TSTP Solution File: SEV238^5 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV238^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n027.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 04:12:29 EDT 2024
% Result : Theorem 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV238^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % 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 : n027.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 19:06:07 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH0_THM_NEQ_NAR problem
% 0.14/0.34 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
% 0.21/0.36 % (27893)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)
% 0.21/0.36 % (27891)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)
% 0.21/0.36 % (27889)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (27887)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)
% 0.21/0.36 % (27886)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.36 % (27888)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)
% 0.21/0.36 % (27889)Instruction limit reached!
% 0.21/0.36 % (27889)------------------------------
% 0.21/0.36 % (27889)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.36 % (27889)Termination reason: Unknown
% 0.21/0.36 % (27889)Termination phase: Property scanning
% 0.21/0.36
% 0.21/0.36 % (27889)Memory used [KB]: 1023
% 0.21/0.36 % (27890)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)
% 0.21/0.36 % (27889)Time elapsed: 0.003 s
% 0.21/0.36 % (27889)Instructions burned: 2 (million)
% 0.21/0.36 % (27889)------------------------------
% 0.21/0.36 % (27889)------------------------------
% 0.21/0.36 % (27893)Instruction limit reached!
% 0.21/0.36 % (27893)------------------------------
% 0.21/0.36 % (27893)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.36 % (27893)Termination reason: Unknown
% 0.21/0.36 % (27893)Termination phase: Property scanning
% 0.21/0.36
% 0.21/0.36 % (27893)Memory used [KB]: 1023
% 0.21/0.36 % (27893)Time elapsed: 0.003 s
% 0.21/0.36 % (27893)Instructions burned: 3 (million)
% 0.21/0.36 % (27893)------------------------------
% 0.21/0.36 % (27893)------------------------------
% 0.21/0.36 % (27892)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (27890)Instruction limit reached!
% 0.21/0.36 % (27890)------------------------------
% 0.21/0.36 % (27890)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.36 % (27890)Termination reason: Unknown
% 0.21/0.36 % (27890)Termination phase: shuffling
% 0.21/0.36
% 0.21/0.36 % (27890)Memory used [KB]: 1023
% 0.21/0.36 % (27890)Time elapsed: 0.003 s
% 0.21/0.36 % (27890)Instructions burned: 2 (million)
% 0.21/0.36 % (27890)------------------------------
% 0.21/0.36 % (27890)------------------------------
% 0.21/0.36 % (27887)Instruction limit reached!
% 0.21/0.36 % (27887)------------------------------
% 0.21/0.36 % (27887)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.36 % (27887)Termination reason: Unknown
% 0.21/0.37 % (27887)Termination phase: Preprocessing 3
% 0.21/0.37
% 0.21/0.37 % (27887)Memory used [KB]: 1023
% 0.21/0.37 % (27887)Time elapsed: 0.004 s
% 0.21/0.37 % (27887)Instructions burned: 4 (million)
% 0.21/0.37 % (27887)------------------------------
% 0.21/0.37 % (27887)------------------------------
% 0.21/0.37 % (27888)Refutation not found, incomplete strategy
% 0.21/0.37 % (27888)------------------------------
% 0.21/0.37 % (27888)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (27888)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.37
% 0.21/0.37
% 0.21/0.37 % (27888)Memory used [KB]: 5628
% 0.21/0.37 % (27888)Time elapsed: 0.010 s
% 0.21/0.37 % (27888)Instructions burned: 13 (million)
% 0.21/0.37 % (27888)------------------------------
% 0.21/0.37 % (27888)------------------------------
% 0.21/0.37 % (27892)Instruction limit reached!
% 0.21/0.37 % (27892)------------------------------
% 0.21/0.37 % (27892)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (27892)Termination reason: Unknown
% 0.21/0.37 % (27892)Termination phase: Saturation
% 0.21/0.37
% 0.21/0.37 % (27892)Memory used [KB]: 5628
% 0.21/0.37 % (27892)Time elapsed: 0.011 s
% 0.21/0.37 % (27892)Instructions burned: 19 (million)
% 0.21/0.37 % (27892)------------------------------
% 0.21/0.37 % (27892)------------------------------
% 0.21/0.38 % (27894)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 % (27896)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 % (27897)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)
% 0.21/0.38 % (27895)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 % (27896)Instruction limit reached!
% 0.21/0.38 % (27896)------------------------------
% 0.21/0.38 % (27896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (27896)Termination reason: Unknown
% 0.21/0.38 % (27896)Termination phase: Preprocessing 1
% 0.21/0.38
% 0.21/0.38 % (27896)Memory used [KB]: 1023
% 0.21/0.38 % (27896)Time elapsed: 0.003 s
% 0.21/0.38 % (27896)Instructions burned: 3 (million)
% 0.21/0.38 % (27896)------------------------------
% 0.21/0.38 % (27896)------------------------------
% 0.21/0.39 % (27898)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 % (27895)Instruction limit reached!
