TSTP Solution File: SYN393^4.002 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN393^4.002 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 11:57:13 EDT 2024
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN393^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % 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 : n008.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 : Fri May 3 17:23:38 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/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977
% 0.15/0.38 % (14225)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.38 % (14226)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.15/0.38 % (14227)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on Vampire---4 for (2999ds/27Mi)
% 0.15/0.38 % (14228)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (14230)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.38 % (14231)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.38 % (14229)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.38 % (14232)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.38 % (14228)Instruction limit reached!
% 0.15/0.38 % (14228)------------------------------
% 0.15/0.38 % (14228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (14228)Termination reason: Unknown
% 0.15/0.38 % (14228)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (14228)Memory used [KB]: 1023
% 0.15/0.38 % (14228)Time elapsed: 0.003 s
% 0.15/0.38 % (14228)Instructions burned: 2 (million)
% 0.15/0.38 % (14228)------------------------------
% 0.15/0.38 % (14228)------------------------------
% 0.15/0.38 % (14229)Instruction limit reached!
% 0.15/0.38 % (14229)------------------------------
% 0.15/0.38 % (14229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (14229)Termination reason: Unknown
% 0.15/0.38 % (14229)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (14229)Memory used [KB]: 1023
% 0.15/0.38 % (14229)Time elapsed: 0.004 s
% 0.15/0.38 % (14229)Instructions burned: 3 (million)
% 0.15/0.38 % (14229)------------------------------
% 0.15/0.38 % (14229)------------------------------
% 0.15/0.38 % (14232)Instruction limit reached!
% 0.15/0.38 % (14232)------------------------------
% 0.15/0.38 % (14232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (14232)Termination reason: Unknown
% 0.15/0.38 % (14232)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (14232)Memory used [KB]: 1023
% 0.15/0.38 % (14232)Time elapsed: 0.004 s
% 0.15/0.38 % (14232)Instructions burned: 3 (million)
% 0.15/0.39 % (14232)------------------------------
% 0.15/0.39 % (14232)------------------------------
% 0.15/0.39 % (14226)Instruction limit reached!
% 0.15/0.39 % (14226)------------------------------
% 0.15/0.39 % (14226)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (14226)Termination reason: Unknown
% 0.15/0.39 % (14226)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (14226)Memory used [KB]: 1023
% 0.15/0.39 % (14226)Time elapsed: 0.005 s
% 0.15/0.39 % (14226)Instructions burned: 6 (million)
% 0.15/0.39 % (14226)------------------------------
% 0.15/0.39 % (14226)------------------------------
% 0.15/0.39 % (14230)Refutation not found, incomplete strategy
% 0.15/0.39 % (14230)------------------------------
% 0.15/0.39 % (14230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (14230)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (14230)Memory used [KB]: 5500
% 0.15/0.39 % (14230)Time elapsed: 0.005 s
% 0.15/0.39 % (14230)Instructions burned: 3 (million)
% 0.15/0.39 % (14230)------------------------------
% 0.15/0.39 % (14230)------------------------------
% 0.15/0.39 % (14231)Instruction limit reached!
% 0.15/0.39 % (14231)------------------------------
% 0.15/0.39 % (14231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (14231)Termination reason: Unknown
% 0.15/0.39 % (14231)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (14231)Memory used [KB]: 5628
% 0.15/0.39 % (14231)Time elapsed: 0.011 s
% 0.15/0.39 % (14231)Instructions burned: 18 (million)
% 0.15/0.39 % (14231)------------------------------
% 0.15/0.39 % (14231)------------------------------
% 0.15/0.40 % (14227)Instruction limit reached!
% 0.15/0.40 % (14227)------------------------------
% 0.15/0.40 % (14227)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (14227)Termination reason: Unknown
% 0.15/0.40 % (14227)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (14227)Memory used [KB]: 5628
% 0.15/0.40 % (14227)Time elapsed: 0.016 s
% 0.15/0.40 % (14227)Instructions burned: 28 (million)
% 0.15/0.40 % (14227)------------------------------
% 0.15/0.40 % (14227)------------------------------
% 0.22/0.40 % (14233)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.22/0.40 % (14234)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.22/0.40 % (14235)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.40 % (14236)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (2999ds/1041Mi)
% 0.22/0.40 % (14237)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.40 % (14235)Instruction limit reached!
