TSTP Solution File: SET019^4 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n009.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 03:07:49 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SET019^4 : TPTP v8.2.0. Released v8.1.0.
% 0.02/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.10/0.30 % Computer : n009.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 20 11:23:37 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 This is a TH0_THM_EQU_NAR problem
% 0.10/0.30 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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.32 % (22464)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)
% 0.14/0.32 % (22463)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)
% 0.14/0.32 % (22465)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.32 % (22468)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.32 % (22462)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.32 % (22465)Instruction limit reached!
% 0.14/0.32 % (22465)------------------------------
% 0.14/0.32 % (22465)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22465)Termination reason: Unknown
% 0.14/0.32 % (22465)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (22465)Memory used [KB]: 1023
% 0.14/0.32 % (22465)Time elapsed: 0.002 s
% 0.14/0.32 % (22465)Instructions burned: 2 (million)
% 0.14/0.32 % (22465)------------------------------
% 0.14/0.32 % (22465)------------------------------
% 0.14/0.32 % (22469)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)
% 0.14/0.32 % (22467)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)
% 0.14/0.32 % (22466)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)
% 0.14/0.32 % (22463)Instruction limit reached!
% 0.14/0.32 % (22463)------------------------------
% 0.14/0.32 % (22463)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22463)Termination reason: Unknown
% 0.14/0.32 % (22463)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (22463)Memory used [KB]: 1023
% 0.14/0.32 % (22463)Time elapsed: 0.003 s
% 0.14/0.32 % (22463)Instructions burned: 4 (million)
% 0.14/0.32 % (22463)------------------------------
% 0.14/0.32 % (22463)------------------------------
% 0.14/0.32 % (22469)Instruction limit reached!
% 0.14/0.32 % (22469)------------------------------
% 0.14/0.32 % (22469)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22469)Termination reason: Unknown
% 0.14/0.32 % (22469)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (22469)Memory used [KB]: 1023
% 0.14/0.32 % (22469)Time elapsed: 0.003 s
% 0.14/0.32 % (22469)Instructions burned: 4 (million)
% 0.14/0.32 % (22466)Instruction limit reached!
% 0.14/0.32 % (22466)------------------------------
% 0.14/0.32 % (22466)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22466)Termination reason: Unknown
% 0.14/0.32 % (22466)Termination phase: shuffling
% 0.14/0.32
% 0.14/0.32 % (22466)Memory used [KB]: 1023
% 0.14/0.32 % (22466)Time elapsed: 0.003 s
% 0.14/0.32 % (22466)Instructions burned: 3 (million)
% 0.14/0.32 % (22466)------------------------------
% 0.14/0.32 % (22466)------------------------------
% 0.14/0.32 % (22469)------------------------------
% 0.14/0.32 % (22469)------------------------------
% 0.14/0.32 % (22468)Instruction limit reached!
% 0.14/0.32 % (22468)------------------------------
% 0.14/0.32 % (22468)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22468)Termination reason: Unknown
% 0.14/0.32 % (22468)Termination phase: Property scanning
% 0.14/0.32
% 0.14/0.32 % (22468)Memory used [KB]: 1151
% 0.14/0.32 % (22468)Time elapsed: 0.008 s
% 0.14/0.32 % (22468)Instructions burned: 18 (million)
% 0.14/0.32 % (22468)------------------------------
% 0.14/0.32 % (22468)------------------------------
% 0.14/0.32 % (22467)Refutation not found, incomplete strategy
% 0.14/0.32 % (22467)------------------------------
% 0.14/0.32 % (22467)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.32 % (22467)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.32
% 0.14/0.32
% 0.14/0.32 % (22467)Memory used [KB]: 5628
% 0.14/0.32 % (22467)Time elapsed: 0.007 s
% 0.14/0.32 % (22467)Instructions burned: 13 (million)
% 0.14/0.32 % (22467)------------------------------
% 0.14/0.32 % (22467)------------------------------
% 0.14/0.33 % (22464)Instruction limit reached!
