TSTP Solution File: SYO443^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO443^1 : TPTP v8.2.0. 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 : n003.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 09:04:27 EDT 2024
% Result : Theorem 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO443^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:03:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36 % (15827)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)
% 0.13/0.37 % (15827)Instruction limit reached!
% 0.13/0.37 % (15827)------------------------------
% 0.13/0.37 % (15827)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (15827)Termination reason: Unknown
% 0.13/0.37 % (15827)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (15827)Memory used [KB]: 1023
% 0.13/0.37 % (15827)Time elapsed: 0.003 s
% 0.13/0.37 % (15827)Instructions burned: 3 (million)
% 0.13/0.37 % (15827)------------------------------
% 0.13/0.37 % (15827)------------------------------
% 0.13/0.37 % (15823)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (15825)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)
% 0.13/0.37 % (15826)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (15828)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)
% 0.13/0.37 % (15824)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)
% 0.13/0.37 % (15830)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)
% 0.13/0.37 % (15829)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (15826)Instruction limit reached!
% 0.13/0.37 % (15826)------------------------------
% 0.13/0.37 % (15826)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (15826)Termination reason: Unknown
% 0.13/0.37 % (15826)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (15826)Memory used [KB]: 1023
% 0.13/0.37 % (15826)Time elapsed: 0.004 s
% 0.13/0.37 % (15826)Instructions burned: 3 (million)
% 0.13/0.37 % (15826)------------------------------
% 0.13/0.37 % (15826)------------------------------
% 0.13/0.37 % (15830)Instruction limit reached!
% 0.13/0.37 % (15830)------------------------------
% 0.13/0.37 % (15830)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (15830)Termination reason: Unknown
% 0.13/0.37 % (15830)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (15830)Memory used [KB]: 1023
% 0.13/0.37 % (15830)Time elapsed: 0.004 s
% 0.13/0.37 % (15830)Instructions burned: 3 (million)
% 0.13/0.37 % (15830)------------------------------
% 0.13/0.37 % (15830)------------------------------
% 0.13/0.37 % (15824)Instruction limit reached!
% 0.13/0.37 % (15824)------------------------------
% 0.13/0.37 % (15824)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (15824)Termination reason: Unknown
% 0.13/0.37 % (15824)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (15824)Memory used [KB]: 1023
% 0.13/0.37 % (15824)Time elapsed: 0.004 s
% 0.13/0.37 % (15824)Instructions burned: 5 (million)
% 0.13/0.37 % (15824)------------------------------
% 0.13/0.37 % (15824)------------------------------
% 0.13/0.37 % (15828)Refutation not found, incomplete strategy
% 0.13/0.37 % (15828)------------------------------
% 0.13/0.37 % (15828)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (15828)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % (15828)Memory used [KB]: 5628
% 0.13/0.37 % (15828)Time elapsed: 0.007 s
% 0.13/0.37 % (15828)Instructions burned: 8 (million)
% 0.13/0.37 % (15828)------------------------------
% 0.13/0.37 % (15828)------------------------------
% 0.13/0.38 % (15831)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)
% 0.13/0.38 % (15829)Instruction limit reached!
% 0.13/0.38 % (15829)------------------------------
% 0.13/0.38 % (15829)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (15829)Termination reason: Unknown
% 0.13/0.38 % (15829)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (15829)Memory used [KB]: 5628
% 0.13/0.38 % (15829)Time elapsed: 0.012 s
% 0.13/0.38 % (15829)Instructions burned: 19 (million)
% 0.13/0.38 % (15829)------------------------------
% 0.13/0.38 % (15829)------------------------------
% 0.13/0.38 % (15825)Instruction limit reached!
% 0.13/0.38 % (15825)------------------------------
% 0.13/0.38 % (15825)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (15825)Termination reason: Unknown
% 0.13/0.38 % (15825)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (15825)Memory used [KB]: 5756
% 0.13/0.38 % (15825)Time elapsed: 0.018 s
% 0.13/0.38 % (15825)Instructions burned: 28 (million)
% 0.13/0.38 % (15825)------------------------------
% 0.13/0.38 % (15825)------------------------------
% 0.13/0.38 % (15832)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)
% 0.13/0.38 % (15833)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)
% 0.13/0.39 % (15834)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)
% 0.13/0.39 % (15833)Instruction limit reached!
% 0.13/0.39 % (15833)------------------------------
% 0.13/0.39 % (15833)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (15833)Termination reason: Unknown
% 0.13/0.39 % (15833)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (15833)Memory used [KB]: 1023
% 0.13/0.39 % (15833)Time elapsed: 0.004 s
% 0.13/0.39 % (15833)Instructions burned: 4 (million)
% 0.13/0.39 % (15833)------------------------------
% 0.13/0.39 % (15833)------------------------------
% 0.13/0.39 % (15835)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.39 % (15832)Instruction limit reached!
% 0.13/0.39 % (15832)------------------------------
% 0.13/0.39 % (15832)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (15831)Instruction limit reached!
% 0.13/0.39 % (15831)------------------------------
% 0.13/0.39 % (15831)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (15831)Termination reason: Unknown
% 0.13/0.39 % (15831)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (15831)Memory used [KB]: 5756
% 0.13/0.39 % (15831)Time elapsed: 0.017 s
% 0.13/0.39 % (15831)Instructions burned: 38 (million)
% 0.13/0.39 % (15831)------------------------------
% 0.13/0.39 % (15831)------------------------------
% 0.13/0.39 % (15832)Termination reason: Unknown
% 0.13/0.39 % (15832)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (15832)Memory used [KB]: 5628
% 0.13/0.39 % (15835)Instruction limit reached!
% 0.13/0.39 % (15835)------------------------------
% 0.13/0.39 % (15835)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (15835)Termination reason: Unknown
% 0.13/0.39 % (15835)Termination phase: Property scanning
% 0.13/0.39
% 0.13/0.39 % (15835)Memory used [KB]: 1023
% 0.13/0.39 % (15835)Time elapsed: 0.006 s
% 0.13/0.39 % (15835)Instructions burned: 8 (million)
% 0.13/0.39 % (15835)------------------------------
% 0.13/0.39 % (15835)------------------------------
% 0.13/0.39 % (15832)Time elapsed: 0.010 s
% 0.13/0.39 % (15832)Instructions burned: 16 (million)
% 0.13/0.39 % (15832)------------------------------
% 0.13/0.39 % (15832)------------------------------
% 0.13/0.39 % (15836)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.40 % (15837)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)
% 0.13/0.40 % (15837)Instruction limit reached!
% 0.13/0.40 % (15837)------------------------------
% 0.13/0.40 % (15837)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (15837)Termination reason: Unknown
% 0.13/0.40 % (15837)Termination phase: shuffling
% 0.13/0.40
% 0.13/0.40 % (15837)Memory used [KB]: 1023
% 0.13/0.40 % (15837)Time elapsed: 0.004 s
% 0.13/0.40 % (15837)Instructions burned: 4 (million)
% 0.13/0.40 % (15837)------------------------------
% 0.13/0.40 % (15837)------------------------------
% 0.13/0.40 % (15838)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)
% 0.19/0.40 % (15836)Instruction limit reached!
% 0.19/0.40 % (15836)------------------------------
% 0.19/0.40 % (15836)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (15836)Termination reason: Unknown
% 0.19/0.40 % (15836)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (15836)Memory used [KB]: 5884
% 0.19/0.40 % (15836)Time elapsed: 0.012 s
% 0.19/0.40 % (15836)Instructions burned: 16 (million)
% 0.19/0.40 % (15836)------------------------------
% 0.19/0.40 % (15836)------------------------------
% 0.19/0.40 % (15838)Instruction limit reached!
% 0.19/0.40 % (15838)------------------------------
% 0.19/0.40 % (15838)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (15839)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)
% 0.19/0.40 % (15838)Termination reason: Unknown
% 0.19/0.40 % (15838)Termination phase: shuffling
% 0.19/0.40
% 0.19/0.40 % (15838)Memory used [KB]: 1023
% 0.19/0.40 % (15838)Time elapsed: 0.004 s
% 0.19/0.40 % (15838)Instructions burned: 4 (million)
% 0.19/0.40 % (15838)------------------------------
% 0.19/0.40 % (15838)------------------------------
% 0.19/0.41 % (15839)Instruction limit reached!
