TSTP Solution File: SYO470^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO470^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:05:11 EDT 2024
% Result : Theorem 0.20s 0.44s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO470^6 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % 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
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:44:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38 % (9690)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 % (9691)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 % (9692)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 % (9693)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (9694)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 % (9695)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 % (9696)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 % (9697)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 % (9694)Instruction limit reached!
% 0.14/0.38 % (9694)------------------------------
% 0.14/0.38 % (9694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (9694)Termination reason: Unknown
% 0.14/0.38 % (9694)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (9694)Memory used [KB]: 1023
% 0.14/0.38 % (9694)Time elapsed: 0.003 s
% 0.14/0.38 % (9694)Instructions burned: 2 (million)
% 0.14/0.38 % (9694)------------------------------
% 0.14/0.38 % (9694)------------------------------
% 0.14/0.38 % (9693)Instruction limit reached!
% 0.14/0.38 % (9693)------------------------------
% 0.14/0.38 % (9693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (9693)Termination reason: Unknown
% 0.14/0.38 % (9693)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (9693)Memory used [KB]: 1023
% 0.14/0.38 % (9693)Time elapsed: 0.004 s
% 0.14/0.38 % (9693)Instructions burned: 3 (million)
% 0.14/0.38 % (9693)------------------------------
% 0.14/0.38 % (9693)------------------------------
% 0.14/0.38 % (9697)Instruction limit reached!
% 0.14/0.38 % (9697)------------------------------
% 0.14/0.38 % (9697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (9697)Termination reason: Unknown
% 0.14/0.38 % (9697)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (9697)Memory used [KB]: 1023
% 0.14/0.38 % (9697)Time elapsed: 0.004 s
% 0.14/0.38 % (9697)Instructions burned: 3 (million)
% 0.14/0.38 % (9697)------------------------------
% 0.14/0.38 % (9697)------------------------------
% 0.14/0.38 % (9691)Instruction limit reached!
% 0.14/0.38 % (9691)------------------------------
% 0.14/0.38 % (9691)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (9691)Termination reason: Unknown
% 0.14/0.38 % (9691)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (9691)Memory used [KB]: 1023
% 0.14/0.38 % (9691)Time elapsed: 0.005 s
% 0.14/0.38 % (9691)Instructions burned: 5 (million)
% 0.14/0.38 % (9691)------------------------------
% 0.14/0.38 % (9691)------------------------------
% 0.14/0.38 % (9695)Refutation not found, incomplete strategy
% 0.14/0.38 % (9695)------------------------------
% 0.14/0.38 % (9695)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (9695)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (9695)Memory used [KB]: 5628
% 0.14/0.38 % (9695)Time elapsed: 0.007 s
% 0.14/0.38 % (9695)Instructions burned: 8 (million)
% 0.14/0.38 % (9695)------------------------------
% 0.14/0.38 % (9695)------------------------------
% 0.14/0.39 % (9696)Instruction limit reached!
% 0.14/0.39 % (9696)------------------------------
% 0.14/0.39 % (9696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (9696)Termination reason: Unknown
% 0.14/0.39 % (9696)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (9696)Memory used [KB]: 5628
% 0.14/0.39 % (9696)Time elapsed: 0.012 s
% 0.14/0.39 % (9696)Instructions burned: 19 (million)
% 0.14/0.39 % (9696)------------------------------
% 0.14/0.39 % (9696)------------------------------
% 0.14/0.39 % (9692)Instruction limit reached!
% 0.14/0.39 % (9692)------------------------------
% 0.14/0.39 % (9692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (9692)Termination reason: Unknown
% 0.14/0.39 % (9692)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (9692)Memory used [KB]: 5756
% 0.14/0.39 % (9692)Time elapsed: 0.018 s
% 0.14/0.39 % (9692)Instructions burned: 27 (million)
% 0.14/0.39 % (9692)------------------------------
% 0.14/0.39 % (9692)------------------------------
% 0.14/0.39 % (9698)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)
% 0.14/0.39 % (9699)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)
% 0.14/0.39 % (9700)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)
% 0.14/0.39 % (9701)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)
% 0.14/0.39 % (9700)Instruction limit reached!
% 0.14/0.39 % (9700)------------------------------
% 0.14/0.39 % (9700)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (9700)Termination reason: Unknown
% 0.14/0.39 % (9700)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (9700)Memory used [KB]: 1023
% 0.14/0.39 % (9700)Time elapsed: 0.004 s
% 0.14/0.39 % (9700)Instructions burned: 4 (million)
% 0.14/0.39 % (9700)------------------------------
% 0.14/0.39 % (9700)------------------------------
% 0.14/0.40 % (9702)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (9699)Instruction limit reached!
