TSTP Solution File: PHI004^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PHI004^1 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n021.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 02:18:41 EDT 2024
% Result : Theorem 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PHI004^1 : TPTP v8.2.0. Released v6.1.0.
% 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
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 14:47:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (8745)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (8746)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)
% 0.14/0.38 % (8747)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)
% 0.14/0.38 % (8744)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)
% 0.14/0.38 % (8743)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)
% 0.14/0.38 % (8742)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (8748)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (8749)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)
% 0.14/0.38 % (8745)Instruction limit reached!
% 0.14/0.38 % (8745)------------------------------
% 0.14/0.38 % (8745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (8745)Termination reason: Unknown
% 0.14/0.38 % (8745)Termination phase: shuffling
% 0.14/0.38 % (8746)Instruction limit reached!
% 0.14/0.38 % (8746)------------------------------
% 0.14/0.38 % (8746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (8746)Termination reason: Unknown
% 0.14/0.38 % (8746)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (8746)Memory used [KB]: 1023
% 0.14/0.38 % (8746)Time elapsed: 0.004 s
% 0.14/0.38 % (8746)Instructions burned: 3 (million)
% 0.14/0.38 % (8746)------------------------------
% 0.14/0.38 % (8746)------------------------------
% 0.14/0.38
% 0.14/0.38 % (8745)Memory used [KB]: 1023
% 0.14/0.38 % (8745)Time elapsed: 0.003 s
% 0.14/0.38 % (8745)Instructions burned: 3 (million)
% 0.14/0.38 % (8745)------------------------------
% 0.14/0.38 % (8745)------------------------------
% 0.14/0.38 % (8749)Instruction limit reached!
% 0.14/0.38 % (8749)------------------------------
% 0.14/0.38 % (8749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (8749)Termination reason: Unknown
% 0.14/0.38 % (8749)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (8749)Memory used [KB]: 1023
% 0.14/0.38 % (8749)Time elapsed: 0.004 s
% 0.14/0.38 % (8749)Instructions burned: 3 (million)
% 0.14/0.38 % (8749)------------------------------
% 0.14/0.38 % (8749)------------------------------
% 0.14/0.38 % (8743)Instruction limit reached!
% 0.14/0.38 % (8743)------------------------------
% 0.14/0.38 % (8743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (8743)Termination reason: Unknown
% 0.14/0.38 % (8743)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (8743)Memory used [KB]: 1023
% 0.14/0.38 % (8743)Time elapsed: 0.004 s
% 0.14/0.38 % (8743)Instructions burned: 5 (million)
% 0.14/0.38 % (8743)------------------------------
% 0.14/0.38 % (8743)------------------------------
% 0.22/0.39 % (8747)Refutation not found, incomplete strategy
% 0.22/0.39 % (8747)------------------------------
% 0.22/0.39 % (8747)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (8747)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39
% 0.22/0.39
% 0.22/0.39 % (8747)Memory used [KB]: 5628
% 0.22/0.39 % (8747)Time elapsed: 0.008 s
% 0.22/0.39 % (8747)Instructions burned: 10 (million)
% 0.22/0.39 % (8747)------------------------------
% 0.22/0.39 % (8747)------------------------------
% 0.22/0.39 % (8748)Instruction limit reached!
% 0.22/0.39 % (8748)------------------------------
% 0.22/0.39 % (8748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (8748)Termination reason: Unknown
% 0.22/0.39 % (8748)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (8748)Memory used [KB]: 5628
% 0.22/0.39 % (8748)Time elapsed: 0.012 s
% 0.22/0.39 % (8748)Instructions burned: 19 (million)
% 0.22/0.39 % (8748)------------------------------
% 0.22/0.39 % (8748)------------------------------
% 0.22/0.40 % (8744)Instruction limit reached!
% 0.22/0.40 % (8744)------------------------------
% 0.22/0.40 % (8744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (8744)Termination reason: Unknown
% 0.22/0.40 % (8744)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (8744)Memory used [KB]: 5756
% 0.22/0.40 % (8744)Time elapsed: 0.017 s
% 0.22/0.40 % (8744)Instructions burned: 28 (million)
% 0.22/0.40 % (8744)------------------------------
% 0.22/0.40 % (8744)------------------------------
% 0.22/0.40 % (8751)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)
% 0.22/0.40 % (8750)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)
% 0.22/0.40 % (8752)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)
% 0.22/0.40 % (8753)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)
% 0.22/0.40 % (8752)Instruction limit reached!
% 0.22/0.40 % (8752)------------------------------
% 0.22/0.40 % (8752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (8752)Termination reason: Unknown
% 0.22/0.40 % (8752)Termination phase: Property scanning
% 0.22/0.40
% 0.22/0.40 % (8752)Memory used [KB]: 1023
% 0.22/0.40 % (8752)Time elapsed: 0.004 s
% 0.22/0.40 % (8752)Instructions burned: 4 (million)
% 0.22/0.40 % (8752)------------------------------
% 0.22/0.40 % (8752)------------------------------
% 0.22/0.40 % (8754)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.40 % (8751)Instruction limit reached!
% 0.22/0.40 % (8751)------------------------------
% 0.22/0.40 % (8751)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (8751)Termination reason: Unknown
% 0.22/0.40 % (8751)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (8751)Memory used [KB]: 5628
% 0.22/0.41 % (8751)Time elapsed: 0.010 s
% 0.22/0.41 % (8751)Instructions burned: 16 (million)
% 0.22/0.41 % (8751)------------------------------
% 0.22/0.41 % (8751)------------------------------
% 0.22/0.41 % (8755)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.41 % (8754)Instruction limit reached!