% 0.19/0.41 % (15839)------------------------------
% 0.19/0.41 % (15839)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (15839)Termination reason: Unknown
% 0.19/0.41 % (15839)Termination phase: Property scanning
% 0.19/0.41
% 0.19/0.41 % (15839)Memory used [KB]: 1023
% 0.19/0.41 % (15839)Time elapsed: 0.004 s
% 0.19/0.41 % (15839)Instructions burned: 7 (million)
% 0.19/0.41 % (15839)------------------------------
% 0.19/0.41 % (15839)------------------------------
% 0.19/0.41 % (15840)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)
% 0.19/0.41 % (15842)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.41 % (15840)Instruction limit reached!
% 0.19/0.41 % (15840)------------------------------
% 0.19/0.41 % (15840)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (15840)Termination reason: Unknown
% 0.19/0.41 % (15840)Termination phase: shuffling
% 0.19/0.41
% 0.19/0.41 % (15840)Memory used [KB]: 1023
% 0.19/0.41 % (15840)Time elapsed: 0.003 s
% 0.19/0.41 % (15840)Instructions burned: 3 (million)
% 0.19/0.41 % (15840)------------------------------
% 0.19/0.41 % (15840)------------------------------
% 0.19/0.41 % (15842)Instruction limit reached!
% 0.19/0.41 % (15842)------------------------------
% 0.19/0.41 % (15842)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (15842)Termination reason: Unknown
% 0.19/0.41 % (15842)Termination phase: shuffling
% 0.19/0.41
% 0.19/0.41 % (15842)Memory used [KB]: 1023
% 0.19/0.41 % (15842)Time elapsed: 0.004 s
% 0.19/0.41 % (15842)Instructions burned: 4 (million)
% 0.19/0.41 % (15842)------------------------------
% 0.19/0.41 % (15842)------------------------------
% 0.19/0.42 % (15843)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)
% 0.19/0.42 % (15846)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)
% 0.19/0.42 % (15844)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.42 % (15845)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.42 % (15845)Instruction limit reached!
% 0.19/0.42 % (15845)------------------------------
% 0.19/0.42 % (15845)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (15846)Refutation not found, incomplete strategy
% 0.19/0.42 % (15846)------------------------------
% 0.19/0.42 % (15846)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (15846)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 % (15846)Memory used [KB]: 5628
% 0.19/0.42 % (15846)Time elapsed: 0.005 s
% 0.19/0.42 % (15846)Instructions burned: 9 (million)
% 0.19/0.42 % (15846)------------------------------
% 0.19/0.42 % (15846)------------------------------
% 0.19/0.42 % (15845)Termination reason: Unknown
% 0.19/0.42 % (15845)Termination phase: Property scanning
% 0.19/0.42
% 0.19/0.42 % (15845)Memory used [KB]: 1023
% 0.19/0.42 % (15845)Time elapsed: 0.005 s
% 0.19/0.42 % (15845)Instructions burned: 6 (million)
% 0.19/0.42 % (15845)------------------------------
% 0.19/0.42 % (15845)------------------------------
% 0.19/0.42 % (15847)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)
% 0.19/0.42 % (15844)Refutation not found, incomplete strategy
% 0.19/0.42 % (15844)------------------------------
% 0.19/0.42 % (15844)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (15844)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.42
% 0.19/0.42
% 0.19/0.42 % (15844)Memory used [KB]: 5628
% 0.19/0.42 % (15844)Time elapsed: 0.008 s
% 0.19/0.42 % (15844)Instructions burned: 11 (million)
% 0.19/0.42 % (15844)------------------------------
% 0.19/0.42 % (15844)------------------------------
% 0.19/0.42 % (15848)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.19/0.43 % (15823)First to succeed.
% 0.19/0.43 % (15848)Instruction limit reached!
% 0.19/0.43 % (15848)------------------------------
% 0.19/0.43 % (15848)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (15848)Termination reason: Unknown
% 0.19/0.43 % (15848)Termination phase: Property scanning
% 0.19/0.43
% 0.19/0.43 % (15848)Memory used [KB]: 1023
% 0.19/0.43 % (15843)Instruction limit reached!
% 0.19/0.43 % (15843)------------------------------
% 0.19/0.43 % (15843)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (15843)Termination reason: Unknown
% 0.19/0.43 % (15843)Termination phase: Saturation
% 0.19/0.43
% 0.19/0.43 % (15843)Memory used [KB]: 5628
% 0.19/0.43 % (15843)Time elapsed: 0.038 s
% 0.19/0.43 % (15843)Instructions burned: 19 (million)
% 0.19/0.43 % (15843)------------------------------
% 0.19/0.43 % (15843)------------------------------
% 0.19/0.43 % (15848)Time elapsed: 0.005 s
% 0.19/0.43 % (15848)Instructions burned: 6 (million)
% 0.19/0.43 % (15848)------------------------------
% 0.19/0.43 % (15848)------------------------------
% 0.19/0.43 % (15850)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.19/0.44 % (15847)Instruction limit reached!
% 0.19/0.44 % (15847)------------------------------
% 0.19/0.44 % (15847)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (15847)Termination reason: Unknown
% 0.19/0.44 % (15847)Termination phase: Saturation
% 0.19/0.44
% 0.19/0.44 % (15847)Memory used [KB]: 5628
% 0.19/0.44 % (15847)Time elapsed: 0.015 s
% 0.19/0.44 % (15847)Instructions burned: 22 (million)
% 0.19/0.44 % (15847)------------------------------
% 0.19/0.44 % (15847)------------------------------
% 0.19/0.44 % (15849)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)
% 0.19/0.44 % (15834)Also succeeded, but the first one will report.
% 0.19/0.44 % (15823)Refutation found. Thanks to Tanya!
% 0.19/0.44 % SZS status Theorem for theBenchmark
% 0.19/0.44 % SZS output start Proof for theBenchmark
% 0.19/0.44 thf(type_def_5, type, mu: $tType).
% 0.19/0.44 thf(func_def_0, type, mu: $tType).
% 0.19/0.44 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.19/0.44 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_15, type, mtrue: $i > $o).
% 0.19/0.44 thf(func_def_16, type, mfalse: $i > $o).
% 0.19/0.44 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.19/0.44 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.19/0.44 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.19/0.44 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.19/0.44 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.19/0.44 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.19/0.44 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.19/0.44 thf(func_def_36, type, p: $i > $o).
% 0.19/0.44 thf(func_def_37, type, q: $i > $o).
% 0.19/0.44 thf(f1376,plain,(
% 0.19/0.44 $false),
% 0.19/0.44 inference(avatar_sat_refutation,[],[f356,f361,f366,f371,f376,f401,f402,f417,f418,f433,f439,f444,f449,f455,f460,f478,f617,f781,f826,f911,f996,f998,f1088,f1352,f1361,f1367,f1375])).
% 0.19/0.44 thf(f1375,plain,(
% 0.19/0.44 ~spl0_5 | ~spl0_38),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f1374])).
% 0.19/0.44 thf(f1374,plain,(
% 0.19/0.44 $false | (~spl0_5 | ~spl0_38)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1371])).
% 0.19/0.44 thf(f1371,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_5 | ~spl0_38)),
% 0.19/0.44 inference(superposition,[],[f365,f1083])).
% 0.19/0.44 thf(f1083,plain,(
% 0.19/0.44 ((p @ sK11) = $false) | ~spl0_38),
% 0.19/0.44 inference(avatar_component_clause,[],[f1081])).
% 0.19/0.44 thf(f1081,plain,(
% 0.19/0.44 spl0_38 <=> ((p @ sK11) = $false)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_38])])).
% 0.19/0.44 thf(f365,plain,(
% 0.19/0.44 ((p @ sK11) = $true) | ~spl0_5),
% 0.19/0.44 inference(avatar_component_clause,[],[f363])).
% 0.19/0.44 thf(f363,plain,(
% 0.19/0.44 spl0_5 <=> ((p @ sK11) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.19/0.44 thf(f1367,plain,(
% 0.19/0.44 ~spl0_7 | ~spl0_45),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f1366])).
% 0.19/0.44 thf(f1366,plain,(
% 0.19/0.44 $false | (~spl0_7 | ~spl0_45)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1363])).
% 0.19/0.44 thf(f1363,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_7 | ~spl0_45)),
% 0.19/0.44 inference(superposition,[],[f375,f1348])).