% 0.14/0.40 % (9699)------------------------------
% 0.14/0.40 % (9699)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (9699)Termination reason: Unknown
% 0.14/0.40 % (9699)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (9699)Memory used [KB]: 5628
% 0.14/0.40 % (9699)Time elapsed: 0.010 s
% 0.14/0.40 % (9699)Instructions burned: 16 (million)
% 0.14/0.40 % (9702)Instruction limit reached!
% 0.14/0.40 % (9702)------------------------------
% 0.14/0.40 % (9702)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (9699)------------------------------
% 0.14/0.40 % (9699)------------------------------
% 0.14/0.40 % (9702)Termination reason: Unknown
% 0.14/0.40 % (9702)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (9702)Memory used [KB]: 1023
% 0.14/0.40 % (9702)Time elapsed: 0.006 s
% 0.14/0.40 % (9702)Instructions burned: 7 (million)
% 0.14/0.40 % (9702)------------------------------
% 0.14/0.40 % (9702)------------------------------
% 0.14/0.40 % (9703)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.41 % (9707)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)
% 0.14/0.41 % (9707)Instruction limit reached!
% 0.14/0.41 % (9707)------------------------------
% 0.14/0.41 % (9707)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (9707)Termination reason: Unknown
% 0.14/0.41 % (9707)Termination phase: shuffling
% 0.14/0.41
% 0.14/0.41 % (9707)Memory used [KB]: 1023
% 0.14/0.41 % (9707)Time elapsed: 0.004 s
% 0.14/0.41 % (9707)Instructions burned: 3 (million)
% 0.14/0.41 % (9707)------------------------------
% 0.14/0.41 % (9707)------------------------------
% 0.20/0.41 % (9708)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)
% 0.20/0.41 % (9703)Instruction limit reached!
% 0.20/0.41 % (9703)------------------------------
% 0.20/0.41 % (9703)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (9703)Termination reason: Unknown
% 0.20/0.41 % (9703)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (9703)Memory used [KB]: 5756
% 0.20/0.41 % (9703)Time elapsed: 0.012 s
% 0.20/0.41 % (9703)Instructions burned: 16 (million)
% 0.20/0.41 % (9703)------------------------------
% 0.20/0.41 % (9703)------------------------------
% 0.20/0.41 % (9708)Instruction limit reached!
% 0.20/0.41 % (9708)------------------------------
% 0.20/0.41 % (9708)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (9708)Termination reason: Unknown
% 0.20/0.41 % (9708)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (9708)Memory used [KB]: 1023
% 0.20/0.41 % (9708)Time elapsed: 0.004 s
% 0.20/0.41 % (9708)Instructions burned: 4 (million)
% 0.20/0.41 % (9708)------------------------------
% 0.20/0.41 % (9708)------------------------------
% 0.20/0.41 % (9698)Instruction limit reached!
% 0.20/0.41 % (9698)------------------------------
% 0.20/0.41 % (9698)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (9698)Termination reason: Unknown
% 0.20/0.41 % (9698)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (9698)Memory used [KB]: 5756
% 0.20/0.41 % (9698)Time elapsed: 0.022 s
% 0.20/0.41 % (9698)Instructions burned: 39 (million)
% 0.20/0.41 % (9698)------------------------------
% 0.20/0.41 % (9698)------------------------------
% 0.20/0.41 % (9711)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)
% 0.20/0.41 % (9712)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)
% 0.20/0.42 % (9712)Instruction limit reached!
% 0.20/0.42 % (9712)------------------------------
% 0.20/0.42 % (9712)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (9712)Termination reason: Unknown
% 0.20/0.42 % (9712)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (9712)Memory used [KB]: 1023
% 0.20/0.42 % (9712)Time elapsed: 0.004 s
% 0.20/0.42 % (9712)Instructions burned: 4 (million)
% 0.20/0.42 % (9712)------------------------------
% 0.20/0.42 % (9712)------------------------------
% 0.20/0.42 % (9711)Instruction limit reached!
% 0.20/0.42 % (9711)------------------------------
% 0.20/0.42 % (9711)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (9711)Termination reason: Unknown
% 0.20/0.42 % (9711)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (9711)Memory used [KB]: 1151
% 0.20/0.42 % (9711)Time elapsed: 0.006 s
% 0.20/0.42 % (9711)Instructions burned: 8 (million)
% 0.20/0.42 % (9711)------------------------------
% 0.20/0.42 % (9711)------------------------------
% 0.20/0.42 % (9717)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (9717)Instruction limit reached!