% 0.21/0.39 % (27895)------------------------------
% 0.21/0.39 % (27895)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (27895)Termination reason: Unknown
% 0.21/0.39 % (27895)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (27895)Memory used [KB]: 5628
% 0.21/0.39 % (27895)Time elapsed: 0.010 s
% 0.21/0.39 % (27895)Instructions burned: 17 (million)
% 0.21/0.39 % (27895)------------------------------
% 0.21/0.39 % (27895)------------------------------
% 0.21/0.39 % (27899)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.39 % (27898)Instruction limit reached!
% 0.21/0.39 % (27898)------------------------------
% 0.21/0.39 % (27898)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (27898)Termination reason: Unknown
% 0.21/0.39 % (27898)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (27898)Memory used [KB]: 1023
% 0.21/0.39 % (27898)Time elapsed: 0.006 s
% 0.21/0.39 % (27898)Instructions burned: 8 (million)
% 0.21/0.39 % (27898)------------------------------
% 0.21/0.39 % (27898)------------------------------
% 0.21/0.39 % (27894)Instruction limit reached!
% 0.21/0.39 % (27894)------------------------------
% 0.21/0.39 % (27894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (27894)Termination reason: Unknown
% 0.21/0.39 % (27894)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (27894)Memory used [KB]: 5756
% 0.21/0.39 % (27894)Time elapsed: 0.018 s
% 0.21/0.39 % (27894)Instructions burned: 37 (million)
% 0.21/0.39 % (27894)------------------------------
% 0.21/0.39 % (27894)------------------------------
% 0.21/0.39 % (27900)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 % (27891)Refutation not found, incomplete strategy
% 0.21/0.40 % (27891)------------------------------
% 0.21/0.40 % (27891)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (27891)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.40
% 0.21/0.40
% 0.21/0.40 % (27891)Memory used [KB]: 5756
% 0.21/0.40 % (27891)Time elapsed: 0.035 s
% 0.21/0.40 % (27891)Instructions burned: 71 (million)
% 0.21/0.40 % (27891)------------------------------
% 0.21/0.40 % (27891)------------------------------
% 0.21/0.40 % (27900)Instruction limit reached!
% 0.21/0.40 % (27900)------------------------------
% 0.21/0.40 % (27900)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (27900)Termination reason: Unknown
% 0.21/0.40 % (27900)Termination phase: Preprocessing 3
% 0.21/0.40
% 0.21/0.40 % (27900)Memory used [KB]: 1023
% 0.21/0.40 % (27900)Time elapsed: 0.004 s
% 0.21/0.40 % (27900)Instructions burned: 4 (million)
% 0.21/0.40 % (27900)------------------------------
% 0.21/0.40 % (27900)------------------------------
% 0.21/0.40 % (27899)Instruction limit reached!
% 0.21/0.40 % (27899)------------------------------
% 0.21/0.40 % (27899)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (27899)Termination reason: Unknown
% 0.21/0.40 % (27899)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (27899)Memory used [KB]: 5628
% 0.21/0.40 % (27899)Time elapsed: 0.010 s
% 0.21/0.40 % (27899)Instructions burned: 17 (million)
% 0.21/0.40 % (27899)------------------------------
% 0.21/0.40 % (27899)------------------------------
% 0.21/0.40 % (27901)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 % (27901)Instruction limit reached!
% 0.21/0.40 % (27901)------------------------------
% 0.21/0.40 % (27901)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (27901)Termination reason: Unknown
% 0.21/0.40 % (27901)Termination phase: Preprocessing 1
% 0.21/0.40
% 0.21/0.40 % (27901)Memory used [KB]: 1023
% 0.21/0.40 % (27901)Time elapsed: 0.003 s
% 0.21/0.40 % (27901)Instructions burned: 3 (million)
% 0.21/0.40 % (27901)------------------------------
% 0.21/0.40 % (27901)------------------------------
% 0.21/0.41 % (27902)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 % (27903)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 % (27903)Instruction limit reached!
% 0.21/0.41 % (27903)------------------------------
% 0.21/0.41 % (27903)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27903)Termination reason: Unknown
% 0.21/0.41 % (27903)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (27903)Memory used [KB]: 1023
% 0.21/0.41 % (27903)Time elapsed: 0.003 s
% 0.21/0.41 % (27903)Instructions burned: 3 (million)
% 0.21/0.41 % (27903)------------------------------
% 0.21/0.41 % (27903)------------------------------
% 0.21/0.41 % (27902)Instruction limit reached!