% 0.19/0.44 thf(f1348,plain,(
% 0.19/0.44 ((q @ sK10) = $true) | ~spl0_45),
% 0.19/0.44 inference(avatar_component_clause,[],[f1346])).
% 0.19/0.44 thf(f1346,plain,(
% 0.19/0.44 spl0_45 <=> ((q @ sK10) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_45])])).
% 0.19/0.44 thf(f375,plain,(
% 0.19/0.44 ((q @ sK10) = $false) | ~spl0_7),
% 0.19/0.44 inference(avatar_component_clause,[],[f373])).
% 0.19/0.44 thf(f373,plain,(
% 0.19/0.44 spl0_7 <=> ((q @ sK10) = $false)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.19/0.44 thf(f1361,plain,(
% 0.19/0.44 ~spl0_4 | ~spl0_44),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f1360])).
% 0.19/0.44 thf(f1360,plain,(
% 0.19/0.44 $false | (~spl0_4 | ~spl0_44)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1353])).
% 0.19/0.44 thf(f1353,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_4 | ~spl0_44)),
% 0.19/0.44 inference(superposition,[],[f1308,f1006])).
% 0.19/0.44 thf(f1006,plain,(
% 0.19/0.44 ((rel_s5 @ sK11 @ sK1) = $true) | ~spl0_4),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1002])).
% 0.19/0.44 thf(f1002,plain,(
% 0.19/0.44 ($false = $true) | ((rel_s5 @ sK11 @ sK1) = $true) | ~spl0_4),
% 0.19/0.44 inference(superposition,[],[f176,f360])).
% 0.19/0.44 thf(f360,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK11) = $true) | ~spl0_4),
% 0.19/0.44 inference(avatar_component_clause,[],[f358])).
% 0.19/0.44 thf(f358,plain,(
% 0.19/0.44 spl0_4 <=> ((rel_s5 @ sK1 @ sK11) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.19/0.44 thf(f176,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ X1 @ X2)) | ((rel_s5 @ X2 @ X1) = $true)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f175])).
% 0.19/0.44 thf(f175,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f174])).
% 0.19/0.44 thf(f174,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2) = $true)) )),
% 0.19/0.44 inference(pi_clausification,[],[f173])).
% 0.19/0.44 thf(f173,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f172])).
% 0.19/0.44 thf(f172,plain,(
% 0.19/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.19/0.44 inference(pi_clausification,[],[f171])).
% 0.19/0.44 thf(f171,plain,(
% 0.19/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f161])).
% 0.19/0.44 thf(f161,plain,(
% 0.19/0.44 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5) = $true)),
% 0.19/0.44 inference(definition_unfolding,[],[f140,f142])).
% 0.19/0.44 thf(f142,plain,(
% 0.19/0.44 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f95])).
% 0.19/0.44 thf(f95,plain,(
% 0.19/0.44 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.19/0.44 inference(fool_elimination,[],[f94])).
% 0.19/0.44 thf(f94,plain,(
% 0.19/0.44 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))) = msymmetric)),
% 0.19/0.44 inference(rectify,[],[f19])).
% 0.19/0.44 thf(f19,axiom,(
% 0.19/0.44 ((^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.19/0.44 thf(f140,plain,(
% 0.19/0.44 ((msymmetric @ rel_s5) = $true)),
% 0.19/0.44 inference(cnf_transformation,[],[f79])).
% 0.19/0.44 thf(f79,plain,(
% 0.19/0.44 ((msymmetric @ rel_s5) = $true)),
% 0.19/0.44 inference(fool_elimination,[],[f78])).
% 0.19/0.44 thf(f78,plain,(
% 0.19/0.44 (msymmetric @ rel_s5)),
% 0.19/0.44 inference(rectify,[],[f36])).
% 0.19/0.44 thf(f36,axiom,(
% 0.19/0.44 (msymmetric @ rel_s5)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.19/0.44 thf(f1308,plain,(
% 0.19/0.44 ($false = (rel_s5 @ sK11 @ sK1)) | ~spl0_44),
% 0.19/0.44 inference(avatar_component_clause,[],[f1306])).
% 0.19/0.44 thf(f1306,plain,(
% 0.19/0.44 spl0_44 <=> ($false = (rel_s5 @ sK11 @ sK1))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_44])])).
% 0.19/0.44 thf(f1352,plain,(
% 0.19/0.44 spl0_44 | spl0_45 | ~spl0_6 | ~spl0_39),
% 0.19/0.44 inference(avatar_split_clause,[],[f1337,f1085,f368,f1346,f1306])).
% 0.19/0.44 thf(f368,plain,(
% 0.19/0.44 spl0_6 <=> ((rel_s5 @ sK1 @ sK10) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.19/0.44 thf(f1085,plain,(
% 0.19/0.44 spl0_39 <=> ! [X0] : (($false = (rel_s5 @ sK11 @ X0)) | ((q @ X0) = $true))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_39])])).
% 0.19/0.44 thf(f1337,plain,(
% 0.19/0.44 ((q @ sK10) = $true) | ($false = (rel_s5 @ sK11 @ sK1)) | (~spl0_6 | ~spl0_39)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1327])).
% 0.19/0.44 thf(f1327,plain,(
% 0.19/0.44 ($false = $true) | ($false = (rel_s5 @ sK11 @ sK1)) | ((q @ sK10) = $true) | (~spl0_6 | ~spl0_39)),
% 0.19/0.44 inference(superposition,[],[f1013,f1086])).
% 0.19/0.44 thf(f1086,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (($false = (rel_s5 @ sK11 @ X0)) | ((q @ X0) = $true)) ) | ~spl0_39),
% 0.19/0.44 inference(avatar_component_clause,[],[f1085])).
% 0.19/0.44 thf(f1013,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (((rel_s5 @ X0 @ sK10) = $true) | ((rel_s5 @ X0 @ sK1) = $false)) ) | ~spl0_6),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1009])).
% 0.19/0.44 thf(f1009,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (((rel_s5 @ X0 @ sK10) = $true) | ($false = $true) | ((rel_s5 @ X0 @ sK1) = $false)) ) | ~spl0_6),
% 0.19/0.44 inference(superposition,[],[f170,f370])).
% 0.19/0.44 thf(f370,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK10) = $true) | ~spl0_6),
% 0.19/0.44 inference(avatar_component_clause,[],[f368])).
% 0.19/0.44 thf(f170,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s5 @ X3 @ X2)) | ($false = (rel_s5 @ X1 @ X3)) | ((rel_s5 @ X1 @ X2) = $true)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f169])).
% 0.19/0.44 thf(f169,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s5 @ X1 @ X2) = $true) | ($false = ((rel_s5 @ X3 @ X2) & (rel_s5 @ X1 @ X3)))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f168])).
% 0.19/0.44 thf(f168,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s5 @ X3 @ X2) & (rel_s5 @ X1 @ X3)) => (rel_s5 @ X1 @ X2)))) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f167])).
% 0.19/0.44 thf(f167,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ Y0 @ X2) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ X1 @ X2))) @ X3))) )),
% 0.19/0.44 inference(pi_clausification,[],[f166])).
% 0.19/0.44 thf(f166,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ Y0 @ X2) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ X1 @ X2)))) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f165])).
% 0.19/0.44 thf(f165,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ X1 @ Y1)) => (rel_s5 @ X1 @ Y0))))) @ X2) = $true)) )),
% 0.19/0.44 inference(pi_clausification,[],[f164])).
% 0.19/0.44 thf(f164,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ X1 @ Y1)) => (rel_s5 @ X1 @ Y0)))))) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f163])).
% 0.19/0.44 thf(f163,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y1) & (rel_s5 @ Y0 @ Y2)) => (rel_s5 @ Y0 @ Y1))))))) @ X1))) )),
% 0.19/0.44 inference(pi_clausification,[],[f162])).
% 0.19/0.44 thf(f162,plain,(
% 0.19/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y1) & (rel_s5 @ Y0 @ Y2)) => (rel_s5 @ Y0 @ Y1)))))))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f158])).
% 0.19/0.44 thf(f158,plain,(
% 0.19/0.44 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s5) = $true)),
% 0.19/0.44 inference(definition_unfolding,[],[f122,f129])).
% 0.19/0.44 thf(f129,plain,(
% 0.19/0.44 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f50])).