% 0.22/0.41 % (8754)------------------------------
% 0.22/0.41 % (8754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (8754)Termination reason: Unknown
% 0.22/0.41 % (8754)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (8754)Memory used [KB]: 1023
% 0.22/0.41 % (8754)Time elapsed: 0.006 s
% 0.22/0.41 % (8754)Instructions burned: 8 (million)
% 0.22/0.41 % (8754)------------------------------
% 0.22/0.41 % (8754)------------------------------
% 0.22/0.41 % (8756)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41 % (8756)Instruction limit reached!
% 0.22/0.41 % (8756)------------------------------
% 0.22/0.41 % (8756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (8756)Termination reason: Unknown
% 0.22/0.41 % (8756)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (8756)Memory used [KB]: 1023
% 0.22/0.41 % (8756)Time elapsed: 0.004 s
% 0.22/0.41 % (8756)Instructions burned: 3 (million)
% 0.22/0.41 % (8756)------------------------------
% 0.22/0.41 % (8756)------------------------------
% 0.22/0.41 % (8757)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41 % (8755)Instruction limit reached!
% 0.22/0.41 % (8755)------------------------------
% 0.22/0.41 % (8755)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (8755)Termination reason: Unknown
% 0.22/0.41 % (8755)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (8755)Memory used [KB]: 5628
% 0.22/0.41 % (8755)Time elapsed: 0.011 s
% 0.22/0.41 % (8755)Instructions burned: 17 (million)
% 0.22/0.41 % (8755)------------------------------
% 0.22/0.41 % (8755)------------------------------
% 0.22/0.42 % (8757)Instruction limit reached!
% 0.22/0.42 % (8757)------------------------------
% 0.22/0.42 % (8757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (8757)Termination reason: Unknown
% 0.22/0.42 % (8757)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (8757)Memory used [KB]: 1023
% 0.22/0.42 % (8757)Time elapsed: 0.004 s
% 0.22/0.42 % (8757)Instructions burned: 4 (million)
% 0.22/0.42 % (8757)------------------------------
% 0.22/0.42 % (8757)------------------------------
% 0.22/0.42 % (8750)Instruction limit reached!
% 0.22/0.42 % (8750)------------------------------
% 0.22/0.42 % (8750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (8750)Termination reason: Unknown
% 0.22/0.42 % (8750)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (8750)Memory used [KB]: 5756
% 0.22/0.42 % (8750)Time elapsed: 0.024 s
% 0.22/0.42 % (8750)Instructions burned: 38 (million)
% 0.22/0.42 % (8750)------------------------------
% 0.22/0.42 % (8750)------------------------------
% 0.22/0.42 % (8758)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.42 % (8759)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.42 % (8759)Instruction limit reached!
% 0.22/0.42 % (8759)------------------------------
% 0.22/0.42 % (8759)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (8759)Termination reason: Unknown
% 0.22/0.42 % (8759)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (8759)Memory used [KB]: 1023
% 0.22/0.42 % (8759)Time elapsed: 0.004 s
% 0.22/0.42 % (8759)Instructions burned: 4 (million)
% 0.22/0.42 % (8759)------------------------------
% 0.22/0.42 % (8759)------------------------------
% 0.22/0.42 % (8758)Instruction limit reached!
% 0.22/0.42 % (8758)------------------------------
% 0.22/0.42 % (8758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (8758)Termination reason: Unknown
% 0.22/0.42 % (8758)Termination phase: Property scanning
% 0.22/0.42
% 0.22/0.42 % (8758)Memory used [KB]: 1023
% 0.22/0.42 % (8758)Time elapsed: 0.006 s
% 0.22/0.42 % (8758)Instructions burned: 8 (million)
% 0.22/0.42 % (8758)------------------------------
% 0.22/0.42 % (8758)------------------------------
% 0.22/0.43 % (8760)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.43 % (8761)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.43 % (8760)Instruction limit reached!
% 0.22/0.43 % (8760)------------------------------
% 0.22/0.43 % (8760)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (8760)Termination reason: Unknown
% 0.22/0.43 % (8760)Termination phase: Preprocessing 3
% 0.22/0.43
% 0.22/0.43 % (8760)Memory used [KB]: 1023
% 0.22/0.43 % (8760)Time elapsed: 0.005 s
% 0.22/0.43 % (8760)Instructions burned: 5 (million)
% 0.22/0.43 % (8760)------------------------------
% 0.22/0.43 % (8760)------------------------------
% 0.22/0.43 % (8762)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.43 % (8763)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.44 % (8763)Instruction limit reached!
% 0.22/0.44 % (8763)------------------------------
% 0.22/0.44 % (8763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (8763)Termination reason: Unknown
% 0.22/0.44 % (8763)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (8763)Memory used [KB]: 1023
% 0.22/0.44 % (8763)Time elapsed: 0.006 s
% 0.22/0.44 % (8763)Instructions burned: 8 (million)
% 0.22/0.44 % (8763)------------------------------
% 0.22/0.44 % (8763)------------------------------
% 0.22/0.44 % (8764)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.22/0.44 % (8765)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.22/0.44 % (8762)Refutation not found, incomplete strategy
% 0.22/0.44 % (8762)------------------------------
% 0.22/0.44 % (8762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (8762)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (8762)Memory used [KB]: 5628
% 0.22/0.44 % (8762)Time elapsed: 0.036 s
% 0.22/0.44 % (8762)Instructions burned: 18 (million)
% 0.22/0.44 % (8762)------------------------------
% 0.22/0.44 % (8762)------------------------------
% 0.22/0.44 % (8761)Instruction limit reached!