% 0.21/0.41 % (27902)------------------------------
% 0.21/0.41 % (27902)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27902)Termination reason: Unknown
% 0.21/0.41 % (27902)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (27902)Memory used [KB]: 5500
% 0.21/0.41 % (27902)Time elapsed: 0.005 s
% 0.21/0.41 % (27902)Instructions burned: 7 (million)
% 0.21/0.41 % (27902)------------------------------
% 0.21/0.41 % (27902)------------------------------
% 0.21/0.41 % (27904)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.41 % (27905)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)
% 0.21/0.41 % (27904)Instruction limit reached!
% 0.21/0.41 % (27904)------------------------------
% 0.21/0.41 % (27904)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27904)Termination reason: Unknown
% 0.21/0.41 % (27904)Termination phase: Preprocessing 3
% 0.21/0.41
% 0.21/0.41 % (27904)Memory used [KB]: 1023
% 0.21/0.41 % (27904)Time elapsed: 0.004 s
% 0.21/0.41 % (27904)Instructions burned: 4 (million)
% 0.21/0.41 % (27904)------------------------------
% 0.21/0.41 % (27904)------------------------------
% 0.21/0.42 % (27907)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.42 % (27906)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 % (27905)Refutation not found, incomplete strategy
% 0.21/0.42 % (27905)------------------------------
% 0.21/0.42 % (27905)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27905)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.42
% 0.21/0.42
% 0.21/0.42 % (27905)Memory used [KB]: 5628
% 0.21/0.42 % (27905)Time elapsed: 0.009 s
% 0.21/0.42 % (27905)Instructions burned: 15 (million)
% 0.21/0.42 % (27905)------------------------------
% 0.21/0.42 % (27905)------------------------------
% 0.21/0.42 % (27907)Instruction limit reached!
% 0.21/0.42 % (27907)------------------------------
% 0.21/0.42 % (27907)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27907)Termination reason: Unknown
% 0.21/0.42 % (27907)Termination phase: Property scanning
% 0.21/0.42
% 0.21/0.42 % (27907)Memory used [KB]: 1023
% 0.21/0.42 % (27907)Time elapsed: 0.004 s
% 0.21/0.42 % (27907)Instructions burned: 6 (million)
% 0.21/0.42 % (27907)------------------------------
% 0.21/0.42 % (27907)------------------------------
% 0.21/0.42 % (27908)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)
% 0.21/0.42 % (27909)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 % (27910)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 % (27910)Instruction limit reached!
% 0.21/0.43 % (27910)------------------------------
% 0.21/0.43 % (27910)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.43 % (27910)Termination reason: Unknown
% 0.21/0.43 % (27910)Termination phase: Saturation
% 0.21/0.43
% 0.21/0.43 % (27910)Memory used [KB]: 5500
% 0.21/0.43 % (27910)Time elapsed: 0.005 s
% 0.21/0.43 % (27910)Instructions burned: 6 (million)
% 0.21/0.43 % (27910)------------------------------
% 0.21/0.43 % (27910)------------------------------
% 0.21/0.43 % (27911)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.44 % (27912)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.21/0.44 % (27911)Instruction limit reached!
% 0.21/0.44 % (27911)------------------------------
% 0.21/0.44 % (27911)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (27911)Termination reason: Unknown
% 0.21/0.44 % (27911)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (27911)Memory used [KB]: 5500
% 0.21/0.44 % (27911)Time elapsed: 0.004 s
% 0.21/0.44 % (27911)Instructions burned: 6 (million)
% 0.21/0.44 % (27911)------------------------------
% 0.21/0.44 % (27911)------------------------------
% 0.21/0.44 % (27909)Instruction limit reached!
% 0.21/0.44 % (27909)------------------------------
% 0.21/0.44 % (27909)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (27909)Termination reason: Unknown
% 0.21/0.44 % (27909)Termination phase: Saturation
% 0.21/0.44
% 0.21/0.44 % (27909)Memory used [KB]: 5628
% 0.21/0.44 % (27909)Time elapsed: 0.013 s
% 0.21/0.44 % (27909)Instructions burned: 22 (million)
% 0.21/0.44 % (27909)------------------------------
% 0.21/0.44 % (27909)------------------------------
% 0.21/0.44 % (27908)Refutation not found, incomplete strategy
% 0.21/0.44 % (27908)------------------------------
% 0.21/0.44 % (27908)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.44 % (27908)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.44
% 0.21/0.44
% 0.21/0.44 % (27908)Memory used [KB]: 5628
% 0.21/0.44 % (27908)Time elapsed: 0.019 s
% 0.21/0.44 % (27908)Instructions burned: 30 (million)
% 0.21/0.44 % (27908)------------------------------
% 0.21/0.44 % (27908)------------------------------
% 0.21/0.45 % (27913)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.21/0.45 % (27915)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.21/0.45 % (27914)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.21/0.45 % (27912)Refutation not found, incomplete strategy
% 0.21/0.45 % (27912)------------------------------
% 0.21/0.45 % (27912)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.45 % (27912)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 % (27912)Memory used [KB]: 5756
% 0.21/0.45 % (27912)Time elapsed: 0.016 s
% 0.21/0.45 % (27912)Instructions burned: 29 (million)
% 0.21/0.45 % (27912)------------------------------
% 0.21/0.45 % (27912)------------------------------
% 0.21/0.46 % (27916)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi)
% 0.21/0.46 % (27914)Instruction limit reached!