% 0.19/0.44 thf(f50,plain,(
% 0.19/0.44 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.19/0.44 inference(fool_elimination,[],[f49])).
% 0.19/0.44 thf(f49,plain,(
% 0.19/0.44 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))) = mtransitive)),
% 0.19/0.44 inference(rectify,[],[f21])).
% 0.19/0.44 thf(f21,axiom,(
% 0.19/0.44 ((^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.19/0.44 thf(f122,plain,(
% 0.19/0.44 ((mtransitive @ rel_s5) = $true)),
% 0.19/0.44 inference(cnf_transformation,[],[f70])).
% 0.19/0.44 thf(f70,plain,(
% 0.19/0.44 ((mtransitive @ rel_s5) = $true)),
% 0.19/0.44 inference(fool_elimination,[],[f69])).
% 0.19/0.44 thf(f69,plain,(
% 0.19/0.44 (mtransitive @ rel_s5)),
% 0.19/0.44 inference(rectify,[],[f35])).
% 0.19/0.44 thf(f35,axiom,(
% 0.19/0.44 (mtransitive @ rel_s5)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.19/0.44 thf(f1088,plain,(
% 0.19/0.44 spl0_39 | spl0_38 | ~spl0_3 | ~spl0_4),
% 0.19/0.44 inference(avatar_split_clause,[],[f1055,f358,f354,f1081,f1085])).
% 0.19/0.44 thf(f354,plain,(
% 0.19/0.44 spl0_3 <=> ! [X4,X3] : (($false = (p @ X3)) | ($false = (rel_s5 @ X3 @ X4)) | ($false = (rel_s5 @ sK1 @ X3)) | ((q @ X4) = $true))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.19/0.44 thf(f1055,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (($false = (rel_s5 @ sK11 @ X0)) | ((q @ X0) = $true) | ((p @ sK11) = $false)) ) | (~spl0_3 | ~spl0_4)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f1050])).
% 0.19/0.44 thf(f1050,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (((q @ X0) = $true) | ((p @ sK11) = $false) | ($false = $true) | ($false = (rel_s5 @ sK11 @ X0))) ) | (~spl0_3 | ~spl0_4)),
% 0.19/0.44 inference(superposition,[],[f360,f355])).
% 0.19/0.44 thf(f355,plain,(
% 0.19/0.44 ( ! [X3 : $i,X4 : $i] : (($false = (rel_s5 @ sK1 @ X3)) | ((q @ X4) = $true) | ($false = (rel_s5 @ X3 @ X4)) | ($false = (p @ X3))) ) | ~spl0_3),
% 0.19/0.44 inference(avatar_component_clause,[],[f354])).
% 0.19/0.44 thf(f998,plain,(
% 0.19/0.44 ~spl0_1 | ~spl0_12 | spl0_30),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f997])).
% 0.19/0.44 thf(f997,plain,(
% 0.19/0.44 $false | (~spl0_1 | ~spl0_12 | spl0_30)),
% 0.19/0.44 inference(subsumption_resolution,[],[f969,f669])).
% 0.19/0.44 thf(f669,plain,(
% 0.19/0.44 ($false != (p @ sK6)) | spl0_30),
% 0.19/0.44 inference(avatar_component_clause,[],[f668])).
% 0.19/0.44 thf(f668,plain,(
% 0.19/0.44 spl0_30 <=> ($false = (p @ sK6))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_30])])).
% 0.19/0.44 thf(f969,plain,(
% 0.19/0.44 ($false = (p @ sK6)) | (~spl0_1 | ~spl0_12)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f967])).
% 0.19/0.44 thf(f967,plain,(
% 0.19/0.44 ($false = (p @ sK6)) | ($false = $true) | (~spl0_1 | ~spl0_12)),
% 0.19/0.44 inference(superposition,[],[f400,f349])).
% 0.19/0.44 thf(f349,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1))) ) | ~spl0_1),
% 0.19/0.44 inference(avatar_component_clause,[],[f348])).
% 0.19/0.44 thf(f348,plain,(
% 0.19/0.44 spl0_1 <=> ! [X1] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1)))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.19/0.44 thf(f400,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK6) = $true) | ~spl0_12),
% 0.19/0.44 inference(avatar_component_clause,[],[f398])).
% 0.19/0.44 thf(f398,plain,(
% 0.19/0.44 spl0_12 <=> ((rel_s5 @ sK1 @ sK6) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_12])])).
% 0.19/0.44 thf(f996,plain,(
% 0.19/0.44 ~spl0_1 | ~spl0_8 | spl0_27),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f995])).
% 0.19/0.44 thf(f995,plain,(
% 0.19/0.44 $false | (~spl0_1 | ~spl0_8 | spl0_27)),
% 0.19/0.44 inference(subsumption_resolution,[],[f970,f657])).
% 0.19/0.44 thf(f657,plain,(
% 0.19/0.44 ((p @ sK2) != $false) | spl0_27),
% 0.19/0.44 inference(avatar_component_clause,[],[f656])).
% 0.19/0.44 thf(f656,plain,(
% 0.19/0.44 spl0_27 <=> ((p @ sK2) = $false)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_27])])).
% 0.19/0.44 thf(f970,plain,(
% 0.19/0.44 ((p @ sK2) = $false) | (~spl0_1 | ~spl0_8)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f954])).
% 0.19/0.44 thf(f954,plain,(
% 0.19/0.44 ((p @ sK2) = $false) | ($false = $true) | (~spl0_1 | ~spl0_8)),
% 0.19/0.44 inference(superposition,[],[f349,f380])).
% 0.19/0.44 thf(f380,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK2) = $true) | ~spl0_8),
% 0.19/0.44 inference(avatar_component_clause,[],[f378])).
% 0.19/0.44 thf(f378,plain,(
% 0.19/0.44 spl0_8 <=> ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.19/0.44 thf(f911,plain,(
% 0.19/0.44 ~spl0_2 | ~spl0_8 | ~spl0_22 | ~spl0_23),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f910])).
% 0.19/0.44 thf(f910,plain,(
% 0.19/0.44 $false | (~spl0_2 | ~spl0_8 | ~spl0_22 | ~spl0_23)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f906])).
% 0.19/0.44 thf(f906,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_2 | ~spl0_8 | ~spl0_22 | ~spl0_23)),
% 0.19/0.44 inference(superposition,[],[f867,f459])).
% 0.19/0.44 thf(f459,plain,(
% 0.19/0.44 ($false = (q @ sK4)) | ~spl0_23),
% 0.19/0.44 inference(avatar_component_clause,[],[f457])).
% 0.19/0.44 thf(f457,plain,(
% 0.19/0.44 spl0_23 <=> ($false = (q @ sK4))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_23])])).
% 0.19/0.44 thf(f867,plain,(
% 0.19/0.44 ($true = (q @ sK4)) | (~spl0_2 | ~spl0_8 | ~spl0_22)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f854])).
% 0.19/0.44 thf(f854,plain,(
% 0.19/0.44 ($false = $true) | ($true = (q @ sK4)) | (~spl0_2 | ~spl0_8 | ~spl0_22)),
% 0.19/0.44 inference(superposition,[],[f851,f352])).
% 0.19/0.44 thf(f352,plain,(
% 0.19/0.44 ( ! [X2 : $i] : (($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true)) ) | ~spl0_2),
% 0.19/0.44 inference(avatar_component_clause,[],[f351])).
% 0.19/0.44 thf(f351,plain,(
% 0.19/0.44 spl0_2 <=> ! [X2] : (((q @ X2) = $true) | ($false = (rel_s5 @ sK1 @ X2)))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.19/0.44 thf(f851,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK4) = $true) | (~spl0_8 | ~spl0_22)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f848])).
% 0.19/0.44 thf(f848,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK4) = $true) | ($false = $true) | (~spl0_8 | ~spl0_22)),
% 0.19/0.44 inference(superposition,[],[f176,f756])).
% 0.19/0.44 thf(f756,plain,(
% 0.19/0.44 ((rel_s5 @ sK4 @ sK1) = $true) | (~spl0_8 | ~spl0_22)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f746])).
% 0.19/0.44 thf(f746,plain,(
% 0.19/0.44 ($false = $true) | ((rel_s5 @ sK4 @ sK1) = $true) | (~spl0_8 | ~spl0_22)),
% 0.19/0.44 inference(superposition,[],[f735,f529])).
