],[f402,f420])).
% 2.21/0.63 thf(f420,plain,(
% 2.21/0.63 ((exists_in_world @ sK8 @ sK7) = $true)),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f402])).
% 2.21/0.63 thf(f402,plain,(
% 2.21/0.63 ($false = ((exists_in_world @ sK8 @ sK7) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_r @ sK8 @ Y0))))))),
% 2.21/0.63 inference(beta_eta_normalization,[],[f401])).
% 2.21/0.63 thf(f401,plain,(
% 2.21/0.63 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1)))))) @ sK8))),
% 2.21/0.63 inference(sigma_clausification,[],[f397])).
% 2.21/0.63 thf(f397,plain,(
% 2.21/0.63 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1))))))))),
% 2.21/0.63 inference(boolean_simplification,[],[f396])).
% 2.21/0.63 thf(f396,plain,(
% 2.21/0.63 ($false = ($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1)))))))))),
% 2.21/0.63 inference(backward_demodulation,[],[f384,f395])).
% 2.21/0.63 thf(f1745,plain,(
% 2.21/0.63 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_r @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0)))))))))),
% 2.21/0.63 inference(boolean_simplification,[],[f1735])).
% 2.21/0.63 thf(f1735,plain,(
% 2.21/0.63 (($true => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_r @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ sK8 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0))))))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f1729,f420])).
% 2.21/0.63 thf(f1729,plain,(
% 2.21/0.63 ( ! [X1 : mu] : (($true = ((exists_in_world @ X1 @ sK7) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_r @ X1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (big_q @ X1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK7 @ Y0)) | (p @ Y0))))))))))) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f1727])).
% 2.21/0.63 thf(f1727,plain,(
% 2.21/0.63 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (p @ Y1)))))))))) @ X1))) )),
% 2.21/0.63 inference(pi_clausification,[],[f486])).
% 2.21/0.63 thf(f486,plain,(
% 2.21/0.63 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f485])).
% 2.21/0.63 thf(f485,plain,(
% 2.21/0.63 (($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f480])).
% 2.21/0.63 thf(f480,plain,(
% 2.21/0.63 (((~ $true) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK7) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK7 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f470,f398])).
% 2.21/0.63 thf(f1190,plain,(
% 2.21/0.63 spl0_5 | spl0_6),
% 2.21/0.63 inference(avatar_split_clause,[],[f1181,f1188,f1185])).
% 2.21/0.63 thf(f1181,plain,(
% 2.21/0.63 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))) = $true) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 2.21/0.63 inference(binary_proxy_clausification,[],[f732])).
% 2.21/0.63 thf(f732,plain,(
% 2.21/0.63 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f730])).
% 2.21/0.63 thf(f730,plain,(
% 2.21/0.63 (($true => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ (sK2 @ sK3) @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f705,f225])).
% 2.21/0.63 thf(f225,plain,(
% 2.21/0.63 ($true = (exists_in_world @ (sK2 @ sK3) @ sK4))),
% 2.21/0.63 inference(boolean_simplification,[],[f222])).
% 2.21/0.63 thf(f222,plain,(
% 2.21/0.63 (($true => (exists_in_world @ (sK2 @ sK3) @ sK4)) = $true)),
% 2.21/0.63 inference(superposition,[],[f183,f216])).
% 2.21/0.63 thf(f216,plain,(
% 2.21/0.63 ($true = (rel_s4 @ sK3 @ sK4))),
% 2.21/0.63 inference(not_proxy_clausification,[],[f215])).
% 2.21/0.63 thf(f215,plain,(
% 2.21/0.63 ($false = (~ (rel_s4 @ sK3 @ sK4)))),
% 2.21/0.63 inference(boolean_simplification,[],[f214])).
% 2.21/0.63 thf(f214,plain,(
% 2.21/0.63 ($false = ((~ (rel_s4 @ sK3 @ sK4)) | $false))),
% 2.21/0.63 inference(backward_demodulation,[],[f211,f212])).
% 2.21/0.63 thf(f183,plain,(
% 2.21/0.63 ( ! [X0 : $i,X1 : $i] : ((((rel_s4 @ X0 @ X1) => (exists_in_world @ (sK2 @ X0) @ X1)) = $true)) )),
% 2.21/0.63 inference(boolean_simplification,[],[f180])).
% 2.21/0.63 thf(f180,plain,(
% 2.21/0.63 ( ! [X0 : $i,X1 : $i] : (($true = (($true & (rel_s4 @ X0 @ X1)) => (exists_in_world @ (sK2 @ X0) @ X1)))) )),
% 2.21/0.63 inference(superposition,[],[f176,f170])).
% 2.21/0.63 thf(f170,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (($true = (exists_in_world @ (sK2 @ X1) @ X1))) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f169])).
% 2.21/0.63 thf(f169,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((^[Y0 : mu]: (exists_in_world @ Y0 @ X1)) @ (sK2 @ X1)) = $true)) )),
% 2.21/0.63 inference(sigma_clausification,[],[f168])).
% 2.21/0.63 thf(f168,plain,(
% 2.21/0.63 ( ! [X1 : $i] : (((?? @ mu @ (^[Y0 : mu]: (exists_in_world @ Y0 @ X1))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f167])).
% 2.21/0.63 thf(f167,plain,(
% 2.21/0.63 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0)))) @ X1) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f141])).