% 0.14/0.33 % (22464)------------------------------
% 0.14/0.33 % (22464)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22464)Termination reason: Unknown
% 0.14/0.33 % (22464)Termination phase: Saturation
% 0.14/0.33
% 0.14/0.33 % (22464)Memory used [KB]: 5756
% 0.14/0.33 % (22464)Time elapsed: 0.012 s
% 0.14/0.33 % (22464)Instructions burned: 29 (million)
% 0.14/0.33 % (22464)------------------------------
% 0.14/0.33 % (22464)------------------------------
% 0.14/0.33 % (22470)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)
% 0.14/0.33 % (22471)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)
% 0.14/0.33 % (22472)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)
% 0.14/0.33 % (22473)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)
% 0.14/0.33 % (22472)Instruction limit reached!
% 0.14/0.33 % (22472)------------------------------
% 0.14/0.33 % (22472)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.33 % (22472)Termination reason: Unknown
% 0.14/0.33 % (22472)Termination phase: shuffling
% 0.14/0.33
% 0.14/0.33 % (22472)Memory used [KB]: 1023
% 0.14/0.33 % (22472)Time elapsed: 0.003 s
% 0.14/0.33 % (22472)Instructions burned: 5 (million)
% 0.14/0.33 % (22472)------------------------------
% 0.14/0.33 % (22472)------------------------------
% 0.14/0.34 % (22474)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.34 % (22471)Instruction limit reached!
% 0.14/0.34 % (22471)------------------------------
% 0.14/0.34 % (22471)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22471)Termination reason: Unknown
% 0.14/0.34 % (22471)Termination phase: Function definition elimination
% 0.14/0.34
% 0.14/0.34 % (22471)Memory used [KB]: 1151
% 0.14/0.34 % (22471)Time elapsed: 0.007 s
% 0.14/0.34 % (22471)Instructions burned: 16 (million)
% 0.14/0.34 % (22471)------------------------------
% 0.14/0.34 % (22471)------------------------------
% 0.14/0.34 % (22475)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.34 % (22474)Instruction limit reached!
% 0.14/0.34 % (22474)------------------------------
% 0.14/0.34 % (22474)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22474)Termination reason: Unknown
% 0.14/0.34 % (22474)Termination phase: shuffling
% 0.14/0.34
% 0.14/0.34 % (22474)Memory used [KB]: 1151
% 0.14/0.34 % (22474)Time elapsed: 0.004 s
% 0.14/0.34 % (22474)Instructions burned: 8 (million)
% 0.14/0.34 % (22474)------------------------------
% 0.14/0.34 % (22474)------------------------------
% 0.14/0.34 % (22476)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)
% 0.14/0.34 % (22476)Instruction limit reached!
% 0.14/0.34 % (22476)------------------------------
% 0.14/0.34 % (22476)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22476)Termination reason: Unknown
% 0.14/0.34 % (22476)Termination phase: shuffling
% 0.14/0.34
% 0.14/0.34 % (22476)Memory used [KB]: 1023
% 0.14/0.34 % (22476)Time elapsed: 0.003 s
% 0.14/0.34 % (22476)Instructions burned: 5 (million)
% 0.14/0.34 % (22476)------------------------------
% 0.14/0.34 % (22476)------------------------------
% 0.14/0.34 % (22470)Instruction limit reached!
% 0.14/0.34 % (22470)------------------------------
% 0.14/0.34 % (22470)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22470)Termination reason: Unknown
% 0.14/0.34 % (22470)Termination phase: Saturation
% 0.14/0.34
% 0.14/0.34 % (22470)Memory used [KB]: 5884
% 0.14/0.34 % (22470)Time elapsed: 0.015 s
% 0.14/0.34 % (22470)Instructions burned: 38 (million)
% 0.14/0.34 % (22470)------------------------------
% 0.14/0.34 % (22470)------------------------------
% 0.14/0.34 % (22475)Instruction limit reached!
% 0.14/0.34 % (22475)------------------------------
% 0.14/0.34 % (22475)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.34 % (22475)Termination reason: Unknown
% 0.14/0.34 % (22475)Termination phase: Function definition elimination
% 0.14/0.34
% 0.14/0.34 % (22475)Memory used [KB]: 1151
% 0.14/0.34 % (22475)Time elapsed: 0.008 s
% 0.14/0.34 % (22475)Instructions burned: 16 (million)
% 0.14/0.34 % (22475)------------------------------
% 0.14/0.34 % (22475)------------------------------
% 0.14/0.34 % (22477)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)
% 0.14/0.35 % (22477)Instruction limit reached!