% 0.20/0.42 % (9717)------------------------------
% 0.20/0.42 % (9717)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (9717)Termination reason: Unknown
% 0.20/0.42 % (9717)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (9717)Memory used [KB]: 1023
% 0.20/0.42 % (9717)Time elapsed: 0.004 s
% 0.20/0.42 % (9717)Instructions burned: 4 (million)
% 0.20/0.42 % (9717)------------------------------
% 0.20/0.42 % (9717)------------------------------
% 0.20/0.42 % (9719)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)
% 0.20/0.43 % (9720)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43 % (9721)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.43 % (9721)Instruction limit reached!
% 0.20/0.43 % (9721)------------------------------
% 0.20/0.43 % (9721)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (9721)Termination reason: Unknown
% 0.20/0.43 % (9721)Termination phase: Preprocessing 3
% 0.20/0.43
% 0.20/0.43 % (9721)Memory used [KB]: 1023
% 0.20/0.43 % (9721)Time elapsed: 0.005 s
% 0.20/0.43 % (9721)Instructions burned: 6 (million)
% 0.20/0.43 % (9721)------------------------------
% 0.20/0.43 % (9721)------------------------------
% 0.20/0.43 % (9701)First to succeed.
% 0.20/0.43 % (9720)Refutation not found, incomplete strategy
% 0.20/0.43 % (9720)------------------------------
% 0.20/0.43 % (9720)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (9720)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 % (9720)Memory used [KB]: 5628
% 0.20/0.43 % (9720)Time elapsed: 0.007 s
% 0.20/0.43 % (9720)Instructions burned: 9 (million)
% 0.20/0.43 % (9720)------------------------------
% 0.20/0.43 % (9720)------------------------------
% 0.20/0.43 % (9725)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)
% 0.20/0.43 % (9726)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)
% 0.20/0.44 % (9719)Instruction limit reached!
% 0.20/0.44 % (9719)------------------------------
% 0.20/0.44 % (9719)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (9725)Refutation not found, incomplete strategy
% 0.20/0.44 % (9725)------------------------------
% 0.20/0.44 % (9725)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (9725)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.44
% 0.20/0.44
% 0.20/0.44 % (9725)Memory used [KB]: 5628
% 0.20/0.44 % (9725)Time elapsed: 0.007 s
% 0.20/0.44 % (9725)Instructions burned: 9 (million)
% 0.20/0.44 % (9725)------------------------------
% 0.20/0.44 % (9725)------------------------------
% 0.20/0.44 % (9719)Termination reason: Unknown
% 0.20/0.44 % (9719)Termination phase: Saturation
% 0.20/0.44
% 0.20/0.44 % (9701)Refutation found. Thanks to Tanya!
% 0.20/0.44 % SZS status Theorem for theBenchmark
% 0.20/0.44 % SZS output start Proof for theBenchmark
% 0.20/0.44 thf(type_def_5, type, mu: $tType).
% 0.20/0.44 thf(func_def_0, type, mu: $tType).
% 0.20/0.44 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.44 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.44 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.44 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.44 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.44 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.20/0.44 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.20/0.44 thf(func_def_36, type, p: $i > $o).
% 0.20/0.44 thf(func_def_53, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.44 thf(f474,plain,(
% 0.20/0.44 $false),
% 0.20/0.44 inference(avatar_sat_refutation,[],[f209,f257,f473])).
% 0.20/0.44 thf(f473,plain,(
% 0.20/0.44 ~spl0_1),
% 0.20/0.44 inference(avatar_contradiction_clause,[],[f472])).
% 0.20/0.44 thf(f472,plain,(
% 0.20/0.44 $false | ~spl0_1),
% 0.20/0.44 inference(trivial_inequality_removal,[],[f471])).
% 0.20/0.44 thf(f471,plain,(
% 0.20/0.44 ($false = $true) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f470])).
% 0.20/0.44 thf(f470,plain,(
% 0.20/0.44 ($true = (~ $true)) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f378,f469])).
% 0.20/0.44 thf(f469,plain,(
% 0.20/0.44 ((rel_s5 @ sK4 @ sK5) = $true) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f461])).
% 0.20/0.44 thf(f461,plain,(
% 0.20/0.44 ($true = ($true => (rel_s5 @ sK4 @ sK5))) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f320,f399])).
% 0.20/0.44 thf(f399,plain,(
% 0.20/0.44 ((rel_s5 @ sK4 @ sK3) = $true) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f393])).
% 0.20/0.44 thf(f393,plain,(
% 0.20/0.44 ($true = ($true => (rel_s5 @ sK4 @ sK3))) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f285,f358])).
% 0.20/0.44 thf(f358,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK4 @ sK2)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f355])).