% 0.19/0.44 thf(f529,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (($false = (rel_s5 @ X0 @ sK2)) | ((rel_s5 @ X0 @ sK1) = $true)) ) | ~spl0_8),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f516])).
% 0.19/0.44 thf(f516,plain,(
% 0.19/0.44 ( ! [X0 : $i] : (($false = $true) | ($false = (rel_s5 @ X0 @ sK2)) | ((rel_s5 @ X0 @ sK1) = $true)) ) | ~spl0_8),
% 0.19/0.44 inference(superposition,[],[f494,f170])).
% 0.19/0.44 thf(f494,plain,(
% 0.19/0.44 ((rel_s5 @ sK2 @ sK1) = $true) | ~spl0_8),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f490])).
% 0.19/0.44 thf(f490,plain,(
% 0.19/0.44 ((rel_s5 @ sK2 @ sK1) = $true) | ($false = $true) | ~spl0_8),
% 0.19/0.44 inference(superposition,[],[f176,f380])).
% 0.19/0.44 thf(f735,plain,(
% 0.19/0.44 ($true = (rel_s5 @ sK4 @ sK2)) | ~spl0_22),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f731])).
% 0.19/0.44 thf(f731,plain,(
% 0.19/0.44 ($true = (rel_s5 @ sK4 @ sK2)) | ($false = $true) | ~spl0_22),
% 0.19/0.44 inference(superposition,[],[f454,f176])).
% 0.19/0.44 thf(f454,plain,(
% 0.19/0.44 ((rel_s5 @ sK2 @ sK4) = $true) | ~spl0_22),
% 0.19/0.44 inference(avatar_component_clause,[],[f452])).
% 0.19/0.44 thf(f452,plain,(
% 0.19/0.44 spl0_22 <=> ((rel_s5 @ sK2 @ sK4) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])).
% 0.19/0.44 thf(f826,plain,(
% 0.19/0.44 ~spl0_15 | ~spl0_30),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f825])).
% 0.19/0.44 thf(f825,plain,(
% 0.19/0.44 $false | (~spl0_15 | ~spl0_30)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f821])).
% 0.19/0.44 thf(f821,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_15 | ~spl0_30)),
% 0.19/0.44 inference(superposition,[],[f670,f416])).
% 0.19/0.44 thf(f416,plain,(
% 0.19/0.44 ($true = (p @ sK6)) | ~spl0_15),
% 0.19/0.44 inference(avatar_component_clause,[],[f414])).
% 0.19/0.44 thf(f414,plain,(
% 0.19/0.44 spl0_15 <=> ($true = (p @ sK6))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_15])])).
% 0.19/0.44 thf(f670,plain,(
% 0.19/0.44 ($false = (p @ sK6)) | ~spl0_30),
% 0.19/0.44 inference(avatar_component_clause,[],[f668])).
% 0.19/0.44 thf(f781,plain,(
% 0.19/0.44 ~spl0_9 | ~spl0_27),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f780])).
% 0.19/0.44 thf(f780,plain,(
% 0.19/0.44 $false | (~spl0_9 | ~spl0_27)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f777])).
% 0.19/0.44 thf(f777,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_9 | ~spl0_27)),
% 0.19/0.44 inference(superposition,[],[f385,f658])).
% 0.19/0.44 thf(f658,plain,(
% 0.19/0.44 ((p @ sK2) = $false) | ~spl0_27),
% 0.19/0.44 inference(avatar_component_clause,[],[f656])).
% 0.19/0.44 thf(f385,plain,(
% 0.19/0.44 ((p @ sK2) = $true) | ~spl0_9),
% 0.19/0.44 inference(avatar_component_clause,[],[f383])).
% 0.19/0.44 thf(f383,plain,(
% 0.19/0.44 spl0_9 <=> ((p @ sK2) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.19/0.44 thf(f617,plain,(
% 0.19/0.44 ~spl0_2 | ~spl0_8 | ~spl0_19 | ~spl0_20),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f616])).
% 0.19/0.44 thf(f616,plain,(
% 0.19/0.44 $false | (~spl0_2 | ~spl0_8 | ~spl0_19 | ~spl0_20)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f612])).
% 0.19/0.44 thf(f612,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_2 | ~spl0_8 | ~spl0_19 | ~spl0_20)),
% 0.19/0.44 inference(superposition,[],[f607,f443])).
% 0.19/0.44 thf(f443,plain,(
% 0.19/0.44 ($false = (q @ sK5)) | ~spl0_20),
% 0.19/0.44 inference(avatar_component_clause,[],[f441])).
% 0.19/0.44 thf(f441,plain,(
% 0.19/0.44 spl0_20 <=> ($false = (q @ sK5))),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])).
% 0.19/0.44 thf(f607,plain,(
% 0.19/0.44 ((q @ sK5) = $true) | (~spl0_2 | ~spl0_8 | ~spl0_19)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f603])).
% 0.19/0.44 thf(f603,plain,(
% 0.19/0.44 ((q @ sK5) = $true) | ($false = $true) | (~spl0_2 | ~spl0_8 | ~spl0_19)),
% 0.19/0.44 inference(superposition,[],[f352,f599])).
% 0.19/0.44 thf(f599,plain,(
% 0.19/0.44 ($true = (rel_s5 @ sK1 @ sK5)) | (~spl0_8 | ~spl0_19)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f593])).
% 0.19/0.44 thf(f593,plain,(
% 0.19/0.44 ($false = $true) | ($true = (rel_s5 @ sK1 @ sK5)) | (~spl0_8 | ~spl0_19)),
% 0.19/0.44 inference(superposition,[],[f589,f176])).
% 0.19/0.44 thf(f589,plain,(
% 0.19/0.44 ((rel_s5 @ sK5 @ sK1) = $true) | (~spl0_8 | ~spl0_19)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f574])).
% 0.19/0.44 thf(f574,plain,(
% 0.19/0.44 ((rel_s5 @ sK5 @ sK1) = $true) | ($false = $true) | (~spl0_8 | ~spl0_19)),
% 0.19/0.44 inference(superposition,[],[f529,f508])).
% 0.19/0.44 thf(f508,plain,(
% 0.19/0.44 ((rel_s5 @ sK5 @ sK2) = $true) | ~spl0_19),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f506])).
% 0.19/0.44 thf(f506,plain,(
% 0.19/0.44 ((rel_s5 @ sK5 @ sK2) = $true) | ($false = $true) | ~spl0_19),
% 0.19/0.44 inference(superposition,[],[f176,f438])).
% 0.19/0.44 thf(f438,plain,(
% 0.19/0.44 ((rel_s5 @ sK2 @ sK5) = $true) | ~spl0_19),
% 0.19/0.44 inference(avatar_component_clause,[],[f436])).
% 0.19/0.44 thf(f436,plain,(
% 0.19/0.44 spl0_19 <=> ((rel_s5 @ sK2 @ sK5) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])).
% 0.19/0.44 thf(f478,plain,(
% 0.19/0.44 ~spl0_2 | ~spl0_18 | ~spl0_21),
% 0.19/0.44 inference(avatar_contradiction_clause,[],[f477])).
% 0.19/0.44 thf(f477,plain,(
% 0.19/0.44 $false | (~spl0_2 | ~spl0_18 | ~spl0_21)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f473])).
% 0.19/0.44 thf(f473,plain,(
% 0.19/0.44 ($false = $true) | (~spl0_2 | ~spl0_18 | ~spl0_21)),
% 0.19/0.44 inference(superposition,[],[f470,f448])).
% 0.19/0.44 thf(f448,plain,(
% 0.19/0.44 ((q @ sK3) = $false) | ~spl0_21),
% 0.19/0.44 inference(avatar_component_clause,[],[f446])).
% 0.19/0.44 thf(f446,plain,(
% 0.19/0.44 spl0_21 <=> ((q @ sK3) = $false)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])).
% 0.19/0.44 thf(f470,plain,(
% 0.19/0.44 ((q @ sK3) = $true) | (~spl0_2 | ~spl0_18)),
% 0.19/0.44 inference(trivial_inequality_removal,[],[f466])).
% 0.19/0.44 thf(f466,plain,(
% 0.19/0.44 ($false = $true) | ((q @ sK3) = $true) | (~spl0_2 | ~spl0_18)),
% 0.19/0.44 inference(superposition,[],[f432,f352])).
