TSTP Solution File: SEU461^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU461^1 : TPTP v8.2.0. Released v3.6.0.
% 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:49:00 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU461^1 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.14 % 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
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 16:54:08 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (6569)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (6565)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)
% 0.21/0.37 % (6563)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (6564)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)
% 0.21/0.37 % (6566)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (6567)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)
% 0.21/0.37 % (6568)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)
% 0.21/0.37 % (6566)Instruction limit reached!
% 0.21/0.37 % (6566)------------------------------
% 0.21/0.37 % (6566)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (6566)Termination reason: Unknown
% 0.21/0.37 % (6566)Termination phase: shuffling
% 0.21/0.37 % (6567)Instruction limit reached!
% 0.21/0.37 % (6567)------------------------------
% 0.21/0.37 % (6567)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37
% 0.21/0.37 % (6566)Memory used [KB]: 1023
% 0.21/0.37 % (6566)Time elapsed: 0.003 s
% 0.21/0.37 % (6566)Instructions burned: 2 (million)
% 0.21/0.37 % (6566)------------------------------
% 0.21/0.37 % (6566)------------------------------
% 0.21/0.37 % (6567)Termination reason: Unknown
% 0.21/0.37 % (6567)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (6567)Memory used [KB]: 1023
% 0.21/0.37 % (6567)Time elapsed: 0.003 s
% 0.21/0.37 % (6567)Instructions burned: 2 (million)
% 0.21/0.37 % (6567)------------------------------
% 0.21/0.37 % (6567)------------------------------
% 0.21/0.37 % (6564)Instruction limit reached!
% 0.21/0.37 % (6564)------------------------------
% 0.21/0.37 % (6564)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (6564)Termination reason: Unknown
% 0.21/0.37 % (6564)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (6564)Memory used [KB]: 1023
% 0.21/0.37 % (6564)Time elapsed: 0.004 s
% 0.21/0.37 % (6564)Instructions burned: 4 (million)
% 0.21/0.37 % (6564)------------------------------
% 0.21/0.37 % (6564)------------------------------
% 0.21/0.37 % (6568)Refutation not found, incomplete strategy
% 0.21/0.37 % (6568)------------------------------
% 0.21/0.37 % (6568)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (6568)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37
% 0.21/0.37
% 0.21/0.37 % (6568)Memory used [KB]: 5628
% 0.21/0.37 % (6568)Time elapsed: 0.006 s
% 0.21/0.37 % (6568)Instructions burned: 7 (million)
% 0.21/0.37 % (6568)------------------------------
% 0.21/0.37 % (6568)------------------------------
% 0.21/0.38 % (6569)Instruction limit reached!
% 0.21/0.38 % (6569)------------------------------
% 0.21/0.38 % (6569)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (6569)Termination reason: Unknown
% 0.21/0.38 % (6569)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (6569)Memory used [KB]: 5628
% 0.21/0.38 % (6569)Time elapsed: 0.010 s
% 0.21/0.38 % (6569)Instructions burned: 19 (million)
% 0.21/0.38 % (6569)------------------------------
% 0.21/0.38 % (6569)------------------------------
% 0.21/0.38 % (6565)Instruction limit reached!
% 0.21/0.38 % (6565)------------------------------
% 0.21/0.38 % (6565)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (6565)Termination reason: Unknown
% 0.21/0.38 % (6565)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (6565)Memory used [KB]: 5756
% 0.21/0.38 % (6565)Time elapsed: 0.017 s
% 0.21/0.38 % (6565)Instructions burned: 27 (million)
% 0.21/0.38 % (6565)------------------------------
% 0.21/0.38 % (6565)------------------------------
% 0.21/0.38 % (6573)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)
% 0.21/0.38 % (6570)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)
% 0.21/0.38 % (6571)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)
% 0.21/0.38 % (6573)Instruction limit reached!