% 0.20/0.44 thf(f355,plain,(
% 0.20/0.44 (($true => (rel_s5 @ sK4 @ sK2)) = $true) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f173,f349])).
% 0.20/0.44 thf(f349,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK2 @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f328])).
% 0.20/0.44 thf(f328,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK2 @ sK4))) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f270])).
% 0.20/0.44 thf(f270,plain,(
% 0.20/0.44 ($false = ((p @ sK4) | (~ (rel_s5 @ sK2 @ sK4)))) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f269])).
% 0.20/0.44 thf(f269,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f263])).
% 0.20/0.44 thf(f263,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f260])).
% 0.20/0.44 thf(f260,plain,(
% 0.20/0.44 (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f205])).
% 0.20/0.44 thf(f205,plain,(
% 0.20/0.44 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))))) | ~spl0_1),
% 0.20/0.44 inference(avatar_component_clause,[],[f204])).
% 0.20/0.44 thf(f204,plain,(
% 0.20/0.44 spl0_1 <=> ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))))))),
% 0.20/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.44 thf(f173,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f172])).
% 0.20/0.44 thf(f172,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2))) )),
% 0.20/0.44 inference(pi_clausification,[],[f171])).
% 0.20/0.44 thf(f171,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f170])).
% 0.20/0.44 thf(f170,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1))) )),
% 0.20/0.44 inference(pi_clausification,[],[f165])).
% 0.20/0.44 thf(f165,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))),
% 0.20/0.44 inference(beta_eta_normalization,[],[f159])).
% 0.20/0.44 thf(f159,plain,(
% 0.20/0.44 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5))),
% 0.20/0.44 inference(definition_unfolding,[],[f122,f140])).
% 0.20/0.44 thf(f140,plain,(
% 0.20/0.44 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f83])).
% 0.20/0.44 thf(f83,plain,(
% 0.20/0.44 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f82])).
% 0.20/0.44 thf(f82,plain,(
% 0.20/0.44 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))) = msymmetric)),
% 0.20/0.44 inference(rectify,[],[f19])).
% 0.20/0.44 thf(f19,axiom,(
% 0.20/0.44 ((^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.20/0.44 thf(f122,plain,(
% 0.20/0.44 ((msymmetric @ rel_s5) = $true)),
% 0.20/0.44 inference(cnf_transformation,[],[f45])).
% 0.20/0.44 thf(f45,plain,(
% 0.20/0.44 ((msymmetric @ rel_s5) = $true)),
% 0.20/0.44 inference(fool_elimination,[],[f44])).
% 0.20/0.44 thf(f44,plain,(
% 0.20/0.44 (msymmetric @ rel_s5)),
% 0.20/0.44 inference(rectify,[],[f36])).
% 0.20/0.44 thf(f36,axiom,(
% 0.20/0.44 (msymmetric @ rel_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 0.20/0.44 thf(f285,plain,(
% 0.20/0.44 ( ! [X0 : $i] : ((((rel_s5 @ X0 @ sK2) => (rel_s5 @ X0 @ sK3)) = $true)) ) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f281])).
% 0.20/0.44 thf(f281,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (((((rel_s5 @ X0 @ sK2) & $true) => (rel_s5 @ X0 @ sK3)) = $true)) ) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f184,f275])).
% 0.20/0.44 thf(f275,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK2 @ sK3)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f271])).
% 0.20/0.44 thf(f271,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK2 @ sK3))) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f268])).
% 0.20/0.44 thf(f268,plain,(
% 0.20/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK3 @ Y0))))) | (~ (rel_s5 @ sK2 @ sK3)))) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f267])).
% 0.20/0.44 thf(f267,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK3)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f266])).
% 0.20/0.44 thf(f266,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f265])).
% 0.20/0.44 thf(f265,plain,(
% 0.20/0.44 ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | $false)) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f260,f263])).
% 0.20/0.44 thf(f184,plain,(
% 0.20/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X2 @ X3) & (rel_s5 @ X3 @ X1)) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f183])).
% 0.20/0.44 thf(f183,plain,(
% 0.20/0.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ X2 @ X1))) @ X3))) )),
% 0.20/0.44 inference(pi_clausification,[],[f182])).
% 0.20/0.44 thf(f182,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ X2 @ X1)))))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f181])).
% 0.20/0.44 thf(f181,plain,(
% 0.20/0.44 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y0 @ X1))))) @ X2))) )),
% 0.20/0.44 inference(pi_clausification,[],[f180])).
% 0.20/0.44 thf(f180,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y0 @ X1)))))))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f179])).
% 0.20/0.44 thf(f179,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 0.20/0.44 inference(pi_clausification,[],[f166])).