% 0.22/0.44 % (8761)------------------------------
% 0.22/0.44 % (8761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (8761)Termination reason: Unknown
% 0.22/0.44 % (8761)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (8761)Memory used [KB]: 5628
% 0.22/0.44 % (8761)Time elapsed: 0.037 s
% 0.22/0.44 % (8761)Instructions burned: 19 (million)
% 0.22/0.44 % (8761)------------------------------
% 0.22/0.44 % (8761)------------------------------
% 0.22/0.44 % (8764)Refutation not found, incomplete strategy
% 0.22/0.44 % (8764)------------------------------
% 0.22/0.44 % (8764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (8764)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (8764)Memory used [KB]: 5500
% 0.22/0.44 % (8764)Time elapsed: 0.027 s
% 0.22/0.44 % (8764)Instructions burned: 7 (million)
% 0.22/0.44 % (8764)------------------------------
% 0.22/0.44 % (8764)------------------------------
% 0.22/0.45 % (8767)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.45 % (8767)Instruction limit reached!
% 0.22/0.45 % (8767)------------------------------
% 0.22/0.45 % (8767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (8767)Termination reason: Unknown
% 0.22/0.45 % (8767)Termination phase: Function definition elimination
% 0.22/0.45
% 0.22/0.45 % (8767)Memory used [KB]: 1023
% 0.22/0.45 % (8767)Time elapsed: 0.005 s
% 0.22/0.45 % (8767)Instructions burned: 6 (million)
% 0.22/0.45 % (8767)------------------------------
% 0.22/0.45 % (8767)------------------------------
% 0.22/0.45 % (8765)Instruction limit reached!
% 0.22/0.45 % (8765)------------------------------
% 0.22/0.45 % (8765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (8765)Termination reason: Unknown
% 0.22/0.45 % (8765)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (8765)Memory used [KB]: 5756
% 0.22/0.45 % (8765)Time elapsed: 0.040 s
% 0.22/0.45 % (8765)Instructions burned: 21 (million)
% 0.22/0.45 % (8765)------------------------------
% 0.22/0.45 % (8765)------------------------------
% 0.22/0.45 % (8770)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45 % (8774)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.22/0.46 % (8770)Instruction limit reached!
% 0.22/0.46 % (8770)------------------------------
% 0.22/0.46 % (8770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (8770)Termination reason: Unknown
% 0.22/0.46 % (8770)Termination phase: Saturation
% 0.22/0.46
% 0.22/0.46 % (8770)Memory used [KB]: 5500
% 0.22/0.46 % (8770)Time elapsed: 0.005 s
% 0.22/0.46 % (8770)Instructions burned: 7 (million)
% 0.22/0.46 % (8770)------------------------------
% 0.22/0.46 % (8770)------------------------------
% 0.22/0.46 % (8772)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.46 % (8775)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.22/0.46 % (8777)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.22/0.46 % (8775)Refutation not found, incomplete strategy
% 0.22/0.46 % (8775)------------------------------
% 0.22/0.46 % (8775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (8775)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 % (8775)Memory used [KB]: 5628
% 0.22/0.46 % (8775)Time elapsed: 0.008 s
% 0.22/0.46 % (8775)Instructions burned: 10 (million)
% 0.22/0.46 % (8775)------------------------------
% 0.22/0.46 % (8775)------------------------------
% 0.22/0.47 % (8774)Refutation not found, incomplete strategy
% 0.22/0.47 % (8774)------------------------------
% 0.22/0.47 % (8774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (8774)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.47
% 0.22/0.47
% 0.22/0.47 % (8774)Memory used [KB]: 5756
% 0.22/0.47 % (8774)Time elapsed: 0.012 s
% 0.22/0.47 % (8774)Instructions burned: 28 (million)
% 0.22/0.47 % (8774)------------------------------
% 0.22/0.47 % (8774)------------------------------
% 0.22/0.47 % (8779)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.22/0.47 % (8780)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.47 % (8753)First to succeed.
% 0.22/0.47 % (8780)Instruction limit reached!
% 0.22/0.47 % (8780)------------------------------
% 0.22/0.47 % (8780)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.47 % (8780)Termination reason: Unknown
% 0.22/0.47 % (8780)Termination phase: shuffling
% 0.22/0.47
% 0.22/0.47 % (8780)Memory used [KB]: 1023
% 0.22/0.47 % (8780)Time elapsed: 0.003 s
% 0.22/0.47 % (8780)Instructions burned: 5 (million)
% 0.22/0.47 % (8780)------------------------------
% 0.22/0.47 % (8780)------------------------------
% 0.22/0.48 % (8753)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Theorem for theBenchmark
% 0.22/0.48 % SZS output start Proof for theBenchmark
% 0.22/0.48 thf(type_def_5, type, mu: $tType).
% 0.22/0.48 thf(func_def_0, type, mu: $tType).
% 0.22/0.48 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.48 thf(func_def_2, type, mtrue: $i > $o).
% 0.22/0.48 thf(func_def_3, type, mfalse: $i > $o).
% 0.22/0.48 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_6, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_7, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_8, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_9, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_10, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_11, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_12, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_13, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_14, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_15, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_16, type, mexists_indset: ((mu > $i > $o) > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_17, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_18, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_19, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_20, type, rel: $i > $i > $o).
% 0.22/0.48 thf(func_def_21, type, mbox: ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_22, type, mdia: ($i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_23, type, mvalid: ($i > $o) > $o).
% 0.22/0.48 thf(func_def_24, type, minvalid: ($i > $o) > $o).
% 0.22/0.48 thf(func_def_25, type, positive: (mu > $i > $o) > $i > $o).
% 0.22/0.48 thf(func_def_26, type, god: mu > $i > $o).
% 0.22/0.48 thf(func_def_27, type, essence: (mu > $i > $o) > mu > $i > $o).
% 0.22/0.48 thf(func_def_28, type, necessary_existence: mu > $i > $o).