% 0.21/0.38 % (6573)------------------------------
% 0.21/0.38 % (6573)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (6573)Termination reason: Unknown
% 0.21/0.38 % (6573)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (6573)Memory used [KB]: 1023
% 0.21/0.38 % (6573)Time elapsed: 0.003 s
% 0.21/0.38 % (6573)Instructions burned: 3 (million)
% 0.21/0.38 % (6573)------------------------------
% 0.21/0.38 % (6573)------------------------------
% 0.21/0.38 % (6572)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)
% 0.21/0.38 % (6570)Instruction limit reached!
% 0.21/0.38 % (6570)------------------------------
% 0.21/0.38 % (6570)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6570)Termination reason: Unknown
% 0.21/0.39 % (6570)Termination phase: shuffling
% 0.21/0.39
% 0.21/0.39 % (6570)Memory used [KB]: 1023
% 0.21/0.39 % (6570)Time elapsed: 0.003 s
% 0.21/0.39 % (6570)Instructions burned: 3 (million)
% 0.21/0.39 % (6570)------------------------------
% 0.21/0.39 % (6570)------------------------------
% 0.21/0.39 % (6575)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.39 % (6574)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)
% 0.21/0.39 % (6572)Instruction limit reached!
% 0.21/0.39 % (6572)------------------------------
% 0.21/0.39 % (6572)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6572)Termination reason: Unknown
% 0.21/0.39 % (6572)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (6572)Memory used [KB]: 5628
% 0.21/0.39 % (6572)Time elapsed: 0.009 s
% 0.21/0.39 % (6572)Instructions burned: 15 (million)
% 0.21/0.39 % (6572)------------------------------
% 0.21/0.39 % (6572)------------------------------
% 0.21/0.39 % (6575)Instruction limit reached!
% 0.21/0.39 % (6575)------------------------------
% 0.21/0.39 % (6575)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (6575)Termination reason: Unknown
% 0.21/0.39 % (6575)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (6575)Memory used [KB]: 1023
% 0.21/0.39 % (6575)Time elapsed: 0.005 s
% 0.21/0.39 % (6575)Instructions burned: 8 (million)
% 0.21/0.39 % (6575)------------------------------
% 0.21/0.39 % (6575)------------------------------
% 0.21/0.40 % (6576)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.40 % (6578)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)
% 0.21/0.40 % (6577)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)
% 0.21/0.40 % (6578)Instruction limit reached!
% 0.21/0.40 % (6578)------------------------------
% 0.21/0.40 % (6578)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (6577)Instruction limit reached!
% 0.21/0.40 % (6577)------------------------------
% 0.21/0.40 % (6577)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (6577)Termination reason: Unknown
% 0.21/0.40 % (6577)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (6577)Memory used [KB]: 1023
% 0.21/0.40 % (6577)Time elapsed: 0.003 s
% 0.21/0.40 % (6577)Instructions burned: 3 (million)
% 0.21/0.40 % (6577)------------------------------
% 0.21/0.40 % (6577)------------------------------
% 0.21/0.40 % (6578)Termination reason: Unknown
% 0.21/0.40 % (6578)Termination phase: shuffling
% 0.21/0.40
% 0.21/0.40 % (6578)Memory used [KB]: 1023
% 0.21/0.40 % (6578)Time elapsed: 0.003 s
% 0.21/0.40 % (6578)Instructions burned: 3 (million)
% 0.21/0.40 % (6578)------------------------------
% 0.21/0.40 % (6578)------------------------------
% 0.21/0.40 % (6571)Instruction limit reached!
% 0.21/0.40 % (6571)------------------------------
% 0.21/0.40 % (6571)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (6571)Termination reason: Unknown
% 0.21/0.40 % (6571)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (6571)Memory used [KB]: 5756
% 0.21/0.40 % (6571)Time elapsed: 0.022 s
% 0.21/0.40 % (6571)Instructions burned: 37 (million)
% 0.21/0.40 % (6571)------------------------------
% 0.21/0.40 % (6571)------------------------------
% 0.21/0.41 % (6579)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)
% 0.21/0.41 % (6576)Instruction limit reached!