% 0.20/0.44 thf(f166,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y1 @ Y0)))))))))),
% 0.20/0.44 inference(beta_eta_normalization,[],[f160])).
% 0.20/0.44 thf(f160,plain,(
% 0.20/0.44 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) @ rel_s5) = $true)),
% 0.20/0.44 inference(definition_unfolding,[],[f132,f117])).
% 0.20/0.44 thf(f117,plain,(
% 0.20/0.44 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f89])).
% 0.20/0.44 thf(f89,plain,(
% 0.20/0.44 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f88])).
% 0.20/0.44 thf(f88,plain,(
% 0.20/0.44 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X2 @ X1)) => (X0 @ X2 @ X3)))) = mtransitive)),
% 0.20/0.44 inference(rectify,[],[f21])).
% 0.20/0.44 thf(f21,axiom,(
% 0.20/0.44 ((^[X6 : $i > $i > $o] : (! [X9,X8,X10] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.20/0.44 thf(f132,plain,(
% 0.20/0.44 ((mtransitive @ rel_s5) = $true)),
% 0.20/0.44 inference(cnf_transformation,[],[f110])).
% 0.20/0.44 thf(f110,plain,(
% 0.20/0.44 ((mtransitive @ rel_s5) = $true)),
% 0.20/0.44 inference(fool_elimination,[],[f109])).
% 0.20/0.44 thf(f109,plain,(
% 0.20/0.44 (mtransitive @ rel_s5)),
% 0.20/0.44 inference(rectify,[],[f35])).
% 0.20/0.44 thf(f35,axiom,(
% 0.20/0.44 (mtransitive @ rel_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.20/0.44 thf(f320,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = ((rel_s5 @ X0 @ sK3) => (rel_s5 @ X0 @ sK5)))) ) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f313])).
% 0.20/0.44 thf(f313,plain,(
% 0.20/0.44 ( ! [X0 : $i] : (($true = (((rel_s5 @ X0 @ sK3) & $true) => (rel_s5 @ X0 @ sK5)))) ) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f184,f307])).
% 0.20/0.44 thf(f307,plain,(
% 0.20/0.44 ($true = (rel_s5 @ sK3 @ sK5)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f290])).
% 0.20/0.44 thf(f290,plain,(
% 0.20/0.44 ($false = (~ (rel_s5 @ sK3 @ sK5))) | ~spl0_1),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f279])).
% 0.20/0.44 thf(f279,plain,(
% 0.20/0.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK5 @ Y0)))))) | (~ (rel_s5 @ sK3 @ sK5))) = $false) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f278])).
% 0.20/0.44 thf(f278,plain,(
% 0.20/0.44 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK3 @ Y0)))) @ sK5)) | ~spl0_1),
% 0.20/0.44 inference(sigma_clausification,[],[f274])).
% 0.20/0.44 thf(f274,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK3 @ Y0))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f273])).
% 0.20/0.44 thf(f273,plain,(
% 0.20/0.44 (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK3 @ Y0))))) | $false) = $false) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f268,f271])).
% 0.20/0.44 thf(f378,plain,(
% 0.20/0.44 ($true = (~ (rel_s5 @ sK4 @ sK5))) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f372])).
% 0.20/0.44 thf(f372,plain,(
% 0.20/0.44 (((rel_s5 @ sK4 @ sK5) => $false) = $true) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f173,f362])).
% 0.20/0.44 thf(f362,plain,(
% 0.20/0.44 ($false = (rel_s5 @ sK5 @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f333])).
% 0.20/0.44 thf(f333,plain,(
% 0.20/0.44 ((~ (rel_s5 @ sK5 @ sK4)) = $true) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f332])).
% 0.20/0.44 thf(f332,plain,(
% 0.20/0.44 ($true = ($false | (~ (rel_s5 @ sK5 @ sK4)))) | ~spl0_1),
% 0.20/0.44 inference(superposition,[],[f311,f331])).
% 0.20/0.44 thf(f331,plain,(
% 0.20/0.44 ($false = (p @ sK4)) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f330])).
% 0.20/0.44 thf(f330,plain,(
% 0.20/0.44 ($false = ((p @ sK4) | $false)) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f270,f328])).
% 0.20/0.44 thf(f311,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((p @ X1) | (~ (rel_s5 @ sK5 @ X1))) = $true)) ) | ~spl0_1),
% 0.20/0.44 inference(beta_eta_normalization,[],[f310])).
% 0.20/0.44 thf(f310,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK5 @ Y0)))) @ X1) = $true)) ) | ~spl0_1),
% 0.20/0.44 inference(pi_clausification,[],[f304])).