% 0.14/0.35 % (22477)------------------------------
% 0.14/0.35 % (22477)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22477)Termination reason: Unknown
% 0.14/0.35 % (22477)Termination phase: shuffling
% 0.14/0.35
% 0.14/0.35 % (22477)Memory used [KB]: 1023
% 0.14/0.35 % (22477)Time elapsed: 0.003 s
% 0.14/0.35 % (22477)Instructions burned: 5 (million)
% 0.14/0.35 % (22477)------------------------------
% 0.14/0.35 % (22477)------------------------------
% 0.14/0.35 % (22478)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)
% 0.14/0.35 % (22479)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)
% 0.14/0.35 % (22478)Instruction limit reached!
% 0.14/0.35 % (22478)------------------------------
% 0.14/0.35 % (22478)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22478)Termination reason: Unknown
% 0.14/0.35 % (22478)Termination phase: shuffling
% 0.14/0.35
% 0.14/0.35 % (22478)Memory used [KB]: 1151
% 0.14/0.35 % (22478)Time elapsed: 0.004 s
% 0.14/0.35 % (22478)Instructions burned: 8 (million)
% 0.14/0.35 % (22478)------------------------------
% 0.14/0.35 % (22478)------------------------------
% 0.14/0.35 % (22479)Instruction limit reached!
% 0.14/0.35 % (22479)------------------------------
% 0.14/0.35 % (22479)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22479)Termination reason: Unknown
% 0.14/0.35 % (22479)Termination phase: shuffling
% 0.14/0.35
% 0.14/0.35 % (22479)Memory used [KB]: 1023
% 0.14/0.35 % (22479)Time elapsed: 0.003 s
% 0.14/0.35 % (22479)Instructions burned: 5 (million)
% 0.14/0.35 % (22479)------------------------------
% 0.14/0.35 % (22479)------------------------------
% 0.14/0.35 % (22480)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.35 % (22480)Instruction limit reached!
% 0.14/0.35 % (22480)------------------------------
% 0.14/0.35 % (22480)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.35 % (22480)Termination reason: Unknown
% 0.14/0.35 % (22480)Termination phase: shuffling
% 0.14/0.35
% 0.14/0.35 % (22480)Memory used [KB]: 1023
% 0.14/0.35 % (22480)Time elapsed: 0.003 s
% 0.14/0.35 % (22480)Instructions burned: 5 (million)
% 0.14/0.35 % (22480)------------------------------
% 0.14/0.35 % (22480)------------------------------
% 0.14/0.35 % (22481)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)
% 0.14/0.36 % (22482)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.14/0.36 % (22483)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.14/0.36 % (22483)Instruction limit reached!
% 0.14/0.36 % (22483)------------------------------
% 0.14/0.36 % (22483)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (22483)Termination reason: Unknown
% 0.14/0.36 % (22483)Termination phase: shuffling
% 0.14/0.36
% 0.14/0.36 % (22483)Memory used [KB]: 1151
% 0.14/0.36 % (22483)Time elapsed: 0.004 s
% 0.14/0.36 % (22483)Instructions burned: 8 (million)
% 0.14/0.36 % (22483)------------------------------
% 0.14/0.36 % (22483)------------------------------
% 0.14/0.36 % (22481)Instruction limit reached!
% 0.14/0.36 % (22481)------------------------------
% 0.14/0.36 % (22481)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (22481)Termination reason: Unknown
% 0.14/0.36 % (22481)Termination phase: Saturation
% 0.14/0.36
% 0.14/0.36 % (22481)Memory used [KB]: 5628
% 0.14/0.36 % (22481)Time elapsed: 0.008 s
% 0.14/0.36 % (22481)Instructions burned: 19 (million)
% 0.14/0.36 % (22481)------------------------------
% 0.14/0.36 % (22481)------------------------------
% 0.14/0.36 % (22484)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)
% 0.14/0.36 % (22485)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)
% 0.14/0.37 % (22486)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.14/0.37 % (22486)Instruction limit reached!