% 0.21/0.41 % (6576)------------------------------
% 0.21/0.41 % (6576)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6576)Termination reason: Unknown
% 0.21/0.41 % (6576)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (6576)Memory used [KB]: 5756
% 0.21/0.41 % (6576)Time elapsed: 0.011 s
% 0.21/0.41 % (6576)Instructions burned: 16 (million)
% 0.21/0.41 % (6576)------------------------------
% 0.21/0.41 % (6576)------------------------------
% 0.21/0.41 % (6580)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)
% 0.21/0.41 % (6579)Instruction limit reached!
% 0.21/0.41 % (6579)------------------------------
% 0.21/0.41 % (6579)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6579)Termination reason: Unknown
% 0.21/0.41 % (6579)Termination phase: Function definition elimination
% 0.21/0.41
% 0.21/0.41 % (6579)Memory used [KB]: 1023
% 0.21/0.41 % (6579)Time elapsed: 0.006 s
% 0.21/0.41 % (6579)Instructions burned: 9 (million)
% 0.21/0.41 % (6580)Instruction limit reached!
% 0.21/0.41 % (6580)------------------------------
% 0.21/0.41 % (6580)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (6580)Termination reason: Unknown
% 0.21/0.41 % (6580)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (6580)Memory used [KB]: 1023
% 0.21/0.41 % (6580)Time elapsed: 0.003 s
% 0.21/0.41 % (6580)Instructions burned: 4 (million)
% 0.21/0.41 % (6580)------------------------------
% 0.21/0.41 % (6580)------------------------------
% 0.21/0.41 % (6579)------------------------------
% 0.21/0.41 % (6579)------------------------------
% 0.21/0.42 % (6581)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.42 % (6582)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)
% 0.21/0.42 % (6581)Instruction limit reached!
% 0.21/0.42 % (6581)------------------------------
% 0.21/0.42 % (6581)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (6581)Termination reason: Unknown
% 0.21/0.42 % (6581)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (6581)Memory used [KB]: 1023
% 0.21/0.42 % (6581)Time elapsed: 0.004 s
% 0.21/0.42 % (6581)Instructions burned: 6 (million)
% 0.21/0.42 % (6581)------------------------------
% 0.21/0.42 % (6581)------------------------------
% 0.21/0.42 % (6583)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.42 % (6584)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.42 % (6584)Instruction limit reached!
% 0.21/0.42 % (6584)------------------------------
% 0.21/0.42 % (6584)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (6584)Termination reason: Unknown
% 0.21/0.42 % (6584)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (6584)Memory used [KB]: 1023
% 0.21/0.42 % (6584)Time elapsed: 0.005 s
% 0.21/0.42 % (6584)Instructions burned: 6 (million)
% 0.21/0.42 % (6584)------------------------------
% 0.21/0.42 % (6584)------------------------------
% 0.21/0.43 % (6586)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)
% 0.21/0.43 % (6585)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)
% 0.21/0.43 % (6574)First to succeed.
% 0.21/0.43 % (6582)Instruction limit reached!
% 0.21/0.43 % (6582)------------------------------
% 0.21/0.43 % (6582)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (6582)Termination reason: Unknown
% 0.21/0.43 % (6582)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (6582)Memory used [KB]: 5756
% 0.21/0.43 % (6582)Time elapsed: 0.013 s
% 0.21/0.43 % (6582)Instructions burned: 19 (million)
% 0.21/0.43 % (6582)------------------------------
% 0.21/0.43 % (6582)------------------------------
% 0.21/0.43 % (6587)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.43 % (6585)Refutation not found, incomplete strategy
% 0.21/0.43 % (6585)------------------------------
% 0.21/0.43 % (6585)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (6585)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.43
% 0.21/0.43
% 0.21/0.43 % (6585)Memory used [KB]: 5628
% 0.21/0.43 % (6585)Time elapsed: 0.006 s
% 0.21/0.43 % (6585)Instructions burned: 10 (million)
% 0.21/0.43 % (6585)------------------------------
% 0.21/0.43 % (6585)------------------------------
% 0.21/0.43 % (6587)Instruction limit reached!