% 0.21/0.46 % (27914)------------------------------
% 0.21/0.46 % (27914)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (27914)Termination reason: Unknown
% 0.21/0.46 % (27914)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (27914)Memory used [KB]: 5500
% 0.21/0.46 % (27914)Time elapsed: 0.010 s
% 0.21/0.46 % (27914)Instructions burned: 19 (million)
% 0.21/0.46 % (27914)------------------------------
% 0.21/0.46 % (27914)------------------------------
% 0.21/0.46 % (27915)Refutation not found, incomplete strategy
% 0.21/0.46 % (27915)------------------------------
% 0.21/0.46 % (27915)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (27915)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % (27915)Memory used [KB]: 5628
% 0.21/0.46 % (27915)Time elapsed: 0.011 s
% 0.21/0.46 % (27915)Instructions burned: 19 (million)
% 0.21/0.46 % (27915)------------------------------
% 0.21/0.46 % (27915)------------------------------
% 0.21/0.46 % (27886)Instruction limit reached!
% 0.21/0.46 % (27886)------------------------------
% 0.21/0.46 % (27886)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.46 % (27886)Termination reason: Unknown
% 0.21/0.46 % (27886)Termination phase: Saturation
% 0.21/0.46
% 0.21/0.46 % (27886)Memory used [KB]: 6396
% 0.21/0.46 % (27886)Time elapsed: 0.103 s
% 0.21/0.46 % (27886)Instructions burned: 183 (million)
% 0.21/0.46 % (27886)------------------------------
% 0.21/0.46 % (27886)------------------------------
% 0.21/0.47 % (27916)Instruction limit reached!
% 0.21/0.47 % (27916)------------------------------
% 0.21/0.47 % (27916)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (27916)Termination reason: Unknown
% 0.21/0.47 % (27916)Termination phase: Saturation
% 0.21/0.47
% 0.21/0.47 % (27916)Memory used [KB]: 5628
% 0.21/0.47 % (27916)Time elapsed: 0.012 s
% 0.21/0.47 % (27917)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.47 % (27916)Instructions burned: 17 (million)
% 0.21/0.47 % (27916)------------------------------
% 0.21/0.47 % (27916)------------------------------
% 0.21/0.47 % (27917)Instruction limit reached!
% 0.21/0.47 % (27917)------------------------------
% 0.21/0.47 % (27917)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.47 % (27917)Termination reason: Unknown
% 0.21/0.47 % (27917)Termination phase: Preprocessing 3
% 0.21/0.47
% 0.21/0.47 % (27917)Memory used [KB]: 1023
% 0.21/0.47 % (27917)Time elapsed: 0.003 s
% 0.21/0.47 % (27917)Instructions burned: 3 (million)
% 0.21/0.47 % (27917)------------------------------
% 0.21/0.47 % (27917)------------------------------
% 0.21/0.47 % (27919)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2999ds/127Mi)
% 0.21/0.48 % (27920)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.48 % (27918)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.21/0.48 % (27921)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.48 % (27921)Instruction limit reached!
% 0.21/0.48 % (27921)------------------------------
% 0.21/0.48 % (27921)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.48 % (27921)Termination reason: Unknown
% 0.21/0.48 % (27921)Termination phase: Property scanning
% 0.21/0.48
% 0.21/0.48 % (27921)Memory used [KB]: 1023
% 0.21/0.48 % (27921)Time elapsed: 0.003 s
% 0.21/0.48 % (27921)Instructions burned: 4 (million)
% 0.21/0.48 % (27921)------------------------------
% 0.21/0.48 % (27921)------------------------------
% 0.21/0.48 % (27922)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2998ds/20Mi)
% 0.21/0.49 % (27924)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2998ds/86Mi)
% 0.21/0.49 % (27920)Refutation not found, incomplete strategy
% 0.21/0.49 % (27920)------------------------------
% 0.21/0.49 % (27920)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (27920)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 % (27920)Memory used [KB]: 5628
% 0.21/0.49 % (27920)Time elapsed: 0.037 s
% 0.21/0.49 % (27920)Instructions burned: 42 (million)
% 0.21/0.49 % (27920)------------------------------
% 0.21/0.49 % (27920)------------------------------
% 0.21/0.49 % (27918)Refutation not found, incomplete strategy
% 0.21/0.49 % (27918)------------------------------
% 0.21/0.49 % (27918)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (27918)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49
% 0.21/0.49
% 0.21/0.49 % (27918)Memory used [KB]: 5628
% 0.21/0.49 % (27918)Time elapsed: 0.037 s
% 0.21/0.49 % (27918)Instructions burned: 27 (million)
% 0.21/0.49 % (27918)------------------------------
% 0.21/0.49 % (27918)------------------------------
% 0.21/0.49 % (27922)Instruction limit reached!