% 0.22/0.40 % (14235)------------------------------
% 0.22/0.40 % (14235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (14235)Termination reason: Unknown
% 0.22/0.40 % (14235)Termination phase: Function definition elimination
% 0.22/0.40
% 0.22/0.40 % (14235)Memory used [KB]: 1023
% 0.22/0.40 % (14235)Time elapsed: 0.004 s
% 0.22/0.40 % (14235)Instructions burned: 4 (million)
% 0.22/0.40 % (14235)------------------------------
% 0.22/0.40 % (14235)------------------------------
% 0.22/0.40 % (14237)Instruction limit reached!
% 0.22/0.40 % (14237)------------------------------
% 0.22/0.40 % (14237)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (14237)Termination reason: Unknown
% 0.22/0.40 % (14237)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.41 % (14237)Memory used [KB]: 1023
% 0.22/0.41 % (14237)Time elapsed: 0.006 s
% 0.22/0.41 % (14237)Instructions burned: 8 (million)
% 0.22/0.41 % (14237)------------------------------
% 0.22/0.41 % (14237)------------------------------
% 0.22/0.41 % (14234)Instruction limit reached!
% 0.22/0.41 % (14234)------------------------------
% 0.22/0.41 % (14234)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (14234)Termination reason: Unknown
% 0.22/0.41 % (14234)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (14234)Memory used [KB]: 5628
% 0.22/0.41 % (14234)Time elapsed: 0.009 s
% 0.22/0.41 % (14234)Instructions burned: 15 (million)
% 0.22/0.41 % (14234)------------------------------
% 0.22/0.41 % (14234)------------------------------
% 0.22/0.41 % (14238)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (2999ds/16Mi)
% 0.22/0.41 % (14239)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.41 % (14239)Instruction limit reached!
% 0.22/0.41 % (14239)------------------------------
% 0.22/0.41 % (14239)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (14239)Termination reason: Unknown
% 0.22/0.41 % (14239)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (14239)Memory used [KB]: 1023
% 0.22/0.41 % (14239)Time elapsed: 0.004 s
% 0.22/0.41 % (14239)Instructions burned: 4 (million)
% 0.22/0.41 % (14239)------------------------------
% 0.22/0.41 % (14239)------------------------------
% 0.22/0.42 % (14240)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.42 % (14238)Instruction limit reached!
% 0.22/0.42 % (14238)------------------------------
% 0.22/0.42 % (14238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14238)Termination reason: Unknown
% 0.22/0.42 % (14238)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (14238)Memory used [KB]: 5884
% 0.22/0.42 % (14238)Time elapsed: 0.013 s
% 0.22/0.42 % (14238)Instructions burned: 17 (million)
% 0.22/0.42 % (14238)------------------------------
% 0.22/0.42 % (14238)------------------------------
% 0.22/0.42 % (14240)Instruction limit reached!
% 0.22/0.42 % (14240)------------------------------
% 0.22/0.42 % (14240)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14240)Termination reason: Unknown
% 0.22/0.42 % (14240)Termination phase: Function definition elimination
% 0.22/0.42 % (14233)Instruction limit reached!
% 0.22/0.42 % (14233)------------------------------
% 0.22/0.42 % (14233)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42
% 0.22/0.42 % (14240)Memory used [KB]: 1023
% 0.22/0.42 % (14240)Time elapsed: 0.004 s
% 0.22/0.42 % (14240)Instructions burned: 4 (million)
% 0.22/0.42 % (14240)------------------------------
% 0.22/0.42 % (14240)------------------------------
% 0.22/0.42 % (14233)Termination reason: Unknown
% 0.22/0.42 % (14233)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (14233)Memory used [KB]: 5628
% 0.22/0.42 % (14233)Time elapsed: 0.022 s
% 0.22/0.42 % (14233)Instructions burned: 38 (million)
% 0.22/0.42 % (14233)------------------------------
% 0.22/0.42 % (14233)------------------------------
% 0.22/0.42 % (14241)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on Vampire---4 for (2999ds/7Mi)
% 0.22/0.42 % (14242)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.42 % (14242)Instruction limit reached!
% 0.22/0.42 % (14242)------------------------------
% 0.22/0.42 % (14242)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14242)Termination reason: Unknown
% 0.22/0.42 % (14242)Termination phase: Function definition elimination
% 0.22/0.42
% 0.22/0.42 % (14242)Memory used [KB]: 1023
% 0.22/0.42 % (14242)Time elapsed: 0.004 s
% 0.22/0.42 % (14242)Instructions burned: 4 (million)
% 0.22/0.42 % (14242)------------------------------
% 0.22/0.42 % (14242)------------------------------
% 0.22/0.42 % (14241)Instruction limit reached!