% 0.21/0.43 % (6587)------------------------------
% 0.21/0.43 % (6587)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (6587)Termination reason: Unknown
% 0.21/0.43 % (6587)Termination phase: Function definition elimination
% 0.21/0.43
% 0.21/0.43 % (6587)Memory used [KB]: 1023
% 0.21/0.43 % (6587)Time elapsed: 0.003 s
% 0.21/0.43 % (6587)Instructions burned: 8 (million)
% 0.21/0.43 % (6587)------------------------------
% 0.21/0.43 % (6587)------------------------------
% 0.21/0.43 % (6574)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% 0.21/0.43 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.21/0.43 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.43 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.21/0.43 thf(func_def_49, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.43 thf(func_def_50, type, sK2: $i > $i > $o).
% 0.21/0.43 thf(func_def_54, type, sK6: $i > $i > $o).
% 0.21/0.43 thf(f302,plain,(
% 0.21/0.43 $false),
% 0.21/0.43 inference(trivial_inequality_removal,[],[f301])).
% 0.21/0.43 thf(f301,plain,(
% 0.21/0.43 ($true = $false)),
% 0.21/0.43 inference(forward_demodulation,[],[f300,f160])).
% 0.21/0.43 thf(f160,plain,(
% 0.21/0.43 ((sK6 @ sK4 @ sK3) = $false)),
% 0.21/0.43 inference(boolean_simplification,[],[f159])).
% 0.21/0.43 thf(f159,plain,(
% 0.21/0.43 (($true => (sK6 @ sK4 @ sK3)) = $false)),
% 0.21/0.43 inference(backward_demodulation,[],[f156,f158])).
% 0.21/0.43 thf(f158,plain,(
% 0.21/0.43 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))))) = $true)),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f156])).
% 0.21/0.43 thf(f156,plain,(
% 0.21/0.43 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))))) => (sK6 @ sK4 @ sK3)) = $false)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f155])).
% 0.21/0.43 thf(f155,plain,(
% 0.21/0.43 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))) @ sK6) = $false)),
% 0.21/0.43 inference(sigma_clausification,[],[f152])).
% 0.21/0.43 thf(f152,plain,(
% 0.21/0.43 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3)))) = $false)),
% 0.21/0.43 inference(boolean_simplification,[],[f151])).
% 0.21/0.43 thf(f151,plain,(
% 0.21/0.43 (($true => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))))) = $false)),
% 0.21/0.43 inference(backward_demodulation,[],[f148,f150])).
% 0.21/0.43 thf(f150,plain,(
% 0.21/0.43 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK5 @ sK3))))) = $true)),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f148])).
% 0.21/0.43 thf(f148,plain,(
% 0.21/0.43 ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK5)))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK5 @ sK3))))) => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))))) = $false)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f147])).
% 0.21/0.43 thf(f147,plain,(
% 0.21/0.43 (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3))))) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ sK3)))))) @ sK5) = $false)),
% 0.21/0.43 inference(sigma_clausification,[],[f146])).
% 0.21/0.43 thf(f146,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3))))) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ sK3))))))) = $false)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f145])).
% 0.21/0.43 thf(f145,plain,(
% 0.21/0.43 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ sK3))))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ sK3)))))))) @ sK4) = $false)),
% 0.21/0.43 inference(sigma_clausification,[],[f144])).
% 0.21/0.43 thf(f144,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ Y1)))) & (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ sK3))))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (Y2 @ Y5 @ Y3)) => (Y2 @ Y4 @ Y3)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y0 @ sK3))))))))) = $false)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f143])).
% 0.21/0.43 thf(f143,plain,(
% 0.21/0.43 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y0)))))))))) @ sK3) = $false)),
% 0.21/0.43 inference(sigma_clausification,[],[f142])).
% 0.21/0.43 thf(f142,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2)))) & (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y0))))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y5 @ Y6) & (Y3 @ Y6 @ Y4)) => (Y3 @ Y5 @ Y4)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y0))))))))))) = $false)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f141])).