% 0.21/0.49 % (27922)------------------------------
% 0.21/0.49 % (27922)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.49 % (27922)Termination reason: Unknown
% 0.21/0.49 % (27922)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (27922)Memory used [KB]: 5628
% 0.21/0.49 % (27922)Time elapsed: 0.012 s
% 0.21/0.49 % (27922)Instructions burned: 21 (million)
% 0.21/0.49 % (27922)------------------------------
% 0.21/0.49 % (27922)------------------------------
% 0.21/0.50 % (27913)Refutation not found, incomplete strategy
% 0.21/0.50 % (27913)------------------------------
% 0.21/0.50 % (27913)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.50 % (27913)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.50
% 0.21/0.50
% 0.21/0.50 % (27913)Memory used [KB]: 6268
% 0.21/0.50 % (27913)Time elapsed: 0.054 s
% 0.21/0.50 % (27913)Instructions burned: 134 (million)
% 0.21/0.50 % (27913)------------------------------
% 0.21/0.50 % (27913)------------------------------
% 0.21/0.50 % (27925)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2998ds/107Mi)
% 0.21/0.51 % (27925)Refutation not found, incomplete strategy
% 0.21/0.51 % (27925)------------------------------
% 0.21/0.51 % (27925)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.51 % (27925)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51
% 0.21/0.51 % (27925)Memory used [KB]: 5628
% 0.21/0.51 % (27925)Time elapsed: 0.007 s
% 0.21/0.51 % (27925)Instructions burned: 17 (million)
% 0.21/0.51 % (27925)------------------------------
% 0.21/0.51 % (27925)------------------------------
% 0.21/0.51 % (27927)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2998ds/448Mi)
% 0.21/0.51 % (27928)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2998ds/46Mi)
% 0.21/0.51 % (27926)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2998ds/39Mi)
% 0.21/0.51 % (27929)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2998ds/98Mi)
% 0.21/0.52 % (27924)Instruction limit reached!
% 0.21/0.52 % (27924)------------------------------
% 0.21/0.52 % (27924)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (27924)Termination reason: Unknown
% 0.21/0.52 % (27924)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (27924)Memory used [KB]: 6140
% 0.21/0.52 % (27924)Time elapsed: 0.032 s
% 0.21/0.52 % (27924)Instructions burned: 87 (million)
% 0.21/0.52 % (27924)------------------------------
% 0.21/0.52 % (27924)------------------------------
% 0.21/0.52 % (27928)Instruction limit reached!
% 0.21/0.52 % (27928)------------------------------
% 0.21/0.52 % (27928)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.52 % (27928)Termination reason: Unknown
% 0.21/0.52 % (27928)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (27928)Memory used [KB]: 5884
% 0.21/0.52 % (27928)Time elapsed: 0.018 s
% 0.21/0.52 % (27928)Instructions burned: 46 (million)
% 0.21/0.52 % (27928)------------------------------
% 0.21/0.52 % (27928)------------------------------
% 0.21/0.53 % (27926)Instruction limit reached!
% 0.21/0.53 % (27926)------------------------------
% 0.21/0.53 % (27926)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (27926)Termination reason: Unknown
% 0.21/0.53 % (27926)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (27926)Memory used [KB]: 5628
% 0.21/0.53 % (27926)Time elapsed: 0.020 s
% 0.21/0.53 % (27926)Instructions burned: 39 (million)
% 0.21/0.53 % (27926)------------------------------
% 0.21/0.53 % (27926)------------------------------
% 0.21/0.53 % (27930)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2998ds/507Mi)
% 0.21/0.53 % (27929)First to succeed.
% 0.21/0.53 % (27931)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2998ds/149Mi)
% 0.21/0.53 % (27919)Instruction limit reached!
% 0.21/0.53 % (27919)------------------------------
% 0.21/0.53 % (27919)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (27919)Termination reason: Unknown
% 0.21/0.53 % (27919)Termination phase: Saturation
% 0.21/0.53
% 0.21/0.53 % (27919)Memory used [KB]: 6012
% 0.21/0.53 % (27919)Time elapsed: 0.085 s
% 0.21/0.53 % (27919)Instructions burned: 127 (million)
% 0.21/0.53 % (27929)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53 % SZS output start Proof for theBenchmark
% 0.21/0.53 thf(func_def_16, type, ph0: !>[X0: $tType]:(X0)).
% 0.21/0.53 thf(func_def_17, type, sK1: ($i > $o) > $i > $o).
% 0.21/0.53 thf(func_def_20, type, sK4: $i > $o).
% 0.21/0.53 thf(func_def_22, type, sK6: ($i > $o) > $i).