% 0.22/0.42 % (14241)------------------------------
% 0.22/0.42 % (14241)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (14241)Termination reason: Unknown
% 0.22/0.42 % (14241)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (14241)Memory used [KB]: 5500
% 0.22/0.42 % (14241)Time elapsed: 0.006 s
% 0.22/0.42 % (14241)Instructions burned: 9 (million)
% 0.22/0.42 % (14241)------------------------------
% 0.22/0.42 % (14241)------------------------------
% 0.22/0.43 % (14243)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (2999ds/4Mi)
% 0.22/0.43 % (14243)Instruction limit reached!
% 0.22/0.43 % (14243)------------------------------
% 0.22/0.43 % (14243)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (14243)Termination reason: Unknown
% 0.22/0.43 % (14243)Termination phase: Function definition elimination
% 0.22/0.43
% 0.22/0.43 % (14243)Memory used [KB]: 1023
% 0.22/0.43 % (14243)Time elapsed: 0.004 s
% 0.22/0.43 % (14243)Instructions burned: 4 (million)
% 0.22/0.43 % (14243)------------------------------
% 0.22/0.43 % (14243)------------------------------
% 0.22/0.43 % (14244)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.43 % (14246)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.43 % (14245)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on Vampire---4 for (2999ds/710Mi)
% 0.22/0.44 % (14246)Instruction limit reached!
% 0.22/0.44 % (14246)------------------------------
% 0.22/0.44 % (14246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (14246)Termination reason: Unknown
% 0.22/0.44 % (14246)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (14246)Memory used [KB]: 1023
% 0.22/0.44 % (14246)Time elapsed: 0.005 s
% 0.22/0.44 % (14246)Instructions burned: 6 (million)
% 0.22/0.44 % (14246)------------------------------
% 0.22/0.44 % (14246)------------------------------
% 0.22/0.44 % (14245)Refutation not found, incomplete strategy
% 0.22/0.44 % (14245)------------------------------
% 0.22/0.44 % (14245)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (14245)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (14245)Memory used [KB]: 5500
% 0.22/0.44 % (14245)Time elapsed: 0.005 s
% 0.22/0.44 % (14245)Instructions burned: 5 (million)
% 0.22/0.44 % (14245)------------------------------
% 0.22/0.44 % (14245)------------------------------
% 0.22/0.44 % (14247)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on Vampire---4 for (2999ds/902Mi)
% 0.22/0.44 % (14249)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (2999ds/21Mi)
% 0.22/0.44 % (14247)Refutation not found, incomplete strategy
% 0.22/0.44 % (14247)------------------------------
% 0.22/0.44 % (14247)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (14247)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (14247)Memory used [KB]: 5500
% 0.22/0.44 % (14247)Time elapsed: 0.005 s
% 0.22/0.44 % (14247)Instructions burned: 5 (million)
% 0.22/0.44 % (14247)------------------------------
% 0.22/0.44 % (14247)------------------------------
% 0.22/0.44 % (14225)Instruction limit reached!
% 0.22/0.44 % (14225)------------------------------
% 0.22/0.44 % (14225)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (14225)Termination reason: Unknown
% 0.22/0.44 % (14225)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (14225)Memory used [KB]: 6908
% 0.22/0.44 % (14225)Time elapsed: 0.066 s
% 0.22/0.44 % (14225)Instructions burned: 185 (million)
% 0.22/0.44 % (14225)------------------------------
% 0.22/0.44 % (14225)------------------------------
% 0.22/0.44 % (14252)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on Vampire---4 for (2999ds/5Mi)
% 0.22/0.45 % (14244)Instruction limit reached!
% 0.22/0.45 % (14244)------------------------------
% 0.22/0.45 % (14244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (14244)Termination reason: Unknown
% 0.22/0.45 % (14244)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (14244)Memory used [KB]: 5628
% 0.22/0.45 % (14244)Time elapsed: 0.014 s
% 0.22/0.45 % (14244)Instructions burned: 19 (million)
% 0.22/0.45 % (14244)------------------------------
% 0.22/0.45 % (14244)------------------------------
% 0.22/0.45 % (14252)Instruction limit reached!
% 0.22/0.45 % (14252)------------------------------
% 0.22/0.45 % (14252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (14252)Termination reason: Unknown
% 0.22/0.45 % (14252)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (14252)Memory used [KB]: 5500
% 0.22/0.45 % (14252)Time elapsed: 0.005 s
% 0.22/0.45 % (14252)Instructions burned: 6 (million)
% 0.22/0.45 % (14252)------------------------------
% 0.22/0.45 % (14252)------------------------------
% 0.22/0.45 % (14259)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on Vampire---4 for (2999ds/779Mi)
% 0.22/0.45 % (14249)Instruction limit reached!