% 0.21/0.43 thf(f141,plain,(
% 0.21/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3)))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1)))))))))))) @ sK2) = $false)),
% 0.21/0.43 inference(sigma_clausification,[],[f138])).
% 0.21/0.43 thf(f138,plain,(
% 0.21/0.43 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3)))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1))))))))))))) = $false)),
% 0.21/0.43 inference(not_proxy_clausification,[],[f137])).
% 0.21/0.43 thf(f137,plain,(
% 0.21/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y3)))) & (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y1))))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5)))))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y2 @ Y1)))))))))))))) = $true)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f136])).
% 0.21/0.43 thf(f136,plain,(
% 0.21/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y8) & (Y5 @ Y8 @ Y6)) => (Y5 @ Y7 @ Y6))))))))) @ Y4) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7))))))))) @ Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0))))) = $true)),
% 0.21/0.43 inference(definition_unfolding,[],[f114,f111,f123])).
% 0.21/0.43 thf(f123,plain,(
% 0.21/0.43 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y6 @ Y7) & (Y4 @ Y7 @ Y5)) => (Y4 @ Y6 @ Y5))))))))) @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.21/0.43 inference(definition_unfolding,[],[f108,f111,f120])).
% 0.21/0.43 thf(f120,plain,(
% 0.21/0.43 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.21/0.43 inference(cnf_transformation,[],[f34])).
% 0.21/0.43 thf(f34,plain,(
% 0.21/0.43 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))),
% 0.21/0.43 inference(fool_elimination,[],[f33])).
% 0.21/0.43 thf(f33,plain,(
% 0.21/0.43 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))) = subrel)),
% 0.21/0.43 inference(rectify,[],[f1])).
% 0.21/0.43 thf(f1,axiom,(
% 0.21/0.43 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))) = subrel)),
% 0.21/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subrel)).
% 0.21/0.43 thf(f108,plain,(
% 0.21/0.43 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.21/0.43 inference(cnf_transformation,[],[f71])).
% 0.21/0.43 thf(f71,plain,(
% 0.21/0.43 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.21/0.43 inference(fool_elimination,[],[f70])).
% 0.21/0.43 thf(f70,plain,(
% 0.21/0.43 (tc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))))),
% 0.21/0.43 inference(rectify,[],[f14])).
% 0.21/0.43 thf(f14,axiom,(
% 0.21/0.43 (tc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)))))),
% 0.21/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure)).
% 0.21/0.43 thf(f111,plain,(
% 0.21/0.43 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.21/0.43 inference(cnf_transformation,[],[f57])).
% 0.21/0.43 thf(f57,plain,(
% 0.21/0.43 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.21/0.43 inference(fool_elimination,[],[f56])).
% 0.21/0.43 thf(f56,plain,(
% 0.21/0.43 (trans = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X2 @ X1)) => (X0 @ X2 @ X3)))))),
% 0.21/0.43 inference(rectify,[],[f13])).
% 0.21/0.43 thf(f13,axiom,(
% 0.21/0.43 (trans = (^[X0 : $i > $i > $o] : (! [X3,X2,X5] : (((X0 @ X3 @ X5) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X5)))))),
% 0.21/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive)).
% 0.21/0.43 thf(f114,plain,(
% 0.21/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (trans @ (tc @ Y0))))) = $true)),
% 0.21/0.43 inference(cnf_transformation,[],[f55])).
% 0.21/0.43 thf(f55,plain,(
% 0.21/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (trans @ (tc @ Y0))))) = $true)),
% 0.21/0.43 inference(fool_elimination,[],[f54])).
% 0.21/0.43 thf(f54,plain,(
% 0.21/0.43 ~! [X0 : $i > $i > $o] : (trans @ (tc @ X0))),
% 0.21/0.43 inference(rectify,[],[f31])).
% 0.21/0.43 thf(f31,negated_conjecture,(
% 0.21/0.43 ~! [X0 : $i > $i > $o] : (trans @ (tc @ X0))),
% 0.21/0.43 inference(negated_conjecture,[],[f30])).