% 0.22/0.48 thf(func_def_47, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.48 thf(func_def_49, type, sK3: mu).
% 0.22/0.48 thf(func_def_50, type, sK4: mu > $i > $o).
% 0.22/0.48 thf(func_def_52, type, sK6: mu).
% 0.22/0.48 thf(f532,plain,(
% 0.22/0.48 $false),
% 0.22/0.48 inference(trivial_inequality_removal,[],[f531])).
% 0.22/0.48 thf(f531,plain,(
% 0.22/0.48 ($true = $false)),
% 0.22/0.48 inference(boolean_simplification,[],[f530])).
% 0.22/0.48 thf(f530,plain,(
% 0.22/0.48 ((~ $true) = $true)),
% 0.22/0.48 inference(forward_demodulation,[],[f528,f355])).
% 0.22/0.48 thf(f355,plain,(
% 0.22/0.48 ($true = (rel @ sK2 @ sK5))),
% 0.22/0.48 inference(not_proxy_clausification,[],[f351])).
% 0.22/0.48 thf(f351,plain,(
% 0.22/0.48 ((~ (rel @ sK2 @ sK5)) = $false)),
% 0.22/0.48 inference(binary_proxy_clausification,[],[f333])).
% 0.22/0.48 thf(f333,plain,(
% 0.22/0.48 (((!! @ mu @ (^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))) => (sK4 @ Y0 @ sK5)))) | (~ (rel @ sK2 @ sK5))) = $false)),
% 0.22/0.48 inference(beta_eta_normalization,[],[f330])).
% 0.22/0.48 thf(f330,plain,(
% 0.22/0.48 (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (sK4 @ Y1 @ Y0)))) | (~ (rel @ sK2 @ Y0)))) @ sK5) = $false)),
% 0.22/0.48 inference(sigma_clausification,[],[f322])).
% 0.22/0.48 thf(f322,plain,(
% 0.22/0.48 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (sK4 @ Y1 @ Y0)))) | (~ (rel @ sK2 @ Y0))))) = $false)),
% 0.22/0.48 inference(binary_proxy_clausification,[],[f312])).
% 0.22/0.48 thf(f312,plain,(
% 0.22/0.48 (((sK4 @ sK3 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (sK4 @ Y1 @ Y0)))) | (~ (rel @ sK2 @ Y0)))))) = $false)),
% 0.22/0.48 inference(beta_eta_normalization,[],[f311])).
% 0.22/0.48 thf(f311,plain,(
% 0.22/0.48 (((^[Y0 : mu > $i > $o]: ((Y0 @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))) | (~ (rel @ sK2 @ Y1))))))) @ sK4) = $false)),
% 0.22/0.48 inference(sigma_clausification,[],[f306])).
% 0.22/0.48 thf(f306,plain,(
% 0.22/0.48 ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((Y0 @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))) | (~ (rel @ sK2 @ Y1)))))))) = $false)),
% 0.22/0.48 inference(boolean_simplification,[],[f305])).
% 0.22/0.48 thf(f305,plain,(
% 0.22/0.48 (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((Y0 @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))) | (~ (rel @ sK2 @ Y1)))))))) & $true) = $false)),
% 0.22/0.48 inference(boolean_simplification,[],[f304])).
% 0.22/0.48 thf(f304,plain,(
% 0.22/0.48 (($true => ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((Y0 @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))) | (~ (rel @ sK2 @ Y1)))))))) & $true)) = $false)),
% 0.22/0.48 inference(backward_demodulation,[],[f289,f303])).
% 0.22/0.48 thf(f303,plain,(
% 0.22/0.48 ($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK2) => (Y0 @ sK3 @ sK2)))))),
% 0.22/0.48 inference(binary_proxy_clausification,[],[f289])).
% 0.22/0.48 thf(f289,plain,(
% 0.22/0.48 (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK2) => (Y0 @ sK3 @ sK2)))) => ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((Y0 @ sK3 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))) | (~ (rel @ sK2 @ Y1)))))))) & (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK2) => (Y0 @ sK3 @ sK2)))))) = $false)),
% 0.22/0.48 inference(beta_eta_normalization,[],[f288])).
% 0.22/0.48 thf(f288,plain,(
% 0.22/0.48 (((^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK2) => (Y1 @ Y0 @ sK2)))) => ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((Y1 @ Y0 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y2) => (Y4 @ Y3 @ Y2)))) => (Y1 @ Y3 @ Y2)))) | (~ (rel @ sK2 @ Y2)))))))) & (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK2) => (Y1 @ Y0 @ sK2))))))) @ sK3) = $false)),
% 0.22/0.48 inference(sigma_clausification,[],[f278])).
% 0.22/0.48 thf(f278,plain,(
% 0.22/0.48 ($false = (!! @ mu @ (^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK2) => (Y1 @ Y0 @ sK2)))) => ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((Y1 @ Y0 @ sK2) => (!! @ $i @ (^[Y2 : $i]: ((!! @ mu @ (^[Y3 : mu]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y2) => (Y4 @ Y3 @ Y2)))) => (Y1 @ Y3 @ Y2)))) | (~ (rel @ sK2 @ Y2)))))))) & (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK2) => (Y1 @ Y0 @ sK2)))))))))),
% 0.22/0.48 inference(beta_eta_normalization,[],[f277])).
% 0.22/0.48 thf(f277,plain,(
% 0.22/0.48 (((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((positive @ Y5 @ Y3) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3)))) | (~ (rel @ Y0 @ Y3)))))))) & (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))) @ sK2) = $false)),
% 0.22/0.48 inference(sigma_clausification,[],[f247])).
% 0.22/0.48 thf(f247,plain,(
% 0.22/0.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((positive @ Y5 @ Y3) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3)))) | (~ (rel @ Y0 @ Y3)))))))) & (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))))) = $false)),
% 0.22/0.48 inference(not_proxy_clausification,[],[f138])).