% 0.14/0.37 % (22486)------------------------------
% 0.14/0.37 % (22486)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22486)Termination reason: Unknown
% 0.14/0.37 % (22486)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (22486)Memory used [KB]: 1023
% 0.14/0.37 % (22486)Time elapsed: 0.003 s
% 0.14/0.37 % (22486)Instructions burned: 5 (million)
% 0.14/0.37 % (22486)------------------------------
% 0.14/0.37 % (22486)------------------------------
% 0.14/0.37 % (22484)Refutation not found, incomplete strategy
% 0.14/0.37 % (22484)------------------------------
% 0.14/0.37 % (22484)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22484)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (22484)Memory used [KB]: 5628
% 0.14/0.37 % (22484)Time elapsed: 0.030 s
% 0.14/0.37 % (22484)Instructions burned: 17 (million)
% 0.14/0.37 % (22484)------------------------------
% 0.14/0.37 % (22484)------------------------------
% 0.14/0.37 % (22485)Instruction limit reached!
% 0.14/0.37 % (22485)------------------------------
% 0.14/0.37 % (22485)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (22485)Termination reason: Unknown
% 0.14/0.37 % (22485)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (22485)Memory used [KB]: 1151
% 0.14/0.37 % (22485)Time elapsed: 0.009 s
% 0.14/0.37 % (22485)Instructions burned: 21 (million)
% 0.14/0.37 % (22485)------------------------------
% 0.14/0.37 % (22485)------------------------------
% 0.14/0.37 % (22487)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)
% 0.14/0.37 % (22488)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.14/0.37 % (22462)First to succeed.
% 0.14/0.37 % (22487)Instruction limit reached!
% 0.14/0.37 % (22487)------------------------------
% 0.14/0.37 % (22487)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22487)Termination reason: Unknown
% 0.14/0.38 % (22487)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (22487)Memory used [KB]: 1151
% 0.14/0.38 % (22487)Time elapsed: 0.004 s
% 0.14/0.38 % (22487)Instructions burned: 8 (million)
% 0.14/0.38 % (22487)------------------------------
% 0.14/0.38 % (22487)------------------------------
% 0.14/0.38 % (22462)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(type_def_5, type, mworld: $tType).
% 0.14/0.38 thf(func_def_0, type, mworld: $tType).
% 0.14/0.38 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.14/0.38 thf(func_def_2, type, mactual: mworld).
% 0.14/0.38 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.14/0.38 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 0.14/0.38 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.14/0.38 thf(func_def_16, type, qmltpeq: $i > $i > mworld > $o).
% 0.14/0.38 thf(func_def_17, type, equal_set: $i > $i > mworld > $o).
% 0.14/0.38 thf(func_def_18, type, member: $i > $i > mworld > $o).
% 0.14/0.38 thf(func_def_19, type, subset: $i > $i > mworld > $o).
% 0.14/0.38 thf(func_def_20, type, singleton: $i > $i).
% 0.14/0.38 thf(func_def_21, type, product: $i > $i).
% 0.14/0.38 thf(func_def_22, type, unordered_pair: $i > $i > $i).
% 0.14/0.38 thf(func_def_23, type, intersection: $i > $i > $i).
% 0.14/0.38 thf(func_def_24, type, difference: $i > $i > $i).
% 0.14/0.38 thf(func_def_25, type, sum: $i > $i).
% 0.14/0.38 thf(func_def_26, type, union: $i > $i > $i).
% 0.14/0.38 thf(func_def_27, type, power_set: $i > $i).
% 0.14/0.38 thf(func_def_41, type, sK0: mworld > $i).
% 0.14/0.38 thf(func_def_47, type, sK4: $i > $i > $i).
% 0.14/0.38 thf(func_def_48, type, sK5: $i > $i > $i).
% 0.14/0.38 thf(func_def_49, type, sK6: $i > $i > $i).
% 0.14/0.38 thf(f853,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(avatar_sat_refutation,[],[f777,f786,f798,f832,f849])).
% 0.14/0.38 thf(f849,plain,(
% 0.14/0.38 ~spl1_8),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f848])).
% 0.14/0.38 thf(f848,plain,(
% 0.14/0.38 $false | ~spl1_8),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f834])).
% 0.14/0.38 thf(f834,plain,(
% 0.14/0.38 ($true = $false) | ~spl1_8),
% 0.14/0.38 inference(superposition,[],[f774,f271])).
% 0.14/0.38 thf(f271,plain,(
% 0.14/0.38 ($true = (subset @ sK2 @ sK3 @ mactual))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f269])).