% 0.22/0.45 % (14249)------------------------------
% 0.22/0.45 % (14249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (14249)Termination reason: Unknown
% 0.22/0.45 % (14249)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (14249)Memory used [KB]: 5628
% 0.22/0.45 % (14249)Time elapsed: 0.014 s
% 0.22/0.45 % (14249)Instructions burned: 21 (million)
% 0.22/0.45 % (14249)------------------------------
% 0.22/0.45 % (14249)------------------------------
% 0.22/0.45 % (14257)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on Vampire---4 for (2999ds/377Mi)
% 0.22/0.45 % (14236)First to succeed.
% 0.22/0.45 % (14256)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (2999ds/6Mi)
% 0.22/0.46 % (14260)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (2999ds/19Mi)
% 0.22/0.46 % (14256)Refutation not found, incomplete strategy
% 0.22/0.46 % (14256)------------------------------
% 0.22/0.46 % (14256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (14256)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 % (14256)Memory used [KB]: 5500
% 0.22/0.46 % (14256)Time elapsed: 0.005 s
% 0.22/0.46 % (14256)Instructions burned: 3 (million)
% 0.22/0.46 % (14256)------------------------------
% 0.22/0.46 % (14256)------------------------------
% 0.22/0.46 % (14260)Refutation not found, incomplete strategy
% 0.22/0.46 % (14260)------------------------------
% 0.22/0.46 % (14260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (14260)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 % (14260)Memory used [KB]: 5500
% 0.22/0.46 % (14260)Time elapsed: 0.004 s
% 0.22/0.46 % (14260)Instructions burned: 4 (million)
% 0.22/0.46 % (14260)------------------------------
% 0.22/0.46 % (14260)------------------------------
% 0.22/0.46 % (14263)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (2999ds/17Mi)
% 0.22/0.46 % (14261)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on Vampire---4 for (2999ds/879Mi)
% 0.22/0.46 % (14236)Refutation found. Thanks to Tanya!
% 0.22/0.46 % SZS status Theorem for Vampire---4
% 0.22/0.46 % SZS output start Proof for Vampire---4
% 0.22/0.46 thf(func_def_0, type, irel: $i > $i > $o).
% 0.22/0.46 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_9, type, itrue: $i > $o).
% 0.22/0.46 thf(func_def_10, type, ifalse: $i > $o).
% 0.22/0.46 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.46 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.22/0.46 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.22/0.46 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.22/0.46 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.22/0.46 thf(func_def_21, type, a1: $i > $o).
% 0.22/0.46 thf(func_def_22, type, a2: $i > $o).
% 0.22/0.46 thf(func_def_36, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.46 thf(f479,plain,(
% 0.22/0.46 $false),
% 0.22/0.46 inference(avatar_sat_refutation,[],[f130,f150,f245,f249,f466,f471,f476])).
% 0.22/0.46 thf(f476,plain,(
% 0.22/0.46 ~spl0_1 | ~spl0_7),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f475])).
% 0.22/0.46 thf(f475,plain,(
% 0.22/0.46 $false | (~spl0_1 | ~spl0_7)),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f474])).
% 0.22/0.46 thf(f474,plain,(
% 0.22/0.46 ($false = $true) | (~spl0_1 | ~spl0_7)),
% 0.22/0.46 inference(boolean_simplification,[],[f473])).
% 0.22/0.46 thf(f473,plain,(
% 0.22/0.46 (($false & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0)))))) = $true) | (~spl0_1 | ~spl0_7)),
% 0.22/0.46 inference(backward_demodulation,[],[f412,f462])).
% 0.22/0.46 thf(f462,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0)))))) | ~spl0_7),
% 0.22/0.46 inference(avatar_component_clause,[],[f461])).
% 0.22/0.46 thf(f461,plain,(
% 0.22/0.46 spl0_7 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.22/0.46 thf(f412,plain,(
% 0.22/0.46 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0)))))) = $true) | ~spl0_1),
% 0.22/0.46 inference(boolean_simplification,[],[f406])).
% 0.22/0.46 thf(f406,plain,(
% 0.22/0.46 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))))) = $true) | ~spl0_1),
% 0.22/0.46 inference(superposition,[],[f282,f401])).
% 0.22/0.46 thf(f401,plain,(
% 0.22/0.46 ((irel @ sK2 @ sK7) = $true) | ~spl0_1),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f392])).
% 0.22/0.46 thf(f392,plain,(
% 0.22/0.46 ($false = ((irel @ sK2 @ sK7) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0)))))))) | ~spl0_1),
% 0.22/0.46 inference(beta_eta_normalization,[],[f391])).