% 0.22/0.48 thf(f138,plain,(
% 0.22/0.48 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((!! @ mu @ (^[Y4 : mu]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((positive @ Y5 @ Y3) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3)))) | (~ (rel @ Y0 @ Y3)))))))) & (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))))))),
% 0.22/0.48 inference(beta_eta_normalization,[],[f129])).
% 0.22/0.48 thf(f129,plain,(
% 0.22/0.48 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ ((^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (Y1 @ Y2) @ ((^[Y3 : (mu > $i > $o) > $i > $o]: ((^[Y4 : $i]: (!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: (Y3 @ Y5 @ Y4)))))) @ (^[Y3 : mu > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) => (Y5 @ Y6))))))) @ (Y3 @ Y2) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ rel @ ((^[Y4 : mu > $i > $o]: ((^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: (Y4 @ Y6 @ Y5)))))) @ (^[Y4 : mu]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (Y1 @ Y4) @ (Y3 @ Y4)))))))))))) @ (^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0)))))))),
% 0.22/0.48 inference(definition_unfolding,[],[f93,f107,f100,f95,f126,f127,f126])).
% 0.22/0.48 thf(f127,plain,(
% 0.22/0.48 (essence = (^[Y0 : mu > $i > $o]: ((^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (Y0 @ Y1) @ ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (Y2 @ Y1) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))))) @ rel @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4)))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) => (Y5 @ Y6))))))) @ (Y0 @ Y3) @ (Y2 @ Y3)))))))))))))),
% 0.22/0.48 inference(definition_unfolding,[],[f108,f105,f121,f95,f124,f100,f95])).
% 0.22/0.48 thf(f124,plain,(
% 0.22/0.48 (mbox = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))) @ rel))),
% 0.22/0.48 inference(definition_unfolding,[],[f96,f109])).
% 0.22/0.48 thf(f109,plain,(
% 0.22/0.48 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f58])).
% 0.22/0.48 thf(f58,plain,(
% 0.22/0.48 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.22/0.48 inference(fool_elimination,[],[f57])).
% 0.22/0.48 thf(f57,plain,(
% 0.22/0.48 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox_generic)),
% 0.22/0.48 inference(rectify,[],[f17])).
% 0.22/0.48 thf(f17,axiom,(
% 0.22/0.48 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox_generic)),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_generic)).
% 0.22/0.48 thf(f96,plain,(
% 0.22/0.48 (mbox = (mbox_generic @ rel))),
% 0.22/0.48 inference(cnf_transformation,[],[f67])).
% 0.22/0.48 thf(f67,plain,(
% 0.22/0.48 (mbox = (mbox_generic @ rel))),
% 0.22/0.48 inference(fool_elimination,[],[f19])).
% 0.22/0.48 thf(f19,axiom,(
% 0.22/0.48 (mbox = (mbox_generic @ rel))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.22/0.48 thf(f121,plain,(
% 0.22/0.48 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f92])).
% 0.22/0.48 thf(f92,plain,(
% 0.22/0.48 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.48 inference(fool_elimination,[],[f91])).
% 0.22/0.48 thf(f91,plain,(
% 0.22/0.48 (mforall_indset = (^[X0 : (mu > $i > $o) > $i > $o, X1 : $i] : (! [X2 : mu > $i > $o] : (X0 @ X2 @ X1))))),
% 0.22/0.48 inference(rectify,[],[f12])).
% 0.22/0.48 thf(f12,axiom,(
% 0.22/0.48 (mforall_indset = (^[X3 : (mu > $i > $o) > $i > $o, X2 : $i] : (! [X0 : mu > $i > $o] : (X3 @ X0 @ X2))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_indset)).
% 0.22/0.48 thf(f105,plain,(
% 0.22/0.48 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f86])).
% 0.22/0.48 thf(f86,plain,(
% 0.22/0.48 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.22/0.48 inference(fool_elimination,[],[f85])).
% 0.22/0.48 thf(f85,plain,(
% 0.22/0.48 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 0.22/0.48 inference(rectify,[],[f6])).
% 0.22/0.48 thf(f6,axiom,(
% 0.22/0.48 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) & (X4 @ X2))) = mand)),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.22/0.48 thf(f108,plain,(
% 0.22/0.48 (essence = (^[Y0 : mu > $i > $o]: ((^[Y1 : mu]: (mand @ (Y0 @ Y1) @ (mforall_indset @ (^[Y2 : mu > $i > $o]: (mimplies @ (Y2 @ Y1) @ (mbox @ (mforall_ind @ (^[Y3 : mu]: (mimplies @ (Y0 @ Y3) @ (Y2 @ Y3)))))))))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f90])).
% 0.22/0.48 thf(f90,plain,(
% 0.22/0.48 (essence = (^[Y0 : mu > $i > $o]: ((^[Y1 : mu]: (mand @ (Y0 @ Y1) @ (mforall_indset @ (^[Y2 : mu > $i > $o]: (mimplies @ (Y2 @ Y1) @ (mbox @ (mforall_ind @ (^[Y3 : mu]: (mimplies @ (Y0 @ Y3) @ (Y2 @ Y3)))))))))))))),
% 0.22/0.48 inference(fool_elimination,[],[f89])).
% 0.22/0.48 thf(f89,plain,(
% 0.22/0.48 (essence = (^[X0 : mu > $i > $o, X1 : mu] : (mand @ (X0 @ X1) @ (mforall_indset @ (^[X2 : mu > $i > $o] : (mimplies @ (X2 @ X1) @ (mbox @ (mforall_ind @ (^[X3 : mu] : (mimplies @ (X0 @ X3) @ (X2 @ X3)))))))))))),
% 0.22/0.48 inference(rectify,[],[f28])).