% 0.20/0.44 thf(f304,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK5 @ Y0)))))) | ~spl0_1),
% 0.20/0.44 inference(not_proxy_clausification,[],[f293])).
% 0.20/0.44 thf(f293,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK5 @ Y0)))))) = $false) | ~spl0_1),
% 0.20/0.44 inference(boolean_simplification,[],[f292])).
% 0.20/0.44 thf(f292,plain,(
% 0.20/0.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK5 @ Y0)))))) | $false) = $false) | ~spl0_1),
% 0.20/0.44 inference(backward_demodulation,[],[f279,f290])).
% 0.20/0.44 thf(f257,plain,(
% 0.20/0.44 ~spl0_2),
% 0.20/0.44 inference(avatar_contradiction_clause,[],[f256])).
% 0.20/0.44 thf(f256,plain,(
% 0.20/0.44 $false | ~spl0_2),
% 0.20/0.44 inference(trivial_inequality_removal,[],[f255])).
% 0.20/0.44 thf(f255,plain,(
% 0.20/0.44 ($false = $true) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f254])).
% 0.20/0.44 thf(f254,plain,(
% 0.20/0.44 ($true = (~ $true)) | ~spl0_2),
% 0.20/0.44 inference(forward_demodulation,[],[f247,f219])).
% 0.20/0.44 thf(f219,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) = $true) | ~spl0_2),
% 0.20/0.44 inference(not_proxy_clausification,[],[f216])).
% 0.20/0.44 thf(f216,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) = $false) | ~spl0_2),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f212])).
% 0.20/0.44 thf(f212,plain,(
% 0.20/0.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))))) = $false) | ~spl0_2),
% 0.20/0.44 inference(not_proxy_clausification,[],[f208])).
% 0.20/0.44 thf(f208,plain,(
% 0.20/0.44 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))))))) | ~spl0_2),
% 0.20/0.44 inference(avatar_component_clause,[],[f207])).
% 0.20/0.44 thf(f207,plain,(
% 0.20/0.44 spl0_2 <=> ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0)))))))))),
% 0.20/0.44 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.44 thf(f247,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) = $true) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f246])).
% 0.20/0.44 thf(f246,plain,(
% 0.20/0.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | $false) = $true) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f244])).
% 0.20/0.44 thf(f244,plain,(
% 0.20/0.44 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ $true)) = $true) | ~spl0_2),
% 0.20/0.44 inference(superposition,[],[f241,f169])).
% 0.20/0.44 thf(f169,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = (rel_s5 @ X1 @ X1))) )),
% 0.20/0.44 inference(beta_eta_normalization,[],[f168])).
% 0.20/0.44 thf(f168,plain,(
% 0.20/0.44 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s5 @ Y0 @ Y0)) @ X1))) )),
% 0.20/0.44 inference(pi_clausification,[],[f167])).
% 0.20/0.44 thf(f167,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: (rel_s5 @ Y0 @ Y0))) = $true)),
% 0.20/0.44 inference(beta_eta_normalization,[],[f161])).
% 0.20/0.44 thf(f161,plain,(
% 0.20/0.44 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s5) = $true)),
% 0.20/0.44 inference(definition_unfolding,[],[f145,f129])).
% 0.20/0.44 thf(f129,plain,(
% 0.20/0.44 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f62])).
% 0.20/0.44 thf(f62,plain,(
% 0.20/0.44 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.44 inference(fool_elimination,[],[f61])).
% 0.20/0.44 thf(f61,plain,(
% 0.20/0.44 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.20/0.44 inference(rectify,[],[f18])).
% 0.20/0.44 thf(f18,axiom,(
% 0.20/0.44 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.20/0.44 thf(f145,plain,(
% 0.20/0.44 ((mreflexive @ rel_s5) = $true)),
% 0.20/0.44 inference(cnf_transformation,[],[f104])).
% 0.20/0.44 thf(f104,plain,(
% 0.20/0.44 ((mreflexive @ rel_s5) = $true)),
% 0.20/0.44 inference(fool_elimination,[],[f103])).
% 0.20/0.44 thf(f103,plain,(
% 0.20/0.44 (mreflexive @ rel_s5)),
% 0.20/0.44 inference(rectify,[],[f34])).
% 0.20/0.44 thf(f34,axiom,(
% 0.20/0.44 (mreflexive @ rel_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.20/0.44 thf(f241,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ X1 @ Y0)))))) | (~ (rel_s5 @ sK2 @ X1))) = $true)) ) | ~spl0_2),
% 0.20/0.44 inference(beta_eta_normalization,[],[f239])).
% 0.20/0.44 thf(f239,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1) = $true)) ) | ~spl0_2),
% 0.20/0.44 inference(pi_clausification,[],[f236])).