% 0.22/0.46 thf(f391,plain,(
% 0.22/0.46 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ sK7)) | ~spl0_1),
% 0.22/0.46 inference(sigma_clausification,[],[f268])).
% 0.22/0.46 thf(f268,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | ~spl0_1),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f126])).
% 0.22/0.46 thf(f126,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl0_1),
% 0.22/0.46 inference(avatar_component_clause,[],[f125])).
% 0.22/0.46 thf(f125,plain,(
% 0.22/0.46 spl0_1 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.22/0.46 thf(f282,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))))) = $true)) ) | ~spl0_1),
% 0.22/0.46 inference(beta_eta_normalization,[],[f281])).
% 0.22/0.46 thf(f281,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ X1) = $true)) ) | ~spl0_1),
% 0.22/0.46 inference(pi_clausification,[],[f274])).
% 0.22/0.46 thf(f274,plain,(
% 0.22/0.46 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))) = $true) | ~spl0_1),
% 0.22/0.46 inference(not_proxy_clausification,[],[f271])).
% 0.22/0.46 thf(f271,plain,(
% 0.22/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl0_1),
% 0.22/0.46 inference(boolean_simplification,[],[f270])).
% 0.22/0.46 thf(f270,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | $false)) | ~spl0_1),
% 0.22/0.46 inference(backward_demodulation,[],[f126,f268])).
% 0.22/0.46 thf(f471,plain,(
% 0.22/0.46 ~spl0_1 | ~spl0_8),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f470])).
% 0.22/0.46 thf(f470,plain,(
% 0.22/0.46 $false | (~spl0_1 | ~spl0_8)),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f469])).
% 0.22/0.46 thf(f469,plain,(
% 0.22/0.46 ($false = $true) | (~spl0_1 | ~spl0_8)),
% 0.22/0.46 inference(boolean_simplification,[],[f467])).
% 0.22/0.46 thf(f467,plain,(
% 0.22/0.46 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) & $false) = $true) | (~spl0_1 | ~spl0_8)),
% 0.22/0.46 inference(backward_demodulation,[],[f412,f465])).
% 0.22/0.46 thf(f465,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0)))))) | ~spl0_8),
% 0.22/0.46 inference(avatar_component_clause,[],[f464])).
% 0.22/0.46 thf(f464,plain,(
% 0.22/0.46 spl0_8 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.22/0.46 thf(f466,plain,(
% 0.22/0.46 spl0_7 | spl0_8 | ~spl0_1),
% 0.22/0.46 inference(avatar_split_clause,[],[f459,f125,f464,f461])).
% 0.22/0.46 thf(f459,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0)))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0)))))) | ~spl0_1),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f400])).
% 0.22/0.46 thf(f400,plain,(
% 0.22/0.46 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK7 @ Y0) => (a1 @ Y0))))))) | ~spl0_1),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f392])).
% 0.22/0.46 thf(f249,plain,(
% 0.22/0.46 ~spl0_2 | ~spl0_4),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f248])).
% 0.22/0.46 thf(f248,plain,(
% 0.22/0.46 $false | (~spl0_2 | ~spl0_4)),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f247])).
% 0.22/0.46 thf(f247,plain,(
% 0.22/0.46 ($false = $true) | (~spl0_2 | ~spl0_4)),
% 0.22/0.46 inference(boolean_simplification,[],[f246])).
% 0.22/0.46 thf(f246,plain,(
% 0.22/0.46 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) & $false) = $true) | (~spl0_2 | ~spl0_4)),
% 0.22/0.46 inference(forward_demodulation,[],[f221,f149])).
% 0.22/0.46 thf(f149,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0)))))) | ~spl0_4),
% 0.22/0.46 inference(avatar_component_clause,[],[f148])).
% 0.22/0.46 thf(f148,plain,(
% 0.22/0.46 spl0_4 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.22/0.46 thf(f221,plain,(
% 0.22/0.46 ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0)))))) = $true) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f216])).
% 0.22/0.46 thf(f216,plain,(
% 0.22/0.46 (($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))))) = $true) | ~spl0_2),
% 0.22/0.46 inference(superposition,[],[f209,f140])).
% 0.22/0.46 thf(f140,plain,(
% 0.22/0.46 ((irel @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f138])).
% 0.22/0.46 thf(f138,plain,(
% 0.22/0.46 ($false = ((irel @ sK2 @ sK3) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))))))) | ~spl0_2),
% 0.22/0.46 inference(beta_eta_normalization,[],[f137])).
% 0.22/0.46 thf(f137,plain,(
% 0.22/0.46 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))) @ sK3)) | ~spl0_2),
% 0.22/0.46 inference(sigma_clausification,[],[f136])).