% 0.22/0.48 thf(f28,axiom,(
% 0.22/0.48 (essence = (^[X3 : mu > $i > $o, X0 : mu] : (mand @ (X3 @ X0) @ (mforall_indset @ (^[X4 : mu > $i > $o] : (mimplies @ (X4 @ X0) @ (mbox @ (mforall_ind @ (^[X1 : mu] : (mimplies @ (X3 @ X1) @ (X4 @ X1)))))))))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD2)).
% 0.22/0.48 thf(f126,plain,(
% 0.22/0.48 (god = (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.22/0.48 inference(definition_unfolding,[],[f114,f121,f95])).
% 0.22/0.48 thf(f114,plain,(
% 0.22/0.48 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f45])).
% 0.22/0.48 thf(f45,plain,(
% 0.22/0.48 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))),
% 0.22/0.48 inference(fool_elimination,[],[f44])).
% 0.22/0.48 thf(f44,plain,(
% 0.22/0.48 (god = (^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (positive @ X1) @ (X1 @ X0))))))),
% 0.22/0.48 inference(rectify,[],[f25])).
% 0.22/0.48 thf(f25,axiom,(
% 0.22/0.48 (god = (^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (X3 @ X0))))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD1)).
% 0.22/0.48 thf(f95,plain,(
% 0.22/0.48 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f71])).
% 0.22/0.48 thf(f71,plain,(
% 0.22/0.48 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.22/0.48 inference(fool_elimination,[],[f70])).
% 0.22/0.48 thf(f70,plain,(
% 0.22/0.48 (mimplies = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 0.22/0.48 inference(rectify,[],[f7])).
% 0.22/0.48 thf(f7,axiom,(
% 0.22/0.48 (mimplies = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) => (X4 @ X2))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.48 thf(f100,plain,(
% 0.22/0.48 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f76])).
% 0.22/0.48 thf(f76,plain,(
% 0.22/0.48 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.48 inference(fool_elimination,[],[f75])).
% 0.22/0.48 thf(f75,plain,(
% 0.22/0.48 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.22/0.48 inference(rectify,[],[f11])).
% 0.22/0.48 thf(f11,axiom,(
% 0.22/0.48 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.22/0.48 thf(f107,plain,(
% 0.22/0.48 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.48 inference(cnf_transformation,[],[f78])).
% 0.22/0.48 thf(f78,plain,(
% 0.22/0.48 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.48 inference(fool_elimination,[],[f77])).
% 0.22/0.48 thf(f77,plain,(
% 0.22/0.48 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.22/0.48 inference(rectify,[],[f21])).
% 0.22/0.48 thf(f21,axiom,(
% 0.22/0.48 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.48 thf(f93,plain,(
% 0.22/0.48 ($true = (~ (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (god @ Y0) @ (essence @ god @ Y0)))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f60])).
% 0.22/0.48 thf(f60,plain,(
% 0.22/0.48 ($true = (~ (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (god @ Y0) @ (essence @ god @ Y0)))))))),
% 0.22/0.48 inference(fool_elimination,[],[f59])).
% 0.22/0.48 thf(f59,plain,(
% 0.22/0.48 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))),
% 0.22/0.48 inference(rectify,[],[f32])).
% 0.22/0.48 thf(f32,negated_conjecture,(
% 0.22/0.48 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))),
% 0.22/0.48 inference(negated_conjecture,[],[f31])).
% 0.22/0.48 thf(f31,conjecture,(
% 0.22/0.48 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT2)).
% 0.22/0.48 thf(f528,plain,(
% 0.22/0.48 ($true = (~ (rel @ sK2 @ sK5)))),
% 0.22/0.48 inference(boolean_simplification,[],[f525])).
% 0.22/0.48 thf(f525,plain,(
% 0.22/0.48 ($true = ($false | (~ (rel @ sK2 @ sK5))))),
% 0.22/0.48 inference(superposition,[],[f417,f450])).
% 0.22/0.48 thf(f450,plain,(
% 0.22/0.48 ($false = (positive @ sK4 @ sK5))),
% 0.22/0.48 inference(not_proxy_clausification,[],[f426])).
% 0.22/0.48 thf(f426,plain,(
% 0.22/0.48 ($true = (~ (positive @ sK4 @ sK5)))),
% 0.22/0.48 inference(boolean_simplification,[],[f422])).
% 0.22/0.48 thf(f422,plain,(
% 0.22/0.48 ($true = ((positive @ sK4 @ sK5) => $false))),
% 0.22/0.48 inference(superposition,[],[f420,f363])).
% 0.22/0.48 thf(f363,plain,(
% 0.22/0.48 ((sK4 @ sK6 @ sK5) = $false)),
% 0.22/0.48 inference(boolean_simplification,[],[f362])).
% 0.22/0.48 thf(f362,plain,(
% 0.22/0.48 (($true => (sK4 @ sK6 @ sK5)) = $false)),
% 0.22/0.48 inference(backward_demodulation,[],[f359,f361])).
% 0.22/0.48 thf(f361,plain,(
% 0.22/0.48 ($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK5) => (Y0 @ sK6 @ sK5)))))),
% 0.22/0.48 inference(binary_proxy_clausification,[],[f359])).
% 0.22/0.48 thf(f359,plain,(
% 0.22/0.48 (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK5) => (Y0 @ sK6 @ sK5)))) => (sK4 @ sK6 @ sK5)) = $false)),
% 0.22/0.48 inference(beta_eta_normalization,[],[f358])).
% 0.22/0.48 thf(f358,plain,(
% 0.22/0.48 ($false = ((^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))) => (sK4 @ Y0 @ sK5))) @ sK6))),
% 0.22/0.48 inference(sigma_clausification,[],[f354])).