% 0.21/0.43 thf(f30,conjecture,(
% 0.21/0.43 ! [X0 : $i > $i > $o] : (trans @ (tc @ X0))),
% 0.21/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_closure_is_transitive)).
% 0.21/0.43 thf(f300,plain,(
% 0.21/0.43 ((sK6 @ sK4 @ sK3) = $true)),
% 0.21/0.43 inference(boolean_simplification,[],[f296])).
% 0.21/0.43 thf(f296,plain,(
% 0.21/0.43 (($true => (sK6 @ sK4 @ sK3)) = $true)),
% 0.21/0.43 inference(superposition,[],[f257,f203])).
% 0.21/0.43 thf(f203,plain,(
% 0.21/0.43 ((sK6 @ sK7 @ sK3) = $true)),
% 0.21/0.43 inference(boolean_simplification,[],[f202])).
% 0.21/0.43 thf(f202,plain,(
% 0.21/0.43 (($true => (sK6 @ sK7 @ sK3)) = $true)),
% 0.21/0.43 inference(forward_demodulation,[],[f201,f162])).
% 0.21/0.43 thf(f162,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) = $true)),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f158])).
% 0.21/0.43 thf(f201,plain,(
% 0.21/0.43 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) => (sK6 @ sK7 @ sK3)))),
% 0.21/0.43 inference(boolean_simplification,[],[f200])).
% 0.21/0.43 thf(f200,plain,(
% 0.21/0.43 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) & $true) => (sK6 @ sK7 @ sK3)) = $true)),
% 0.21/0.43 inference(superposition,[],[f194,f164])).
% 0.21/0.43 thf(f164,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0)))))) = $true)),
% 0.21/0.43 inference(boolean_simplification,[],[f163])).
% 0.21/0.43 thf(f163,plain,(
% 0.21/0.43 ($true = ($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK6 @ Y1 @ Y0))))))))),
% 0.21/0.43 inference(backward_demodulation,[],[f158,f162])).
% 0.21/0.43 thf(f194,plain,(
% 0.21/0.43 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y1 @ Y2) & (X1 @ Y2 @ Y0)) => (X1 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK7 @ sK3)))) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f193])).
% 0.21/0.43 thf(f193,plain,(
% 0.21/0.43 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK7 @ sK3))) @ X1) = $true)) )),
% 0.21/0.43 inference(pi_clausification,[],[f174])).
% 0.21/0.43 thf(f174,plain,(
% 0.21/0.43 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK7 @ sK3)))) = $true)),
% 0.21/0.43 inference(binary_proxy_clausification,[],[f169])).
% 0.21/0.43 thf(f169,plain,(
% 0.21/0.43 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK7 @ sK3))))) = $true)),
% 0.21/0.43 inference(not_proxy_clausification,[],[f166])).
% 0.21/0.43 thf(f166,plain,(
% 0.21/0.43 ((~ ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK7)))) & (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK7 @ sK3)))))) = $false)),
% 0.21/0.43 inference(beta_eta_normalization,[],[f165])).
% 0.21/0.43 thf(f165,plain,(
% 0.21/0.43 (((^[Y0 : $i]: (~ ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3))))))) @ sK7) = $false)),
% 0.21/0.43 inference(sigma_clausification,[],[f154])).
% 0.21/0.43 thf(f154,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (~ ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3)))))))) = $false)),
% 0.21/0.43 inference(boolean_simplification,[],[f153])).
% 0.21/0.43 thf(f153,plain,(
% 0.21/0.43 ((!! @ $i @ (^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ sK4 @ Y0)))) & (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y4) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3))))) => $false))) = $false)),
% 0.21/0.43 inference(backward_demodulation,[],[f146,f152])).
% 0.21/0.43 thf(f257,plain,(
% 0.21/0.43 ( ! [X0 : $i] : ((((sK6 @ sK7 @ X0) => (sK6 @ sK4 @ X0)) = $true)) )),
% 0.21/0.43 inference(boolean_simplification,[],[f251])).