% 0.20/0.44 thf(f236,plain,(
% 0.20/0.44 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f235])).
% 0.20/0.44 thf(f235,plain,(
% 0.20/0.44 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | $false)) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f234])).
% 0.20/0.44 thf(f234,plain,(
% 0.20/0.44 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ $true))) | ~spl0_2),
% 0.20/0.44 inference(superposition,[],[f228,f169])).
% 0.20/0.44 thf(f228,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ X1 @ Y0))))) | (~ (rel_s5 @ sK2 @ X1))) = $true)) ) | ~spl0_2),
% 0.20/0.44 inference(beta_eta_normalization,[],[f227])).
% 0.20/0.44 thf(f227,plain,(
% 0.20/0.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1) = $true)) ) | ~spl0_2),
% 0.20/0.44 inference(pi_clausification,[],[f222])).
% 0.20/0.44 thf(f222,plain,(
% 0.20/0.44 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) = $true) | ~spl0_2),
% 0.20/0.44 inference(not_proxy_clausification,[],[f218])).
% 0.20/0.44 thf(f218,plain,(
% 0.20/0.44 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))))) | ~spl0_2),
% 0.20/0.44 inference(boolean_simplification,[],[f217])).
% 0.20/0.44 thf(f217,plain,(
% 0.20/0.44 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))))) = $false) | ~spl0_2),
% 0.20/0.44 inference(backward_demodulation,[],[f212,f216])).
% 0.20/0.44 thf(f209,plain,(
% 0.20/0.44 spl0_1 | spl0_2),
% 0.20/0.44 inference(avatar_split_clause,[],[f202,f207,f204])).
% 0.20/0.44 thf(f202,plain,(
% 0.20/0.44 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))))))) | ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))))))),
% 0.20/0.44 inference(binary_proxy_clausification,[],[f199])).
% 0.20/0.44 thf(f199,plain,(
% 0.20/0.44 (((~ ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))))))) = $true)),
% 0.20/0.44 inference(not_proxy_clausification,[],[f198])).
% 0.20/0.44 thf(f198,plain,(
% 0.20/0.44 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (rel_s5 @ sK2 @ Y0)))))))))) = $false)),
% 0.20/0.44 inference(beta_eta_normalization,[],[f197])).
% 0.20/0.44 thf(f197,plain,(
% 0.20/0.44 (((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))) @ sK2) = $false)),
% 0.20/0.44 inference(sigma_clausification,[],[f194])).
% 0.20/0.44 thf(f194,plain,(
% 0.20/0.44 ($false = (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))))),
% 0.20/0.44 inference(not_proxy_clausification,[],[f164])).
% 0.20/0.44 thf(f164,plain,(
% 0.20/0.44 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.20/0.44 inference(boolean_simplification,[],[f163])).
% 0.20/0.44 thf(f163,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))) = $true)),
% 0.20/0.44 inference(boolean_simplification,[],[f162])).
% 0.20/0.44 thf(f162,plain,(
% 0.20/0.44 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((p @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))) | (~ (rel_s5 @ Y1 @ Y2))))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))) = $true)),
% 0.20/0.44 inference(beta_eta_normalization,[],[f158])).
% 0.20/0.44 thf(f158,plain,(
% 0.20/0.44 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ p))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ p)))) = $true)),
% 0.20/0.44 inference(definition_unfolding,[],[f113,f141,f151,f157,f157,f127,f127])).
% 0.20/0.44 thf(f127,plain,(
% 0.20/0.44 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f102])).
% 0.20/0.44 thf(f102,plain,(
% 0.20/0.44 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f101])).
% 0.20/0.44 thf(f101,plain,(
% 0.20/0.44 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))) = mbox_s5)),
% 0.20/0.44 inference(rectify,[],[f32])).
% 0.20/0.44 thf(f32,axiom,(
% 0.20/0.44 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))) = mbox_s5)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.20/0.44 thf(f157,plain,(
% 0.20/0.44 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.20/0.44 inference(definition_unfolding,[],[f144,f147,f127,f147])).
% 0.20/0.44 thf(f147,plain,(
% 0.20/0.44 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f47])).
% 0.20/0.44 thf(f47,plain,(
% 0.20/0.44 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.44 inference(fool_elimination,[],[f46])).
% 0.20/0.44 thf(f46,plain,(
% 0.20/0.44 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.44 inference(rectify,[],[f3])).
% 0.20/0.44 thf(f3,axiom,(
% 0.20/0.44 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.44 thf(f144,plain,(
% 0.20/0.44 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f64])).
% 0.20/0.44 thf(f64,plain,(
% 0.20/0.44 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.44 inference(fool_elimination,[],[f63])).