% 0.22/0.48 thf(f354,plain,(
% 0.22/0.48 ($false = (!! @ mu @ (^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))) => (sK4 @ Y0 @ sK5)))))),
% 0.22/0.48 inference(boolean_simplification,[],[f353])).
% 0.22/0.48 thf(f353,plain,(
% 0.22/0.48 (((!! @ mu @ (^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))) => (sK4 @ Y0 @ sK5)))) | $false) = $false)),
% 0.22/0.48 inference(backward_demodulation,[],[f333,f351])).
% 0.22/0.48 thf(f420,plain,(
% 0.22/0.48 ( ! [X1 : mu > $i > $o] : (($true = ((positive @ X1 @ sK5) => (X1 @ sK6 @ sK5)))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f419])).
% 0.22/0.48 thf(f419,plain,(
% 0.22/0.48 ( ! [X1 : mu > $i > $o] : (($true = ((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK5) => (Y0 @ sK6 @ sK5))) @ X1))) )),
% 0.22/0.48 inference(pi_clausification,[],[f361])).
% 0.22/0.48 thf(f417,plain,(
% 0.22/0.48 ( ! [X1 : $i] : (($true = ((positive @ sK4 @ X1) | (~ (rel @ sK2 @ X1))))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f415])).
% 0.22/0.48 thf(f415,plain,(
% 0.22/0.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((positive @ sK4 @ Y0) | (~ (rel @ sK2 @ Y0)))) @ X1))) )),
% 0.22/0.48 inference(pi_clausification,[],[f389])).
% 0.22/0.48 thf(f389,plain,(
% 0.22/0.48 ($true = (!! @ $i @ (^[Y0 : $i]: ((positive @ sK4 @ Y0) | (~ (rel @ sK2 @ Y0))))))),
% 0.22/0.48 inference(boolean_simplification,[],[f372])).
% 0.22/0.48 thf(f372,plain,(
% 0.22/0.48 ($true = ($true => (!! @ $i @ (^[Y0 : $i]: ((positive @ sK4 @ Y0) | (~ (rel @ sK2 @ Y0)))))))),
% 0.22/0.48 inference(superposition,[],[f152,f350])).
% 0.22/0.48 thf(f350,plain,(
% 0.22/0.48 ((positive @ sK4 @ sK2) = $true)),
% 0.22/0.48 inference(boolean_simplification,[],[f349])).
% 0.22/0.48 thf(f349,plain,(
% 0.22/0.48 ($true = (~ (~ (positive @ sK4 @ sK2))))),
% 0.22/0.48 inference(boolean_simplification,[],[f348])).
% 0.22/0.48 thf(f348,plain,(
% 0.22/0.48 (((~ (positive @ sK4 @ sK2)) => $false) = $true)),
% 0.22/0.48 inference(boolean_simplification,[],[f335])).
% 0.22/0.48 thf(f335,plain,(
% 0.22/0.48 ($true = ((~ (positive @ sK4 @ sK2)) => (~ $true)))),
% 0.22/0.48 inference(superposition,[],[f317,f323])).
% 0.22/0.48 thf(f323,plain,(
% 0.22/0.48 ($true = (sK4 @ sK3 @ sK2))),
% 0.22/0.48 inference(binary_proxy_clausification,[],[f312])).
% 0.22/0.48 thf(f317,plain,(
% 0.22/0.48 ( ! [X0 : mu > $i > $o] : (($true = ((~ (positive @ X0 @ sK2)) => (~ (X0 @ sK3 @ sK2))))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f315])).
% 0.22/0.48 thf(f315,plain,(
% 0.22/0.48 ( ! [X0 : mu > $i > $o] : (($true = ((~ (positive @ X0 @ sK2)) => ((^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ sK3 @ sK2)))) )),
% 0.22/0.48 inference(superposition,[],[f310,f146])).
% 0.22/0.48 thf(f146,plain,(
% 0.22/0.48 ( ! [X2 : mu > $i > $o,X1 : $i] : (((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1) = (~ (positive @ X2 @ X1)))) )),
% 0.22/0.48 inference(binary_proxy_clausification,[],[f145])).
% 0.22/0.48 thf(f145,plain,(
% 0.22/0.48 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((~ (positive @ X2 @ X1)) = (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1)))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f144])).
% 0.22/0.48 thf(f144,plain,(
% 0.22/0.48 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((^[Y0 : mu > $i > $o]: ((~ (positive @ Y0 @ X1)) = (positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1))) @ X2))) )),
% 0.22/0.48 inference(pi_clausification,[],[f143])).
% 0.22/0.48 thf(f143,plain,(
% 0.22/0.48 ( ! [X1 : $i] : (($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((~ (positive @ Y0 @ X1)) = (positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1)))))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f142])).
% 0.22/0.48 thf(f142,plain,(
% 0.22/0.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((~ (positive @ Y1 @ Y0)) = (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0))))) @ X1))) )),
% 0.22/0.48 inference(pi_clausification,[],[f135])).
% 0.22/0.48 thf(f135,plain,(
% 0.22/0.48 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((~ (positive @ Y1 @ Y0)) = (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0)))))))),
% 0.22/0.48 inference(beta_eta_normalization,[],[f131])).
% 0.22/0.48 thf(f131,plain,(
% 0.22/0.48 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y2 @ Y3) = (Y1 @ Y3))))))) @ (positive @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ (positive @ Y0)))))))),
% 0.22/0.48 inference(definition_unfolding,[],[f98,f107,f121,f118,f115,f115])).
% 0.22/0.48 thf(f115,plain,(
% 0.22/0.48 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f54])).