% 0.14/0.38 thf(f269,plain,(
% 0.14/0.38 (((subset @ sK2 @ sK3 @ mactual) & (subset @ sK3 @ sK2 @ mactual)) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f266])).
% 0.14/0.38 thf(f266,plain,(
% 0.14/0.38 ((((subset @ sK2 @ sK3 @ mactual) & (subset @ sK3 @ sK2 @ mactual)) => (equal_set @ sK2 @ sK3 @ mactual)) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f265])).
% 0.14/0.38 thf(f265,plain,(
% 0.14/0.38 (((eiw_di @ sK3 @ mactual) => (((subset @ sK2 @ sK3 @ mactual) & (subset @ sK3 @ sK2 @ mactual)) => (equal_set @ sK2 @ sK3 @ mactual))) = $false)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f264])).
% 0.14/0.38 thf(f264,plain,(
% 0.14/0.38 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ sK2 @ Y0 @ mactual) & (subset @ Y0 @ sK2 @ mactual)) => (equal_set @ sK2 @ Y0 @ mactual)))) @ sK3))),
% 0.14/0.38 inference(sigma_clausification,[],[f262])).
% 0.14/0.38 thf(f262,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ sK2 @ Y0 @ mactual) & (subset @ Y0 @ sK2 @ mactual)) => (equal_set @ sK2 @ Y0 @ mactual))))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f261])).
% 0.14/0.38 thf(f261,plain,(
% 0.14/0.38 (((eiw_di @ sK2 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (((subset @ sK2 @ Y0 @ mactual) & (subset @ Y0 @ sK2 @ mactual)) => (equal_set @ sK2 @ Y0 @ mactual)))))) = $false)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f260])).
% 0.14/0.38 thf(f260,plain,(
% 0.14/0.38 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) => (equal_set @ Y0 @ Y1 @ mactual))))))) @ sK2) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f259])).
% 0.14/0.38 thf(f259,plain,(
% 0.14/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => (((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)) => (equal_set @ Y0 @ Y1 @ mactual)))))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f204])).
% 0.14/0.38 thf(f204,plain,(
% 0.14/0.38 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f166,f153,f147,f147,f163,f184])).
% 0.14/0.38 thf(f184,plain,(
% 0.14/0.38 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f76])).
% 0.14/0.38 thf(f76,plain,(
% 0.14/0.38 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f75])).
% 0.14/0.38 thf(f75,plain,(
% 0.14/0.38 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 0.14/0.38 inference(rectify,[],[f3])).
% 0.14/0.38 thf(f3,axiom,(
% 0.14/0.38 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def)).
% 0.14/0.38 thf(f163,plain,(
% 0.14/0.38 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f109])).
% 0.14/0.38 thf(f109,plain,(
% 0.14/0.38 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f108])).
% 0.14/0.38 thf(f108,plain,(
% 0.14/0.38 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.14/0.38 inference(rectify,[],[f5])).
% 0.14/0.38 thf(f5,axiom,(
% 0.14/0.38 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.14/0.38 thf(f147,plain,(
% 0.14/0.38 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f137])).
% 0.14/0.38 thf(f137,plain,(
% 0.14/0.38 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f136])).
% 0.14/0.38 thf(f136,plain,(
% 0.14/0.38 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.14/0.38 inference(rectify,[],[f12])).
% 0.14/0.38 thf(f12,axiom,(
% 0.14/0.38 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def)).
% 0.14/0.38 thf(f153,plain,(
% 0.14/0.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.14/0.38 inference(cnf_transformation,[],[f103])).
% 0.14/0.38 thf(f103,plain,(
% 0.14/0.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.14/0.38 inference(fool_elimination,[],[f1])).
% 0.14/0.38 thf(f1,axiom,(
% 0.14/0.38 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.14/0.38 thf(f166,plain,(
% 0.14/0.38 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))) != $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f140])).
% 0.14/0.38 thf(f140,plain,(
% 0.14/0.38 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))) != $true)),
% 0.14/0.38 inference(flattening,[],[f92])).
% 0.14/0.38 thf(f92,plain,(
% 0.14/0.38 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)) @ (equal_set @ Y0 @ Y1))))))) = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f91])).
% 0.14/0.38 thf(f91,plain,(
% 0.14/0.38 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mimplies @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0)) @ (equal_set @ X0 @ X1)))))))),
% 0.14/0.38 inference(rectify,[],[f47])).