% 0.21/0.53 thf(func_def_23, type, sK7: ($i > $o) > $i).
% 0.21/0.53 thf(f151,plain,(
% 0.21/0.53 $false),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f150])).
% 0.21/0.53 thf(f150,plain,(
% 0.21/0.53 ($false = $true)),
% 0.21/0.53 inference(backward_demodulation,[],[f100,f149])).
% 0.21/0.53 thf(f149,plain,(
% 0.21/0.53 ((sK4 @ (sK6 @ sK4)) = $false)),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f148])).
% 0.21/0.53 thf(f148,plain,(
% 0.21/0.53 ((sK4 @ (sK6 @ sK4)) = $false) | ($false = $true)),
% 0.21/0.53 inference(forward_demodulation,[],[f146,f39])).
% 0.21/0.53 thf(f39,plain,(
% 0.21/0.53 ((sK4 @ sK3) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f37])).
% 0.21/0.53 thf(f37,plain,(
% 0.21/0.53 ($true = ((sK4 @ sK3) & (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK1 @ sK4 @ Y0))))))),
% 0.21/0.53 inference(beta_eta_normalization,[],[f36])).
% 0.21/0.53 thf(f36,plain,(
% 0.21/0.53 (((^[Y0 : $i > $o]: ((Y0 @ sK3) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))))) @ sK4) = $true)),
% 0.21/0.53 inference(sigma_clausification,[],[f35])).
% 0.21/0.53 thf(f35,plain,(
% 0.21/0.53 ($true = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK3) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1))))))))),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f33])).
% 0.21/0.53 thf(f33,plain,(
% 0.21/0.53 ($false = ((?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ sK3) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1))))))) => (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3)))),
% 0.21/0.53 inference(beta_eta_normalization,[],[f32])).
% 0.21/0.53 thf(f32,plain,(
% 0.21/0.53 ($false = ((^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))) @ sK3))),
% 0.21/0.53 inference(sigma_clausification,[],[f31])).
% 0.21/0.53 thf(f31,plain,(
% 0.21/0.53 ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f30])).
% 0.21/0.53 thf(f30,plain,(
% 0.21/0.53 ($false = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 0.21/0.53 inference(backward_demodulation,[],[f14,f29])).
% 0.21/0.53 thf(f29,plain,(
% 0.21/0.53 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))))),
% 0.21/0.53 inference(boolean_simplification,[],[f28])).
% 0.21/0.53 thf(f28,plain,(
% 0.21/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & $true))),
% 0.21/0.53 inference(forward_demodulation,[],[f27,f25])).
% 0.21/0.53 thf(f25,plain,(
% 0.21/0.53 ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2) = $true)),
% 0.21/0.53 inference(duplicate_literal_removal,[],[f23])).
% 0.21/0.53 thf(f23,plain,(
% 0.21/0.53 ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2) = $true) | ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f21])).
% 0.21/0.53 thf(f21,plain,(
% 0.21/0.53 ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f20])).
% 0.21/0.53 thf(f20,plain,(
% 0.21/0.53 (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)) != (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f19])).
% 0.21/0.53 thf(f19,plain,(
% 0.21/0.53 ($false = ((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2) = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))))),
% 0.21/0.53 inference(beta_eta_normalization,[],[f18])).
% 0.21/0.53 thf(f18,plain,(
% 0.21/0.53 ($false = ((^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) = ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (sK1 @ (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4))))))))) @ Y1)))) & (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))) @ sK2))),
% 0.21/0.53 inference(sigma_clausification,[],[f10])).
% 0.21/0.53 thf(f10,plain,(
% 0.21/0.53 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) = ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (sK1 @ (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4))))))))) @ Y1)))) & (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))))))),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f9])).
% 0.21/0.53 thf(f9,plain,(
% 0.21/0.53 ($false = ((((!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))))))))) => (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))))) => (!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) = ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (sK1 @ (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4))))))))) @ Y1)))) & (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))))),
% 0.21/0.53 inference(beta_eta_normalization,[],[f8])).
% 0.21/0.53 thf(f8,plain,(
% 0.21/0.53 ($false = ((^[Y0 : ($i > $o) > $i > $o]: ((((!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (Y0 @ (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4))))))))) @ Y1))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))))) => (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2)))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) = ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2) => (Y0 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((Y4 @ Y3) & (!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5))))))))) @ Y2)))) & (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1))))))) @ sK1))),
% 0.21/0.53 inference(sigma_clausification,[],[f7])).
% 0.21/0.53 thf(f7,plain,(
% 0.21/0.53 ($false = (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((((!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (Y0 @ (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4))))))))) @ Y1))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))))) => (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2)))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) = ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2) => (Y0 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((Y4 @ Y3) & (!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5))))))))) @ Y2)))) & (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))))))),
% 0.21/0.53 inference(not_proxy_clausification,[],[f6])).