% 0.20/0.44 thf(f63,plain,(
% 0.20/0.44 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.20/0.44 inference(rectify,[],[f33])).
% 0.20/0.44 thf(f33,axiom,(
% 0.20/0.44 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.20/0.44 thf(f151,plain,(
% 0.20/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.20/0.44 inference(definition_unfolding,[],[f120,f148,f149,f149])).
% 0.20/0.44 thf(f149,plain,(
% 0.20/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.44 inference(definition_unfolding,[],[f119,f126,f147])).
% 0.20/0.44 thf(f126,plain,(
% 0.20/0.44 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f79])).
% 0.20/0.44 thf(f79,plain,(
% 0.20/0.44 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.44 inference(fool_elimination,[],[f78])).
% 0.20/0.44 thf(f78,plain,(
% 0.20/0.44 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.44 inference(rectify,[],[f4])).
% 0.20/0.44 thf(f4,axiom,(
% 0.20/0.44 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.44 thf(f119,plain,(
% 0.20/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f81])).
% 0.20/0.44 thf(f81,plain,(
% 0.20/0.44 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.44 inference(fool_elimination,[],[f80])).
% 0.20/0.44 thf(f80,plain,(
% 0.20/0.44 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.44 inference(rectify,[],[f6])).
% 0.20/0.44 thf(f6,axiom,(
% 0.20/0.44 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.44 thf(f148,plain,(
% 0.20/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.44 inference(definition_unfolding,[],[f115,f147,f126,f147,f147])).
% 0.20/0.44 thf(f115,plain,(
% 0.20/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f98])).
% 0.20/0.44 thf(f98,plain,(
% 0.20/0.44 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.44 inference(fool_elimination,[],[f97])).
% 0.20/0.44 thf(f97,plain,(
% 0.20/0.44 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.44 inference(rectify,[],[f5])).
% 0.20/0.44 thf(f5,axiom,(
% 0.20/0.44 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.44 thf(f120,plain,(
% 0.20/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.44 inference(cnf_transformation,[],[f58])).
% 0.20/0.44 thf(f58,plain,(
% 0.20/0.44 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.44 inference(fool_elimination,[],[f57])).
% 0.20/0.44 thf(f57,plain,(
% 0.20/0.44 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.20/0.44 inference(rectify,[],[f8])).
% 0.20/0.44 thf(f8,axiom,(
% 0.20/0.44 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.20/0.44 thf(f141,plain,(
% 0.20/0.44 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f60])).
% 0.20/0.44 thf(f60,plain,(
% 0.20/0.44 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.44 inference(fool_elimination,[],[f59])).
% 0.20/0.44 thf(f59,plain,(
% 0.20/0.44 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.44 inference(rectify,[],[f28])).
% 0.20/0.44 thf(f28,axiom,(
% 0.20/0.44 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.44 thf(f113,plain,(
% 0.20/0.44 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p))) @ (mbox_s5 @ p)))))),
% 0.20/0.44 inference(cnf_transformation,[],[f96])).
% 0.20/0.44 thf(f96,plain,(
% 0.20/0.44 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p))) @ (mbox_s5 @ p)))))),
% 0.20/0.44 inference(fool_elimination,[],[f95])).
% 0.20/0.44 thf(f95,plain,(
% 0.20/0.44 ~(mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p))) @ (mbox_s5 @ p)))),
% 0.20/0.44 inference(rectify,[],[f38])).
% 0.20/0.44 thf(f38,negated_conjecture,(
% 0.20/0.44 ~(mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p))) @ (mbox_s5 @ p)))),
% 0.20/0.44 inference(negated_conjecture,[],[f37])).
% 0.20/0.44 thf(f37,conjecture,(
% 0.20/0.44 (mvalid @ (mequiv @ (mdia_s5 @ (mdia_s5 @ (mbox_s5 @ p))) @ (mbox_s5 @ p)))),
% 0.20/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.20/0.44 % SZS output end Proof for theBenchmark
% 0.20/0.44 % (9701)------------------------------
% 0.20/0.44 % (9701)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (9701)Termination reason: Refutation
% 0.20/0.44
% 0.20/0.44 % (9701)Memory used [KB]: 6012
% 0.20/0.44 % (9701)Time elapsed: 0.044 s
% 0.20/0.44 % (9701)Instructions burned: 55 (million)
% 0.20/0.44 % (9701)------------------------------
% 0.20/0.44 % (9701)------------------------------
% 0.20/0.44 % (9689)Success in time 0.077 s
% 0.20/0.44 % Vampire---4.8 exiting
%------------------------------------------------------------------------------