% 0.14/0.38 thf(f47,negated_conjecture,(
% 0.14/0.38 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mimplies @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1)) @ (equal_set @ X1 @ X3)))))))),
% 0.14/0.38 inference(negated_conjecture,[],[f46])).
% 0.14/0.38 thf(f46,conjecture,(
% 0.14/0.38 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mimplies @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1)) @ (equal_set @ X1 @ X3)))))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02)).
% 0.14/0.38 thf(f774,plain,(
% 0.14/0.38 ($false = (subset @ sK2 @ sK3 @ mactual)) | ~spl1_8),
% 0.14/0.38 inference(avatar_component_clause,[],[f772])).
% 0.14/0.38 thf(f772,plain,(
% 0.14/0.38 spl1_8 <=> ($false = (subset @ sK2 @ sK3 @ mactual))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 0.14/0.38 thf(f832,plain,(
% 0.14/0.38 ~spl1_7),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f831])).
% 0.14/0.38 thf(f831,plain,(
% 0.14/0.38 $false | ~spl1_7),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f828])).
% 0.14/0.38 thf(f828,plain,(
% 0.14/0.38 ($true = $false) | ~spl1_7),
% 0.14/0.38 inference(superposition,[],[f268,f770])).
% 0.14/0.38 thf(f770,plain,(
% 0.14/0.38 ($true = (equal_set @ sK2 @ sK3 @ mactual)) | ~spl1_7),
% 0.14/0.38 inference(avatar_component_clause,[],[f768])).
% 0.14/0.38 thf(f768,plain,(
% 0.14/0.38 spl1_7 <=> ($true = (equal_set @ sK2 @ sK3 @ mactual))),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.14/0.38 thf(f268,plain,(
% 0.14/0.38 ((equal_set @ sK2 @ sK3 @ mactual) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f266])).
% 0.14/0.38 thf(f798,plain,(
% 0.14/0.38 ~spl1_6),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f797])).
% 0.14/0.38 thf(f797,plain,(
% 0.14/0.38 $false | ~spl1_6),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f790])).
% 0.14/0.38 thf(f790,plain,(
% 0.14/0.38 ($true = $false) | ~spl1_6),
% 0.14/0.38 inference(superposition,[],[f765,f263])).
% 0.14/0.38 thf(f263,plain,(
% 0.14/0.38 ($true = (eiw_di @ sK2 @ mactual))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f261])).
% 0.14/0.38 thf(f765,plain,(
% 0.14/0.38 ((eiw_di @ sK2 @ mactual) = $false) | ~spl1_6),
% 0.14/0.38 inference(avatar_component_clause,[],[f763])).
% 0.14/0.38 thf(f763,plain,(
% 0.14/0.38 spl1_6 <=> ((eiw_di @ sK2 @ mactual) = $false)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.14/0.38 thf(f786,plain,(
% 0.14/0.38 ~spl1_4),
% 0.14/0.38 inference(avatar_contradiction_clause,[],[f785])).
% 0.14/0.38 thf(f785,plain,(
% 0.14/0.38 $false | ~spl1_4),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f778])).
% 0.14/0.38 thf(f778,plain,(
% 0.14/0.38 ($true = $false) | ~spl1_4),
% 0.14/0.38 inference(superposition,[],[f757,f267])).
% 0.14/0.38 thf(f267,plain,(
% 0.14/0.38 ($true = (eiw_di @ sK3 @ mactual))),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f265])).
% 0.14/0.38 thf(f757,plain,(
% 0.14/0.38 ((eiw_di @ sK3 @ mactual) = $false) | ~spl1_4),
% 0.14/0.38 inference(avatar_component_clause,[],[f755])).
% 0.14/0.38 thf(f755,plain,(
% 0.14/0.38 spl1_4 <=> ((eiw_di @ sK3 @ mactual) = $false)),
% 0.14/0.38 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.14/0.38 thf(f777,plain,(
% 0.14/0.38 spl1_6 | spl1_4 | spl1_8 | spl1_7),
% 0.14/0.38 inference(avatar_split_clause,[],[f732,f768,f772,f755,f763])).