% 0.22/0.46 thf(f136,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f135])).
% 0.22/0.46 thf(f135,plain,(
% 0.22/0.46 ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f129,f134])).
% 0.22/0.46 thf(f134,plain,(
% 0.22/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f129])).
% 0.22/0.46 thf(f129,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ~spl0_2),
% 0.22/0.46 inference(avatar_component_clause,[],[f128])).
% 0.22/0.46 thf(f128,plain,(
% 0.22/0.46 spl0_2 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.22/0.46 thf(f209,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((irel @ sK2 @ X1) => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a1 @ Y0))))))) = $true)) ) | ~spl0_2),
% 0.22/0.46 inference(beta_eta_normalization,[],[f208])).
% 0.22/0.46 thf(f208,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))) @ X1) = $true)) ) | ~spl0_2),
% 0.22/0.46 inference(pi_clausification,[],[f195])).
% 0.22/0.46 thf(f195,plain,(
% 0.22/0.46 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))) = $true) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f134])).
% 0.22/0.46 thf(f245,plain,(
% 0.22/0.46 ~spl0_2 | ~spl0_3),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f244])).
% 0.22/0.46 thf(f244,plain,(
% 0.22/0.46 $false | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f243])).
% 0.22/0.46 thf(f243,plain,(
% 0.22/0.46 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(forward_demodulation,[],[f242,f159])).
% 0.22/0.46 thf(f159,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | ~spl0_3),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f146])).
% 0.22/0.46 thf(f146,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))))) | ~spl0_3),
% 0.22/0.46 inference(avatar_component_clause,[],[f145])).
% 0.22/0.46 thf(f145,plain,(
% 0.22/0.46 spl0_3 <=> ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.22/0.46 thf(f242,plain,(
% 0.22/0.46 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(boolean_simplification,[],[f241])).
% 0.22/0.46 thf(f241,plain,(
% 0.22/0.46 (($true => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(forward_demodulation,[],[f220,f140])).
% 0.22/0.46 thf(f220,plain,(
% 0.22/0.46 (((irel @ sK2 @ sK3) => (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(boolean_simplification,[],[f219])).
% 0.22/0.46 thf(f219,plain,(
% 0.22/0.46 (((irel @ sK2 @ sK3) => ($false | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(boolean_simplification,[],[f218])).
% 0.22/0.46 thf(f218,plain,(
% 0.22/0.46 (((irel @ sK2 @ sK3) => ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(boolean_simplification,[],[f217])).
% 0.22/0.46 thf(f217,plain,(
% 0.22/0.46 (((irel @ sK2 @ sK3) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) & $true)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(boolean_simplification,[],[f214])).
% 0.22/0.46 thf(f214,plain,(
% 0.22/0.46 (((irel @ sK2 @ sK3) => (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | $true))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.22/0.46 inference(superposition,[],[f209,f170])).
% 0.22/0.46 thf(f170,plain,(
% 0.22/0.46 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0)))) = $true) | ~spl0_3),
% 0.22/0.46 inference(not_proxy_clausification,[],[f162])).
% 0.22/0.46 thf(f162,plain,(
% 0.22/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0)))))) | ~spl0_3),
% 0.22/0.46 inference(boolean_simplification,[],[f161])).
% 0.22/0.46 thf(f161,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | $false)) | ~spl0_3),
% 0.22/0.46 inference(backward_demodulation,[],[f146,f159])).
% 0.22/0.46 thf(f150,plain,(
% 0.22/0.46 spl0_3 | spl0_4 | ~spl0_2),
% 0.22/0.46 inference(avatar_split_clause,[],[f143,f128,f148,f145])).
% 0.22/0.46 thf(f143,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0)))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))))) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f142])).
% 0.22/0.46 thf(f142,plain,(
% 0.22/0.46 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f141])).
% 0.22/0.46 thf(f141,plain,(
% 0.22/0.46 ($false = ($true => (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK3 @ Y0) => (a2 @ Y0)))))))) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f138,f140])).
% 0.22/0.46 thf(f130,plain,(
% 0.22/0.46 spl0_1 | spl0_2),
% 0.22/0.46 inference(avatar_split_clause,[],[f123,f128,f125])).
% 0.22/0.46 thf(f123,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))))),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f122])).
% 0.22/0.46 thf(f122,plain,(
% 0.22/0.46 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) & ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1)))))))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a1 @ Y1))))))))))))),
% 0.22/0.47 inference(beta_eta_normalization,[],[f121])).
% 0.22/0.47 thf(f121,plain,(
% 0.22/0.47 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))) @ sK2))),
% 0.22/0.47 inference(sigma_clausification,[],[f118])).