% 0.19/0.44 thf(f432,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ~spl0_18),
% 0.19/0.44 inference(avatar_component_clause,[],[f430])).
% 0.19/0.44 thf(f430,plain,(
% 0.19/0.44 spl0_18 <=> ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.19/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_18])])).
% 0.19/0.44 thf(f460,plain,(
% 0.19/0.44 spl0_21 | spl0_23),
% 0.19/0.44 inference(avatar_split_clause,[],[f203,f457,f446])).
% 0.19/0.44 thf(f203,plain,(
% 0.19/0.44 ($false = (q @ sK4)) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f201])).
% 0.19/0.44 thf(f201,plain,(
% 0.19/0.44 ($false = ((q @ sK4) | (~ (rel_s5 @ sK2 @ sK4)))) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(beta_eta_normalization,[],[f200])).
% 0.19/0.44 thf(f200,plain,(
% 0.19/0.44 ((q @ sK3) = $false) | (((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK4) = $false)),
% 0.19/0.44 inference(sigma_clausification,[],[f199])).
% 0.19/0.44 thf(f199,plain,(
% 0.19/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f197])).
% 0.19/0.44 thf(f197,plain,(
% 0.19/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2)))) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f195])).
% 0.19/0.44 thf(f195,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2)))) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f193])).
% 0.19/0.44 thf(f193,plain,(
% 0.19/0.44 (((q @ sK3) | (~ (rel_s5 @ sK1 @ sK3))) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f192])).
% 0.19/0.44 thf(f192,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2)))) | ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK3))),
% 0.19/0.44 inference(sigma_clausification,[],[f191])).
% 0.19/0.44 thf(f191,plain,(
% 0.19/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f189])).
% 0.19/0.44 thf(f189,plain,(
% 0.19/0.44 (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f187])).
% 0.19/0.44 thf(f187,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f186])).
% 0.19/0.44 thf(f186,plain,(
% 0.19/0.44 ($false = ((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2)) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))))))),
% 0.19/0.44 inference(sigma_clausification,[],[f185])).
% 0.19/0.44 thf(f185,plain,(
% 0.19/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))))))),
% 0.19/0.44 inference(not_proxy_clausification,[],[f184])).
% 0.19/0.44 thf(f184,plain,(
% 0.19/0.44 ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f182])).
% 0.19/0.44 thf(f182,plain,(
% 0.19/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0))))))))) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f181])).
% 0.19/0.44 thf(f181,plain,(
% 0.19/0.44 ((~ ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0))))))))) = $true) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f180])).
% 0.19/0.44 thf(f180,plain,(
% 0.19/0.44 (((~ ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0))))))))) | (~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))))))) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f179])).
% 0.19/0.44 thf(f179,plain,(
% 0.19/0.44 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0))))))))) | (~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f178])).
% 0.19/0.44 thf(f178,plain,(
% 0.19/0.44 ($false = ((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (p @ Y1))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (p @ Y1))) | (~ (rel_s5 @ Y0 @ Y1))))))))))) @ sK1))),
% 0.19/0.44 inference(sigma_clausification,[],[f177])).
% 0.19/0.44 thf(f177,plain,(
% 0.19/0.44 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (p @ Y1))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (p @ Y1))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))) != $true)),
% 0.19/0.44 inference(beta_eta_normalization,[],[f160])).
% 0.19/0.44 thf(f160,plain,(
% 0.19/0.44 (((^[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]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ q)))) != $true)),
% 0.19/0.44 inference(definition_unfolding,[],[f134,f118,f151,f144,f116,f128,f144,f116,f144,f128,f144])).
% 0.19/0.44 thf(f128,plain,(
% 0.19/0.44 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f97])).
% 0.19/0.44 thf(f97,plain,(
% 0.19/0.44 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.44 inference(fool_elimination,[],[f96])).
% 0.19/0.44 thf(f96,plain,(
% 0.19/0.44 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.19/0.44 inference(rectify,[],[f3])).
% 0.19/0.44 thf(f3,axiom,(
% 0.19/0.44 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.19/0.44 thf(f116,plain,(
% 0.19/0.44 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f101])).
% 0.19/0.44 thf(f101,plain,(
% 0.19/0.44 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.19/0.44 inference(fool_elimination,[],[f100])).
% 0.19/0.44 thf(f100,plain,(
% 0.19/0.44 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.19/0.44 inference(rectify,[],[f4])).
% 0.19/0.44 thf(f4,axiom,(
% 0.19/0.44 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.19/0.44 thf(f144,plain,(
% 0.19/0.44 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f54])).
% 0.19/0.44 thf(f54,plain,(
% 0.19/0.44 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.19/0.44 inference(fool_elimination,[],[f53])).
% 0.19/0.44 thf(f53,plain,(
% 0.19/0.44 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))) = mbox_s5)),
% 0.19/0.44 inference(rectify,[],[f32])).
% 0.19/0.44 thf(f32,axiom,(
% 0.19/0.44 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))) = mbox_s5)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.19/0.44 thf(f151,plain,(
% 0.19/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.19/0.44 inference(definition_unfolding,[],[f141,f148,f149,f149])).
% 0.19/0.44 thf(f149,plain,(
% 0.19/0.44 (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)))))),
% 0.19/0.44 inference(definition_unfolding,[],[f123,f116,f128])).
% 0.19/0.44 thf(f123,plain,(
% 0.19/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.44 inference(cnf_transformation,[],[f91])).
% 0.19/0.44 thf(f91,plain,(
% 0.19/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.44 inference(fool_elimination,[],[f90])).
% 0.19/0.44 thf(f90,plain,(
% 0.19/0.44 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.19/0.44 inference(rectify,[],[f6])).
% 0.19/0.44 thf(f6,axiom,(
% 0.19/0.44 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.19/0.44 thf(f148,plain,(
% 0.19/0.44 (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)))))))),
% 0.19/0.44 inference(definition_unfolding,[],[f114,f128,f116,f128,f128])).
% 0.19/0.44 thf(f114,plain,(
% 0.19/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f89])).
% 0.19/0.44 thf(f89,plain,(
% 0.19/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.19/0.44 inference(fool_elimination,[],[f88])).
% 0.19/0.44 thf(f88,plain,(
% 0.19/0.44 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.19/0.44 inference(rectify,[],[f5])).
% 0.19/0.44 thf(f5,axiom,(
% 0.19/0.44 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.19/0.44 thf(f141,plain,(
% 0.19/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.19/0.44 inference(cnf_transformation,[],[f62])).
% 0.19/0.44 thf(f62,plain,(
% 0.19/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.19/0.44 inference(fool_elimination,[],[f61])).
% 0.19/0.44 thf(f61,plain,(
% 0.19/0.44 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.19/0.44 inference(rectify,[],[f8])).
% 0.19/0.44 thf(f8,axiom,(
% 0.19/0.44 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.19/0.44 thf(f118,plain,(
% 0.19/0.44 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.44 inference(cnf_transformation,[],[f85])).
% 0.19/0.44 thf(f85,plain,(
% 0.19/0.44 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.44 inference(fool_elimination,[],[f84])).
% 0.19/0.44 thf(f84,plain,(
% 0.19/0.44 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.19/0.44 inference(rectify,[],[f28])).
% 0.19/0.44 thf(f28,axiom,(
% 0.19/0.44 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.19/0.44 thf(f134,plain,(
% 0.19/0.44 ((mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mbox_s5 @ q))) @ (mor @ (mbox_s5 @ (mnot @ p)) @ (mbox_s5 @ q)))) != $true)),
% 0.19/0.44 inference(cnf_transformation,[],[f110])).
% 0.19/0.44 thf(f110,plain,(
% 0.19/0.44 ((mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mbox_s5 @ q))) @ (mor @ (mbox_s5 @ (mnot @ p)) @ (mbox_s5 @ q)))) != $true)),
% 0.19/0.44 inference(flattening,[],[f109])).
% 0.19/0.44 thf(f109,plain,(
% 0.19/0.44 ~((mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mbox_s5 @ q))) @ (mor @ (mbox_s5 @ (mnot @ p)) @ (mbox_s5 @ q)))) = $true)),
% 0.19/0.44 inference(fool_elimination,[],[f108])).
% 0.19/0.44 thf(f108,plain,(
% 0.19/0.44 ~(mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mbox_s5 @ q))) @ (mor @ (mbox_s5 @ (mnot @ p)) @ (mbox_s5 @ q))))),
% 0.19/0.44 inference(rectify,[],[f38])).