% 2.21/0.63 thf(f141,plain,(
% 2.21/0.63 ((!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0))))) = $true)),
% 2.21/0.63 inference(cnf_transformation,[],[f45])).
% 2.21/0.63 thf(f45,plain,(
% 2.21/0.63 ((!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0))))) = $true)),
% 2.21/0.63 inference(fool_elimination,[],[f44])).
% 2.21/0.63 thf(f44,plain,(
% 2.21/0.63 ! [X0] : ? [X1 : mu] : (exists_in_world @ X1 @ X0)),
% 2.21/0.63 inference(rectify,[],[f14])).
% 2.21/0.63 thf(f14,axiom,(
% 2.21/0.63 ! [X6] : ? [X0 : mu] : (exists_in_world @ X0 @ X6)),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax)).
% 2.21/0.63 thf(f176,plain,(
% 2.21/0.63 ( ! [X2 : $i,X3 : $i,X1 : mu] : (((((exists_in_world @ X1 @ X2) & (rel_s4 @ X2 @ X3)) => (exists_in_world @ X1 @ X3)) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f175])).
% 2.21/0.63 thf(f175,plain,(
% 2.21/0.63 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($true = ((^[Y0 : $i]: (((exists_in_world @ X1 @ X2) & (rel_s4 @ X2 @ Y0)) => (exists_in_world @ X1 @ Y0))) @ X3))) )),
% 2.21/0.63 inference(pi_clausification,[],[f174])).
% 2.21/0.63 thf(f174,plain,(
% 2.21/0.63 ( ! [X2 : $i,X1 : mu] : (((!! @ $i @ (^[Y0 : $i]: (((exists_in_world @ X1 @ X2) & (rel_s4 @ X2 @ Y0)) => (exists_in_world @ X1 @ Y0)))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f173])).
% 2.21/0.63 thf(f173,plain,(
% 2.21/0.63 ( ! [X2 : $i,X1 : mu] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((exists_in_world @ X1 @ Y0) & (rel_s4 @ Y0 @ Y1)) => (exists_in_world @ X1 @ Y1))))) @ X2) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f172])).
% 2.21/0.63 thf(f172,plain,(
% 2.21/0.63 ( ! [X1 : mu] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((exists_in_world @ X1 @ Y0) & (rel_s4 @ Y0 @ Y1)) => (exists_in_world @ X1 @ Y1)))))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f171])).
% 2.21/0.63 thf(f171,plain,(
% 2.21/0.63 ( ! [X1 : mu] : ((((^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y0 @ Y1) & (rel_s4 @ Y1 @ Y2)) => (exists_in_world @ Y0 @ Y2))))))) @ X1) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f130])).
% 2.21/0.63 thf(f130,plain,(
% 2.21/0.63 ($true = (!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y0 @ Y1) & (rel_s4 @ Y1 @ Y2)) => (exists_in_world @ Y0 @ Y2)))))))))),
% 2.21/0.63 inference(cnf_transformation,[],[f98])).
% 2.21/0.63 thf(f98,plain,(
% 2.21/0.63 ($true = (!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y0 @ Y1) & (rel_s4 @ Y1 @ Y2)) => (exists_in_world @ Y0 @ Y2)))))))))),
% 2.21/0.63 inference(fool_elimination,[],[f97])).
% 2.21/0.63 thf(f97,plain,(
% 2.21/0.63 ! [X0,X1,X2 : mu] : (((rel_s4 @ X1 @ X0) & (exists_in_world @ X2 @ X1)) => (exists_in_world @ X2 @ X0))),
% 2.21/0.63 inference(rectify,[],[f36])).
% 2.21/0.63 thf(f36,axiom,(
% 2.21/0.63 ! [X2,X6,X0 : mu] : (((rel_s4 @ X6 @ X2) & (exists_in_world @ X0 @ X6)) => (exists_in_world @ X0 @ X2))),
% 2.21/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax)).
% 2.21/0.63 thf(f705,plain,(
% 2.21/0.63 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK4) => ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_r @ X1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (big_q @ X1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))))))) = $true)) )),
% 2.21/0.63 inference(beta_eta_normalization,[],[f702])).
% 2.21/0.63 thf(f702,plain,(
% 2.21/0.63 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (p @ Y1)))))))))) @ X1) = $true)) )),
% 2.21/0.63 inference(pi_clausification,[],[f484])).
% 2.21/0.63 thf(f484,plain,(
% 2.21/0.63 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f483])).
% 2.21/0.63 thf(f483,plain,(
% 2.21/0.63 (($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(boolean_simplification,[],[f478])).
% 2.21/0.63 thf(f478,plain,(
% 2.21/0.63 (((~ $true) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_r @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (big_q @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 2.21/0.63 inference(superposition,[],[f470,f166])).
% 2.21/0.63 % SZS output end Proof for theBenchmark
% 2.21/0.63 % (28502)------------------------------
% 2.21/0.63 % (28502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.21/0.63 % (28502)Termination reason: Refutation
% 2.21/0.63
% 2.21/0.63 % (28502)Memory used [KB]: 7164
% 2.21/0.63 % (28502)Time elapsed: 0.257 s
% 2.21/0.63 % (28502)Instructions burned: 513 (million)
% 2.21/0.63 % (28502)------------------------------
% 2.21/0.63 % (28502)------------------------------
% 2.21/0.63 % (28490)Success in time 0.257 s
% 2.21/0.63 % Vampire---4.8 exiting
%------------------------------------------------------------------------------