% 0.22/0.47 thf(f118,plain,(
% 0.22/0.47 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))))))))))))),
% 0.22/0.47 inference(not_proxy_clausification,[],[f100])).
% 0.22/0.47 thf(f100,plain,(
% 0.22/0.47 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) & ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2)))))))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) & ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (a1 @ Y2)))))))))))))) = $true)),
% 0.22/0.47 inference(beta_eta_normalization,[],[f99])).
% 0.22/0.47 thf(f99,plain,(
% 0.22/0.47 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a1) @ ((^[Y0 : $i > $o]: (Y0)) @ a2)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: (Y0)) @ a2) @ ((^[Y0 : $i > $o]: (Y0)) @ a1))))) = $true)),
% 0.22/0.47 inference(definition_unfolding,[],[f77,f87,f97,f97,f76,f76,f97,f76,f76])).
% 0.22/0.47 thf(f76,plain,(
% 0.22/0.47 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.22/0.47 inference(cnf_transformation,[],[f47])).
% 0.22/0.47 thf(f47,plain,(
% 0.22/0.47 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.22/0.47 inference(fool_elimination,[],[f46])).
% 0.22/0.47 thf(f46,plain,(
% 0.22/0.47 (iatom = (^[X0 : $i > $o] : (X0)))),
% 0.22/0.47 inference(rectify,[],[f8])).
% 0.22/0.47 thf(f8,axiom,(
% 0.22/0.47 (iatom = (^[X5 : $i > $o] : (X5)))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',iatom)).
% 0.22/0.47 thf(f97,plain,(
% 0.22/0.47 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ Y6))))))) @ Y2 @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((irel @ Y5 @ Y6) => (Y4 @ Y6))))))) @ Y3))))) @ Y1 @ Y0))))))),
% 0.22/0.47 inference(definition_unfolding,[],[f68,f93,f95,f95])).
% 0.22/0.47 thf(f95,plain,(
% 0.22/0.47 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.22/0.47 inference(definition_unfolding,[],[f73,f90,f72,f72])).
% 0.22/0.47 thf(f72,plain,(
% 0.22/0.47 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f59])).
% 0.22/0.47 thf(f59,plain,(
% 0.22/0.47 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.22/0.47 inference(fool_elimination,[],[f58])).
% 0.22/0.47 thf(f58,plain,(
% 0.22/0.47 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))) = mbox_s4)),
% 0.22/0.47 inference(rectify,[],[f7])).
% 0.22/0.47 thf(f7,axiom,(
% 0.22/0.47 ((^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))) = mbox_s4)),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',mbox_s4)).
% 0.22/0.47 thf(f90,plain,(
% 0.22/0.47 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.22/0.47 inference(definition_unfolding,[],[f74,f83,f84])).
% 0.22/0.47 thf(f84,plain,(
% 0.22/0.47 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f57])).
% 0.22/0.47 thf(f57,plain,(
% 0.22/0.47 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.47 inference(fool_elimination,[],[f56])).
% 0.22/0.47 thf(f56,plain,(
% 0.22/0.47 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.22/0.47 inference(rectify,[],[f3])).
% 0.22/0.47 thf(f3,axiom,(
% 0.22/0.47 (mnot = (^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',mnot)).
% 0.22/0.47 thf(f83,plain,(
% 0.22/0.47 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f32])).
% 0.22/0.47 thf(f32,plain,(
% 0.22/0.47 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.47 inference(fool_elimination,[],[f31])).
% 0.22/0.47 thf(f31,plain,(
% 0.22/0.47 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.22/0.47 inference(rectify,[],[f4])).
% 0.22/0.47 thf(f4,axiom,(
% 0.22/0.47 ((^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))) = mor)),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',mor)).
% 0.22/0.47 thf(f74,plain,(
% 0.22/0.47 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.47 inference(cnf_transformation,[],[f45])).
% 0.22/0.47 thf(f45,plain,(
% 0.22/0.47 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.47 inference(fool_elimination,[],[f44])).
% 0.22/0.47 thf(f44,plain,(
% 0.22/0.47 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.22/0.47 inference(rectify,[],[f6])).
% 0.22/0.47 thf(f6,axiom,(
% 0.22/0.47 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',mimplies)).
% 0.22/0.47 thf(f73,plain,(
% 0.22/0.47 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f49])).
% 0.22/0.47 thf(f49,plain,(
% 0.22/0.47 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.22/0.47 inference(fool_elimination,[],[f48])).
% 0.22/0.47 thf(f48,plain,(
% 0.22/0.47 (iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.22/0.47 inference(rectify,[],[f14])).