% 0.19/0.44 thf(f38,negated_conjecture,(
% 0.19/0.44 ~(mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mbox_s5 @ q))) @ (mor @ (mbox_s5 @ (mnot @ p)) @ (mbox_s5 @ q))))),
% 0.19/0.44 inference(negated_conjecture,[],[f37])).
% 0.19/0.44 thf(f37,conjecture,(
% 0.19/0.44 (mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mbox_s5 @ q))) @ (mor @ (mbox_s5 @ (mnot @ p)) @ (mbox_s5 @ q))))),
% 0.19/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.19/0.44 thf(f455,plain,(
% 0.19/0.44 spl0_22 | spl0_21),
% 0.19/0.44 inference(avatar_split_clause,[],[f204,f446,f452])).
% 0.19/0.44 thf(f204,plain,(
% 0.19/0.44 ((q @ sK3) = $false) | ((rel_s5 @ sK2 @ sK4) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f202])).
% 0.19/0.44 thf(f202,plain,(
% 0.19/0.44 ((q @ sK3) = $false) | ($false = (~ (rel_s5 @ sK2 @ sK4)))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f201])).
% 0.19/0.44 thf(f449,plain,(
% 0.19/0.44 spl0_21 | spl0_8),
% 0.19/0.44 inference(avatar_split_clause,[],[f206,f378,f446])).
% 0.19/0.44 thf(f206,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK2) = $true) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f196])).
% 0.19/0.44 thf(f196,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK1 @ sK2))) | ((q @ sK3) = $false)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f195])).
% 0.19/0.44 thf(f444,plain,(
% 0.19/0.44 spl0_18 | spl0_20),
% 0.19/0.44 inference(avatar_split_clause,[],[f215,f441,f430])).
% 0.19/0.44 thf(f215,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ($false = (q @ sK5))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f213])).
% 0.19/0.44 thf(f213,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ($false = ((q @ sK5) | (~ (rel_s5 @ sK2 @ sK5))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f212])).
% 0.19/0.44 thf(f212,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK5))),
% 0.19/0.44 inference(sigma_clausification,[],[f211])).
% 0.19/0.44 thf(f211,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f209])).
% 0.19/0.44 thf(f209,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f207])).
% 0.19/0.44 thf(f207,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2)))) | ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f194])).
% 0.19/0.44 thf(f194,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK1 @ sK3))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f193])).
% 0.19/0.44 thf(f439,plain,(
% 0.19/0.44 spl0_18 | spl0_19),
% 0.19/0.44 inference(avatar_split_clause,[],[f216,f436,f430])).
% 0.19/0.44 thf(f216,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ((rel_s5 @ sK2 @ sK5) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f214])).
% 0.19/0.44 thf(f214,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK2 @ sK5))) | ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f213])).
% 0.19/0.44 thf(f433,plain,(
% 0.19/0.44 spl0_18 | spl0_8),
% 0.19/0.44 inference(avatar_split_clause,[],[f218,f378,f430])).
% 0.19/0.44 thf(f218,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK3) = $true) | ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f208])).
% 0.19/0.44 thf(f208,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK1 @ sK2))) | ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f207])).
% 0.19/0.44 thf(f418,plain,(
% 0.19/0.44 spl0_9 | spl0_15),
% 0.19/0.44 inference(avatar_split_clause,[],[f235,f414,f383])).
% 0.19/0.44 thf(f235,plain,(
% 0.19/0.44 ((p @ sK2) = $true) | ($true = (p @ sK6))),
% 0.19/0.44 inference(not_proxy_clausification,[],[f234])).
% 0.19/0.44 thf(f234,plain,(
% 0.19/0.44 ($false = (~ (p @ sK2))) | ($true = (p @ sK6))),
% 0.19/0.44 inference(not_proxy_clausification,[],[f225])).
% 0.19/0.44 thf(f225,plain,(
% 0.19/0.44 ($false = (~ (p @ sK6))) | ($false = (~ (p @ sK2)))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f224])).
% 0.19/0.44 thf(f224,plain,(
% 0.19/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2)))) | ($false = (~ (p @ sK6)))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f222])).
% 0.19/0.44 thf(f222,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2)))) | ($false = (~ (p @ sK6)))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f220])).
% 0.19/0.44 thf(f220,plain,(
% 0.19/0.44 (((~ (p @ sK6)) | (~ (rel_s5 @ sK1 @ sK6))) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(beta_eta_normalization,[],[f219])).
% 0.19/0.44 thf(f219,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2)))) | (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK6) = $false)),
% 0.19/0.44 inference(sigma_clausification,[],[f190])).
% 0.19/0.44 thf(f190,plain,(
% 0.19/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f189])).
% 0.19/0.44 thf(f417,plain,(
% 0.19/0.44 spl0_8 | spl0_15),
% 0.19/0.44 inference(avatar_split_clause,[],[f237,f414,f378])).
% 0.19/0.44 thf(f237,plain,(
% 0.19/0.44 ($true = (p @ sK6)) | ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f236])).
% 0.19/0.44 thf(f236,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK1 @ sK2))) | ($true = (p @ sK6))),
% 0.19/0.44 inference(not_proxy_clausification,[],[f223])).
% 0.19/0.44 thf(f223,plain,(
% 0.19/0.44 ($false = (~ (p @ sK6))) | ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f222])).
% 0.19/0.44 thf(f402,plain,(
% 0.19/0.44 spl0_12 | spl0_9),
% 0.19/0.44 inference(avatar_split_clause,[],[f248,f383,f398])).
% 0.19/0.44 thf(f248,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK6) = $true) | ((p @ sK2) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f241])).
% 0.19/0.44 thf(f241,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK6) = $true) | ($false = (~ (p @ sK2)))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f240])).
% 0.19/0.44 thf(f240,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK6) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f238])).
% 0.19/0.44 thf(f238,plain,(
% 0.19/0.44 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2)))) | ((rel_s5 @ sK1 @ sK6) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f221])).
% 0.19/0.44 thf(f221,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK1 @ sK6))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ (p @ sK2))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f220])).
% 0.19/0.44 thf(f401,plain,(
% 0.19/0.44 spl0_8 | spl0_12),
% 0.19/0.44 inference(avatar_split_clause,[],[f249,f398,f378])).
% 0.19/0.44 thf(f249,plain,(
% 0.19/0.44 ((rel_s5 @ sK1 @ sK2) = $true) | ((rel_s5 @ sK1 @ sK6) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f239])).
% 0.19/0.44 thf(f239,plain,(
% 0.19/0.44 ($false = (~ (rel_s5 @ sK1 @ sK2))) | ((rel_s5 @ sK1 @ sK6) = $true)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f238])).
% 0.19/0.44 thf(f376,plain,(
% 0.19/0.44 spl0_2 | spl0_7 | spl0_1),
% 0.19/0.44 inference(avatar_split_clause,[],[f323,f348,f373,f351])).
% 0.19/0.44 thf(f323,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (p @ X1)) | ((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ((q @ sK10) = $false) | ($false = (rel_s5 @ sK1 @ X2))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f321])).
% 0.19/0.44 thf(f321,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = ((q @ sK10) | (~ (rel_s5 @ sK1 @ sK10))))) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f320])).
% 0.19/0.44 thf(f320,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X2)) | ($false = (p @ X1)) | ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK10)) | ((rel_s5 @ sK1 @ X1) = $false) | ((q @ X2) = $true)) )),
% 0.19/0.44 inference(sigma_clausification,[],[f319])).
% 0.19/0.44 thf(f319,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) | ($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f317])).
% 0.19/0.44 thf(f317,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1)) | (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false) | ((q @ X2) = $true) | ($false = (rel_s5 @ sK1 @ X2))) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f316])).
% 0.19/0.44 thf(f316,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((q @ X2) = $true) | ($false = (p @ X1)) | ((rel_s5 @ sK1 @ X1) = $false) | ($true = (~ (rel_s5 @ sK1 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f315])).
% 0.19/0.44 thf(f315,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : ((((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f313])).
% 0.19/0.44 thf(f313,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) | (((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f312])).
% 0.19/0.44 thf(f312,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(pi_clausification,[],[f311])).
% 0.19/0.44 thf(f311,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ($false = (p @ X1)) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f310])).