% 0.21/0.53 thf(f6,plain,(
% 0.21/0.53 ((~ (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((((!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (Y0 @ (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4))))))))) @ Y1))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))))) => (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2)))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) = ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2) => (Y0 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((Y4 @ Y3) & (!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5))))))))) @ Y2)))) & (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1))))))))) = $true)),
% 0.21/0.53 inference(cnf_transformation,[],[f5])).
% 0.21/0.53 thf(f5,plain,(
% 0.21/0.53 ((~ (!! @ (($i > $o) > $i > $o) @ (^[Y0 : ($i > $o) > $i > $o]: ((((!! @ $i @ (^[Y1 : $i]: ((?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (Y0 @ Y2 @ Y3))))))) => (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) => (Y0 @ (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4))))))))) @ Y1))))) & (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((Y3 @ Y2) & (!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))))))))) => (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2)))))))) => (!! @ $i @ (^[Y1 : $i]: ((Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1) = ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5)))) & (Y4 @ Y3))))) @ Y2) => (Y0 @ (Y0 @ (^[Y3 : $i]: (?? @ ($i > $o) @ (^[Y4 : $i > $o]: ((Y4 @ Y3) & (!! @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) => (Y0 @ Y4 @ Y5))))))))) @ Y2)))) & (Y0 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (Y0 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1))))))))) = $true)),
% 0.21/0.53 inference(fool_elimination,[],[f4])).
% 0.21/0.53 thf(f4,plain,(
% 0.21/0.53 ~! [X0 : ($i > $o) > $i > $o] : ((! [X1 : $i > $o] : (! [X2] : ((X1 @ X2) => ? [X3 : $i > $o] : (! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))) => ! [X5] : ((X0 @ X1 @ X5) => (X0 @ (^[X6 : $i] : (? [X7 : $i > $o] : ((X7 @ X6) & ! [X8] : ((X7 @ X8) => (X0 @ X7 @ X8))))) @ X5))) & (! [X9] : (? [X10 : $i > $o] : (! [X11] : ((X10 @ X11) => (X0 @ X10 @ X11)) & (X10 @ X9)) => (X0 @ (^[X12 : $i] : (? [X13 : $i > $o] : ((X13 @ X12) & ! [X14] : ((X13 @ X14) => (X0 @ X13 @ X14))))) @ X9)) => ! [X15] : ((X0 @ (^[X16 : $i] : (? [X17 : $i > $o] : ((X17 @ X16) & ! [X18] : ((X17 @ X18) => (X0 @ X17 @ X18))))) @ X15) => (X0 @ (X0 @ (^[X19 : $i] : (? [X20 : $i > $o] : (! [X21] : ((X20 @ X21) => (X0 @ X20 @ X21)) & (X20 @ X19))))) @ X15)))) => ! [X22] : ((X0 @ (^[X23 : $i] : (? [X24 : $i > $o] : ((X24 @ X23) & ! [X25] : ((X24 @ X25) => (X0 @ X24 @ X25))))) @ X22) <=> ((X0 @ (^[X26 : $i] : (? [X27 : $i > $o] : ((X27 @ X26) & ! [X28] : ((X27 @ X28) => (X0 @ X27 @ X28))))) @ X22) & ! [X29] : ((X0 @ (^[X30 : $i] : (? [X31 : $i > $o] : ((X31 @ X30) & ! [X32] : ((X31 @ X32) => (X0 @ X31 @ X32))))) @ X29) => (X0 @ (X0 @ (^[X33 : $i] : (? [X34 : $i > $o] : (! [X35] : ((X34 @ X35) => (X0 @ X34 @ X35)) & (X34 @ X33))))) @ X29)))))),
% 0.21/0.53 inference(rectify,[],[f2])).
% 0.21/0.53 thf(f2,negated_conjecture,(
% 0.21/0.53 ~! [X0 : ($i > $o) > $i > $o] : ((! [X1 : $i > $o] : (! [X2] : ((X1 @ X2) => ? [X3 : $i > $o] : (! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))) => ! [X2] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2))) & (! [X1] : (? [X3 : $i > $o] : (! [X2] : ((X3 @ X2) => (X0 @ X3 @ X2)) & (X3 @ X1)) => (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1] : ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))))) @ X1)))) => ! [X1] : ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) <=> ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) & ! [X2] : ((X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2) => (X0 @ (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : (! [X5] : ((X3 @ X5) => (X0 @ X3 @ X5)) & (X3 @ X4))))) @ X2)))))),
% 0.21/0.53 inference(negated_conjecture,[],[f1])).