% 0.21/0.43 thf(f251,plain,(
% 0.21/0.43 ( ! [X0 : $i] : (((($true & (sK6 @ sK7 @ X0)) => (sK6 @ sK4 @ X0)) = $true)) )),
% 0.21/0.43 inference(superposition,[],[f240,f190])).
% 0.21/0.43 thf(f190,plain,(
% 0.21/0.43 ((sK6 @ sK4 @ sK7) = $true)),
% 0.21/0.43 inference(boolean_simplification,[],[f189])).
% 0.21/0.43 thf(f189,plain,(
% 0.21/0.43 (($true => (sK6 @ sK4 @ sK7)) = $true)),
% 0.21/0.43 inference(forward_demodulation,[],[f188,f162])).
% 0.21/0.43 thf(f188,plain,(
% 0.21/0.43 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) => (sK6 @ sK4 @ sK7)) = $true)),
% 0.21/0.43 inference(boolean_simplification,[],[f187])).
% 0.21/0.43 thf(f187,plain,(
% 0.21/0.43 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0)))))))) & $true) => (sK6 @ sK4 @ sK7)) = $true)),
% 0.21/0.43 inference(superposition,[],[f182,f164])).
% 0.21/0.43 thf(f182,plain,(
% 0.21/0.43 ( ! [X1 : $i > $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y1 @ Y2) & (X1 @ Y2 @ Y0)) => (X1 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK4 @ sK7)) = $true)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f181])).
% 0.21/0.43 thf(f181,plain,(
% 0.21/0.43 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK7))) @ X1) = $true)) )),
% 0.21/0.43 inference(pi_clausification,[],[f177])).
% 0.21/0.43 thf(f177,plain,(
% 0.21/0.43 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK7)))) = $true)),
% 0.21/0.43 inference(boolean_simplification,[],[f176])).
% 0.21/0.43 thf(f176,plain,(
% 0.21/0.43 ($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK7)))) & $true))),
% 0.21/0.43 inference(backward_demodulation,[],[f169,f174])).
% 0.21/0.43 thf(f240,plain,(
% 0.21/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK6 @ X2 @ X3) & (sK6 @ X3 @ X1)) => (sK6 @ X2 @ X1)) = $true)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f239])).
% 0.21/0.43 thf(f239,plain,(
% 0.21/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK6 @ X2 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ X2 @ X1))) @ X3))) )),
% 0.21/0.43 inference(pi_clausification,[],[f225])).
% 0.21/0.43 thf(f225,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK6 @ X2 @ Y0) & (sK6 @ Y0 @ X1)) => (sK6 @ X2 @ X1)))))) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f224])).
% 0.21/0.43 thf(f224,plain,(
% 0.21/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ X1)) => (sK6 @ Y0 @ X1))))) @ X2) = $true)) )),
% 0.21/0.43 inference(pi_clausification,[],[f217])).
% 0.21/0.43 thf(f217,plain,(
% 0.21/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK6 @ Y0 @ Y1) & (sK6 @ Y1 @ X1)) => (sK6 @ Y0 @ X1)))))) = $true)) )),
% 0.21/0.43 inference(beta_eta_normalization,[],[f212])).
% 0.21/0.43 thf(f212,plain,(
% 0.21/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK6 @ Y1 @ Y2) & (sK6 @ Y2 @ Y0)) => (sK6 @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 0.21/0.43 inference(pi_clausification,[],[f162])).
% 0.21/0.43 % SZS output end Proof for theBenchmark
% 0.21/0.43 % (6574)------------------------------
% 0.21/0.43 % (6574)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (6574)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (6574)Memory used [KB]: 6012
% 0.21/0.43 % (6574)Time elapsed: 0.063 s
% 0.21/0.43 % (6574)Instructions burned: 59 (million)
% 0.21/0.43 % (6574)------------------------------
% 0.21/0.43 % (6574)------------------------------
% 0.21/0.43 % (6562)Success in time 0.083 s
% 0.21/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------