% 0.22/0.47 thf(f14,axiom,(
% 0.22/0.47 (iimplies = (^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',iimplies)).
% 0.22/0.47 thf(f93,plain,(
% 0.22/0.47 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ Y0 @ Y1)))))),
% 0.22/0.47 inference(definition_unfolding,[],[f81,f69])).
% 0.22/0.47 thf(f69,plain,(
% 0.22/0.47 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f63])).
% 0.22/0.47 thf(f63,plain,(
% 0.22/0.47 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.22/0.47 inference(fool_elimination,[],[f62])).
% 0.22/0.47 thf(f62,plain,(
% 0.22/0.47 (mand = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))))),
% 0.22/0.47 inference(rectify,[],[f5])).
% 0.22/0.47 thf(f5,axiom,(
% 0.22/0.47 (mand = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) & (X1 @ X3))))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',mand)).
% 0.22/0.47 thf(f81,plain,(
% 0.22/0.47 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.22/0.47 inference(cnf_transformation,[],[f61])).
% 0.22/0.47 thf(f61,plain,(
% 0.22/0.47 (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ Y0 @ Y1)))))),
% 0.22/0.47 inference(fool_elimination,[],[f60])).
% 0.22/0.47 thf(f60,plain,(
% 0.22/0.47 (iand = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ X0 @ X1)))),
% 0.22/0.47 inference(rectify,[],[f12])).
% 0.22/0.47 thf(f12,axiom,(
% 0.22/0.47 (iand = (^[X5 : $i > $o, X7 : $i > $o] : (mand @ X5 @ X7)))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',iand)).
% 0.22/0.47 thf(f68,plain,(
% 0.22/0.47 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f30])).
% 0.22/0.47 thf(f30,plain,(
% 0.22/0.47 (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
% 0.22/0.47 inference(fool_elimination,[],[f29])).
% 0.22/0.47 thf(f29,plain,(
% 0.22/0.47 (iequiv = (^[X0 : $i > $o, X1 : $i > $o] : (iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0))))),
% 0.22/0.47 inference(rectify,[],[f16])).
% 0.22/0.47 thf(f16,axiom,(
% 0.22/0.47 (iequiv = (^[X5 : $i > $o, X7 : $i > $o] : (iand @ (iimplies @ X5 @ X7) @ (iimplies @ X7 @ X5))))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',iequiv)).
% 0.22/0.47 thf(f87,plain,(
% 0.22/0.47 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.47 inference(cnf_transformation,[],[f34])).
% 0.22/0.47 thf(f34,plain,(
% 0.22/0.47 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.47 inference(fool_elimination,[],[f33])).
% 0.22/0.47 thf(f33,plain,(
% 0.22/0.47 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.22/0.47 inference(rectify,[],[f18])).
% 0.22/0.47 thf(f18,axiom,(
% 0.22/0.47 ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',ivalid)).
% 0.22/0.47 thf(f77,plain,(
% 0.22/0.47 ($true = (~ (ivalid @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 0.22/0.47 inference(cnf_transformation,[],[f42])).
% 0.22/0.47 thf(f42,plain,(
% 0.22/0.47 ($true = (~ (ivalid @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))))),
% 0.22/0.47 inference(fool_elimination,[],[f41])).
% 0.22/0.47 thf(f41,plain,(
% 0.22/0.47 ~(ivalid @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))),
% 0.22/0.47 inference(rectify,[],[f23])).
% 0.22/0.47 thf(f23,negated_conjecture,(
% 0.22/0.47 ~(ivalid @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))),
% 0.22/0.47 inference(negated_conjecture,[],[f22])).
% 0.22/0.47 thf(f22,conjecture,(
% 0.22/0.47 (ivalid @ (iequiv @ (iequiv @ (iatom @ a1) @ (iatom @ a2)) @ (iequiv @ (iatom @ a2) @ (iatom @ a1))))),
% 0.22/0.47 file('/export/starexec/sandbox/tmp/tmp.jXQ4D7OPfo/Vampire---4.8_13977',con)).
% 0.22/0.47 % SZS output end Proof for Vampire---4
% 0.22/0.47 % (14236)------------------------------
% 0.22/0.47 % (14236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (14236)Termination reason: Refutation
% 0.22/0.47
% 0.22/0.47 % (14236)Memory used [KB]: 6012
% 0.22/0.47 % (14236)Time elapsed: 0.064 s
% 0.22/0.47 % (14236)Instructions burned: 79 (million)
% 0.22/0.47 % (14236)------------------------------
% 0.22/0.47 % (14236)------------------------------
% 0.22/0.47 % (14224)Success in time 0.092 s
% 0.22/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------