% 0.14/0.38 thf(f732,plain,(
% 0.14/0.38 ($true = (equal_set @ sK2 @ sK3 @ mactual)) | ((eiw_di @ sK3 @ mactual) = $false) | ($false = (subset @ sK2 @ sK3 @ mactual)) | ((eiw_di @ sK2 @ mactual) = $false)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f721])).
% 0.14/0.38 thf(f721,plain,(
% 0.14/0.38 ((eiw_di @ sK3 @ mactual) = $false) | ($true = (equal_set @ sK2 @ sK3 @ mactual)) | ((eiw_di @ sK2 @ mactual) = $false) | ($true = $false) | ($false = (subset @ sK2 @ sK3 @ mactual))),
% 0.14/0.38 inference(superposition,[],[f604,f270])).
% 0.14/0.38 thf(f270,plain,(
% 0.14/0.38 ((subset @ sK3 @ sK2 @ mactual) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f269])).
% 0.14/0.38 thf(f604,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (((subset @ X2 @ X1 @ mactual) = $false) | ((equal_set @ X1 @ X2 @ mactual) = $true) | ($false = (eiw_di @ X2 @ mactual)) | ((subset @ X1 @ X2 @ mactual) = $false) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f603])).
% 0.14/0.38 thf(f603,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ mactual)) | (((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual)) = $false) | ((eiw_di @ X1 @ mactual) = $false) | ((equal_set @ X1 @ X2 @ mactual) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f601])).
% 0.14/0.38 thf(f601,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual)) = (equal_set @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X2 @ mactual)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f600])).
% 0.14/0.38 thf(f600,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ mactual)) | ((eiw_di @ X1 @ mactual) = $false) | ($true = ((equal_set @ X1 @ X2 @ mactual) = ((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual))))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f599])).
% 0.14/0.38 thf(f599,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => ((equal_set @ X1 @ X2 @ mactual) = ((subset @ X1 @ X2 @ mactual) & (subset @ X2 @ X1 @ mactual))))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f598])).
% 0.14/0.38 thf(f598,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual))))) @ X2)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.14/0.38 inference(pi_clausification,[],[f597])).
% 0.14/0.38 thf(f597,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual))))))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f596])).
% 0.14/0.38 thf(f596,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ X1 @ Y0 @ mactual) & (subset @ Y0 @ X1 @ mactual))))))))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f595])).
% 0.14/0.38 thf(f595,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((equal_set @ Y0 @ Y1 @ mactual) = ((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual)))))))) @ X1))) )),
% 0.14/0.38 inference(pi_clausification,[],[f594])).
% 0.14/0.38 thf(f594,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((equal_set @ Y0 @ Y1 @ mactual) = ((subset @ Y0 @ Y1 @ mactual) & (subset @ Y1 @ Y0 @ mactual))))))))) = $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f219])).
% 0.14/0.38 thf(f219,plain,(
% 0.14/0.38 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (equal_set @ Y0 @ Y1) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f185,f153,f147,f147,f169,f184])).
% 0.14/0.38 thf(f169,plain,(
% 0.14/0.38 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f66])).
% 0.14/0.38 thf(f66,plain,(
% 0.14/0.38 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f65])).
% 0.14/0.38 thf(f65,plain,(
% 0.14/0.38 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))) = mequiv)),
% 0.14/0.38 inference(rectify,[],[f6])).
% 0.14/0.38 thf(f6,axiom,(
% 0.14/0.38 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))) = mequiv)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv_def)).
% 0.14/0.38 thf(f185,plain,(
% 0.14/0.38 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f62])).
% 0.14/0.38 thf(f62,plain,(
% 0.14/0.38 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f61])).
% 0.14/0.38 thf(f61,plain,(
% 0.14/0.38 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (equal_set @ X0 @ X1) @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0))))))))),
% 0.14/0.38 inference(rectify,[],[f36])).
% 0.14/0.38 thf(f36,axiom,(
% 0.14/0.38 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (equal_set @ X1 @ X3) @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1))))))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_0)).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (22462)------------------------------
% 0.14/0.38 % (22462)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (22462)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (22462)Memory used [KB]: 6652
% 0.14/0.38 % (22462)Time elapsed: 0.061 s
% 0.14/0.38 % (22462)Instructions burned: 124 (million)
% 0.14/0.38 % (22462)------------------------------
% 0.14/0.38 % (22462)------------------------------
% 0.14/0.38 % (22461)Success in time 0.076 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------