% 0.19/0.44 thf(f310,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((~ (rel_s5 @ sK1 @ X1)) = $true) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) | ($false = (p @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f309])).
% 0.19/0.44 thf(f309,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ($false = (p @ X1)) | ((~ (rel_s5 @ sK1 @ X1)) = $true)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f308])).
% 0.19/0.44 thf(f308,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ((~ (rel_s5 @ sK1 @ X1)) = $true) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f307])).
% 0.19/0.44 thf(f307,plain,(
% 0.19/0.44 ( ! [X1 : $i] : ((((~ (p @ X1)) | (~ (rel_s5 @ sK1 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f306])).
% 0.19/0.44 thf(f306,plain,(
% 0.19/0.44 ( ! [X1 : $i] : (((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true) | (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))) @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true)) )),
% 0.19/0.44 inference(pi_clausification,[],[f305])).
% 0.19/0.44 thf(f305,plain,(
% 0.19/0.44 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f304])).
% 0.19/0.44 thf(f304,plain,(
% 0.19/0.44 (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) = $true) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)),
% 0.19/0.44 inference(not_proxy_clausification,[],[f183])).
% 0.19/0.44 thf(f183,plain,(
% 0.19/0.44 ($false = (~ ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))))) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $true)),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f182])).
% 0.19/0.44 thf(f371,plain,(
% 0.19/0.44 spl0_1 | spl0_2 | spl0_6),
% 0.19/0.44 inference(avatar_split_clause,[],[f324,f368,f351,f348])).
% 0.19/0.44 thf(f324,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (p @ X1)) | ((rel_s5 @ sK1 @ sK10) = $true) | ((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (rel_s5 @ sK1 @ X2))) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f322])).
% 0.19/0.44 thf(f322,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (~ (rel_s5 @ sK1 @ sK10))) | ((rel_s5 @ sK1 @ X1) = $false) | ((q @ X2) = $true) | ($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f321])).
% 0.19/0.44 thf(f366,plain,(
% 0.19/0.44 spl0_5 | spl0_1 | spl0_2),
% 0.19/0.44 inference(avatar_split_clause,[],[f329,f351,f348,f363])).
% 0.19/0.44 thf(f329,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X2)) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ((q @ X2) = $true) | ((p @ sK11) = $true)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f328])).
% 0.19/0.44 thf(f328,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (p @ X1)) | ($false = (~ (p @ sK11))) | ($false = (rel_s5 @ sK1 @ X2)) | ((rel_s5 @ sK1 @ X1) = $false) | ((q @ X2) = $true)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f326])).
% 0.19/0.44 thf(f326,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = ((~ (p @ sK11)) | (~ (rel_s5 @ sK1 @ sK11)))) | ($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f325])).
% 0.19/0.44 thf(f325,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((q @ X2) = $true) | ($false = ((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK11)) | ($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2)) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.19/0.44 inference(sigma_clausification,[],[f318])).
% 0.19/0.44 thf(f318,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK1 @ Y0)))))) | ($false = (rel_s5 @ sK1 @ X2))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f317])).
% 0.19/0.44 thf(f361,plain,(
% 0.19/0.44 spl0_1 | spl0_2 | spl0_4),
% 0.19/0.44 inference(avatar_split_clause,[],[f330,f358,f351,f348])).
% 0.19/0.44 thf(f330,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = (rel_s5 @ sK1 @ X2)) | ((rel_s5 @ sK1 @ sK11) = $true) | ($false = (p @ X1)) | ((q @ X2) = $true)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f327])).
% 0.19/0.44 thf(f327,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ($false = (~ (rel_s5 @ sK1 @ sK11)))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f326])).
% 0.19/0.44 thf(f356,plain,(
% 0.19/0.44 spl0_1 | spl0_2 | spl0_3),
% 0.19/0.44 inference(avatar_split_clause,[],[f343,f354,f351,f348])).
% 0.19/0.44 thf(f343,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((q @ X2) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X3)) | ((q @ X4) = $true) | ($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X3)) | ($false = (rel_s5 @ sK1 @ X2)) | ($false = (rel_s5 @ X3 @ X4))) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f342])).
% 0.19/0.44 thf(f342,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2)) | ((q @ X4) = $true) | ($false = (rel_s5 @ sK1 @ X3)) | ((rel_s5 @ sK1 @ X1) = $false) | ((~ (rel_s5 @ X3 @ X4)) = $true) | ((q @ X2) = $true) | ($false = (p @ X3))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f341])).
% 0.19/0.44 thf(f341,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (p @ X3)) | (((q @ X4) | (~ (rel_s5 @ X3 @ X4))) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (rel_s5 @ sK1 @ X3)) | ($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f340])).
% 0.19/0.44 thf(f340,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (rel_s5 @ sK1 @ X2)) | (((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0)))) @ X4) = $true) | ($false = (p @ X3)) | ($false = (rel_s5 @ sK1 @ X3)) | ((rel_s5 @ sK1 @ X1) = $false) | ((q @ X2) = $true) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(pi_clausification,[],[f339])).
% 0.19/0.44 thf(f339,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ($false = (rel_s5 @ sK1 @ X2)) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) = $true) | ($false = (p @ X3)) | ((q @ X2) = $true) | ($false = (rel_s5 @ sK1 @ X3))) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f338])).
% 0.19/0.44 thf(f338,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s5 @ sK1 @ X2)) | ((rel_s5 @ sK1 @ X1) = $false) | ((~ (p @ X3)) = $true) | ($false = (rel_s5 @ sK1 @ X3)) | ($false = (p @ X1)) | ((q @ X2) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) = $true)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f337])).
% 0.19/0.44 thf(f337,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (rel_s5 @ sK1 @ X3)) = $true) | ((~ (p @ X3)) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | ($false = (rel_s5 @ sK1 @ X2)) | ((q @ X2) = $true) | ($false = (p @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) = $true)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f336])).
% 0.19/0.44 thf(f336,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((q @ X2) = $true) | ($false = (rel_s5 @ sK1 @ X2)) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) | (~ (p @ X3)))) | ((rel_s5 @ sK1 @ X1) = $false) | ((~ (rel_s5 @ sK1 @ X3)) = $true) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f335])).
% 0.19/0.44 thf(f335,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p @ X1)) | ((q @ X2) = $true) | ($true = (~ (rel_s5 @ sK1 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) | (~ (p @ X3)))) | ((~ (rel_s5 @ sK1 @ X3)) = $true) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f334])).
% 0.19/0.44 thf(f334,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) | (~ (p @ X3)))) | ($false = (p @ X1)) | ((~ (rel_s5 @ sK1 @ X3)) = $true) | ((rel_s5 @ sK1 @ X1) = $false)) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f333])).
% 0.19/0.44 thf(f333,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p @ X1)) | ((((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ X3 @ Y0))))) | (~ (p @ X3))) | (~ (rel_s5 @ sK1 @ X3))) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | (((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true)) )),
% 0.19/0.44 inference(beta_eta_normalization,[],[f332])).
% 0.19/0.44 thf(f332,plain,(
% 0.19/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0)))) @ X3) = $true) | ((rel_s5 @ sK1 @ X1) = $false) | (((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(pi_clausification,[],[f331])).
% 0.19/0.44 thf(f331,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ($false = (p @ X1)) | (((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true)) )),
% 0.19/0.44 inference(not_proxy_clausification,[],[f314])).
% 0.19/0.44 thf(f314,plain,(
% 0.19/0.44 ( ! [X2 : $i,X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (p @ Y0))) | (~ (rel_s5 @ sK1 @ Y0))))))) | ((rel_s5 @ sK1 @ X1) = $false) | (((q @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | ($false = (p @ X1))) )),
% 0.19/0.44 inference(binary_proxy_clausification,[],[f313])).
% 0.19/0.44 % SZS output end Proof for theBenchmark
% 0.19/0.44 % (15823)------------------------------
% 0.19/0.44 % (15823)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (15823)Termination reason: Refutation
% 0.19/0.44
% 0.19/0.44 % (15823)Memory used [KB]: 6396
% 0.19/0.44 % (15823)Time elapsed: 0.070 s
% 0.19/0.44 % (15823)Instructions burned: 90 (million)
% 0.19/0.44 % (15823)------------------------------
% 0.19/0.44 % (15823)------------------------------
% 0.19/0.44 % (15822)Success in time 0.087 s
% 0.19/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------