% 0.22/0.48 thf(f54,plain,(
% 0.22/0.48 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.48 inference(fool_elimination,[],[f53])).
% 0.22/0.48 thf(f53,plain,(
% 0.22/0.48 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.22/0.48 inference(rectify,[],[f4])).
% 0.22/0.48 thf(f4,axiom,(
% 0.22/0.48 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.22/0.48 thf(f118,plain,(
% 0.22/0.48 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f47])).
% 0.22/0.48 thf(f47,plain,(
% 0.22/0.48 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 0.22/0.48 inference(fool_elimination,[],[f46])).
% 0.22/0.48 thf(f46,plain,(
% 0.22/0.48 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) <=> (X0 @ X2))) = mequiv)),
% 0.22/0.48 inference(rectify,[],[f9])).
% 0.22/0.48 thf(f9,axiom,(
% 0.22/0.48 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) <=> (X3 @ X2))) = mequiv)),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.22/0.48 thf(f98,plain,(
% 0.22/0.48 ($true = (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mequiv @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @ (mnot @ (positive @ Y0)))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f69])).
% 0.22/0.48 thf(f69,plain,(
% 0.22/0.48 ($true = (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mequiv @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @ (mnot @ (positive @ Y0)))))))),
% 0.22/0.48 inference(fool_elimination,[],[f68])).
% 0.22/0.48 thf(f68,plain,(
% 0.22/0.48 (mvalid @ (mforall_indset @ (^[X0 : mu > $i > $o] : (mequiv @ (positive @ (^[X1 : mu] : (mnot @ (X0 @ X1)))) @ (mnot @ (positive @ X0))))))),
% 0.22/0.48 inference(rectify,[],[f23])).
% 0.22/0.48 thf(f23,axiom,(
% 0.22/0.48 (mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mequiv @ (positive @ (^[X0 : mu] : (mnot @ (X3 @ X0)))) @ (mnot @ (positive @ X3))))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1)).
% 0.22/0.48 thf(f310,plain,(
% 0.22/0.48 ( ! [X1 : mu > $i > $o] : (($true = ((positive @ X1 @ sK2) => (X1 @ sK3 @ sK2)))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f309])).
% 0.22/0.48 thf(f309,plain,(
% 0.22/0.48 ( ! [X1 : mu > $i > $o] : ((((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ sK2) => (Y0 @ sK3 @ sK2))) @ X1) = $true)) )),
% 0.22/0.48 inference(pi_clausification,[],[f303])).
% 0.22/0.48 thf(f152,plain,(
% 0.22/0.48 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((positive @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((positive @ X2 @ Y0) | (~ (rel @ X1 @ Y0)))))))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f151])).
% 0.22/0.48 thf(f151,plain,(
% 0.22/0.48 ( ! [X2 : mu > $i > $o,X1 : $i] : (($true = ((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((positive @ Y0 @ Y1) | (~ (rel @ X1 @ Y1))))))) @ X2))) )),
% 0.22/0.48 inference(pi_clausification,[],[f150])).
% 0.22/0.48 thf(f150,plain,(
% 0.22/0.48 ( ! [X1 : $i] : (($true = (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((positive @ Y0 @ Y1) | (~ (rel @ X1 @ Y1)))))))))) )),
% 0.22/0.48 inference(beta_eta_normalization,[],[f149])).
% 0.22/0.48 thf(f149,plain,(
% 0.22/0.48 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((positive @ Y1 @ Y2) | (~ (rel @ Y0 @ Y2))))))))) @ X1))) )),
% 0.22/0.48 inference(pi_clausification,[],[f136])).
% 0.22/0.48 thf(f136,plain,(
% 0.22/0.48 ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((positive @ Y1 @ Y2) | (~ (rel @ Y0 @ Y2)))))))))) = $true)),
% 0.22/0.48 inference(beta_eta_normalization,[],[f132])).
% 0.22/0.48 thf(f132,plain,(
% 0.22/0.48 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ (positive @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (Y1 @ Y3 @ Y4)))))))))) @ rel @ (positive @ Y0)))))))),
% 0.22/0.48 inference(definition_unfolding,[],[f101,f107,f121,f95,f124])).
% 0.22/0.48 thf(f101,plain,(
% 0.22/0.48 ($true = (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mbox @ (positive @ Y0)))))))),
% 0.22/0.48 inference(cnf_transformation,[],[f64])).
% 0.22/0.48 thf(f64,plain,(
% 0.22/0.48 ($true = (mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mbox @ (positive @ Y0)))))))),
% 0.22/0.48 inference(fool_elimination,[],[f63])).
% 0.22/0.48 thf(f63,plain,(
% 0.22/0.48 (mvalid @ (mforall_indset @ (^[X0 : mu > $i > $o] : (mimplies @ (positive @ X0) @ (mbox @ (positive @ X0))))))),
% 0.22/0.48 inference(rectify,[],[f27])).
% 0.22/0.48 thf(f27,axiom,(
% 0.22/0.48 (mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (mbox @ (positive @ X3))))))),
% 0.22/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA4)).
% 0.22/0.48 % SZS output end Proof for theBenchmark
% 0.22/0.48 % (8753)------------------------------
% 0.22/0.48 % (8753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.48 % (8753)Termination reason: Refutation
% 0.22/0.48
% 0.22/0.48 % (8753)Memory used [KB]: 6396
% 0.22/0.48 % (8753)Time elapsed: 0.078 s
% 0.22/0.48 % (8753)Instructions burned: 127 (million)
% 0.22/0.48 % (8753)------------------------------
% 0.22/0.48 % (8753)------------------------------
% 0.22/0.48 % (8741)Success in time 0.108 s
% 0.22/0.48 % Vampire---4.8 exiting
%------------------------------------------------------------------------------