% 0.21/0.53 thf(f1,conjecture,(
% 0.21/0.53 ! [X0 : ($i > $o) > $i > $o] : ((! [X1 : $i > $o] : (! [X2] : ((X1 @ X2) => ? [X3 : $i > $o] : (! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))) => ! [X2] : ((X0 @ X1 @ X2) => (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2))) & (! [X1] : (? [X3 : $i > $o] : (! [X2] : ((X3 @ X2) => (X0 @ X3 @ X2)) & (X3 @ X1)) => (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1)) => ! [X1] : ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) => (X0 @ (X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : (! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4)) & (X3 @ X2))))) @ X1)))) => ! [X1] : ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) <=> ((X0 @ (^[X2 : $i] : (? [X3 : $i > $o] : ((X3 @ X2) & ! [X4] : ((X3 @ X4) => (X0 @ X3 @ X4))))) @ X1) & ! [X2] : ((X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : ((X3 @ X4) & ! [X5] : ((X3 @ X5) => (X0 @ X3 @ X5))))) @ X2) => (X0 @ (X0 @ (^[X4 : $i] : (? [X3 : $i > $o] : (! [X5] : ((X3 @ X5) => (X0 @ X3 @ X5)) & (X3 @ X4))))) @ X2)))))),
% 0.21/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM2D_pme)).
% 0.21/0.53 thf(f27,plain,(
% 0.21/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f26])).
% 0.21/0.53 thf(f26,plain,(
% 0.21/0.53 ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2))) | ($false = $true)),
% 0.21/0.53 inference(forward_demodulation,[],[f22,f25])).
% 0.21/0.53 thf(f22,plain,(
% 0.21/0.53 ($false = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) & (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK2)))),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f20])).
% 0.21/0.53 thf(f14,plain,(
% 0.21/0.53 ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0)))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))))),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f13])).
% 0.21/0.53 thf(f13,plain,(
% 0.21/0.53 (((!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0))))) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f11])).
% 0.21/0.53 thf(f11,plain,(
% 0.21/0.53 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))) => (!! @ $i @ (^[Y0 : $i]: ((sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0) => (sK1 @ (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3))))))))) @ Y0))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))))))))) => (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))))) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f9])).
% 0.21/0.53 thf(f146,plain,(
% 0.21/0.53 ((sK4 @ (sK6 @ sK4)) = $false) | ($false = (sK4 @ sK3))),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f141])).
% 0.21/0.53 thf(f141,plain,(
% 0.21/0.53 ((sK4 @ (sK6 @ sK4)) = $false) | ($false = $true) | ($false = (sK4 @ sK3))),
% 0.21/0.53 inference(superposition,[],[f131,f42])).
% 0.21/0.53 thf(f42,plain,(
% 0.21/0.53 ( ! [X1 : $i] : (((sK1 @ sK4 @ X1) = $true) | ($false = (sK4 @ X1))) )),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f41])).
% 0.21/0.53 thf(f41,plain,(
% 0.21/0.53 ( ! [X1 : $i] : ((((sK4 @ X1) => (sK1 @ sK4 @ X1)) = $true)) )),
% 0.21/0.53 inference(beta_eta_normalization,[],[f40])).
% 0.21/0.53 thf(f40,plain,(
% 0.21/0.53 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK4 @ Y0) => (sK1 @ sK4 @ Y0))) @ X1) = $true)) )),
% 0.21/0.53 inference(pi_clausification,[],[f38])).
% 0.21/0.53 thf(f38,plain,(
% 0.21/0.53 ((!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) => (sK1 @ sK4 @ Y0)))) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f37])).
% 0.21/0.53 thf(f131,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = (sK1 @ X0 @ sK3)) | ($false = (sK4 @ (sK6 @ X0)))) )),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f114])).
% 0.21/0.53 thf(f114,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = (sK4 @ (sK6 @ X0))) | ($false = (sK1 @ X0 @ sK3)) | ($false = $true)) )),
% 0.21/0.53 inference(superposition,[],[f38,f103])).
% 0.21/0.53 thf(f103,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o,X1 : $i > $o] : (($false = (sK1 @ X0 @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (sK1 @ X1 @ Y0))))) | ($false = (X1 @ (sK6 @ X0)))) )),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f102])).
% 0.21/0.53 thf(f102,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o,X1 : $i > $o] : (($false = (sK1 @ X0 @ sK3)) | ($false = ((X1 @ (sK6 @ X0)) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (sK1 @ X1 @ Y0))))))) )),
% 0.21/0.53 inference(beta_eta_normalization,[],[f101])).
% 0.21/0.53 thf(f101,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o,X1 : $i > $o] : (($false = ((^[Y0 : $i > $o]: ((Y0 @ (sK6 @ X0)) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))))) @ X1)) | ($false = (sK1 @ X0 @ sK3))) )),
% 0.21/0.53 inference(pi_clausification,[],[f83])).
% 0.21/0.53 thf(f83,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK6 @ X0)) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1)))))))) | ($false = (sK1 @ X0 @ sK3))) )),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f82])).
% 0.21/0.53 thf(f82,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = ((X0 @ (sK6 @ X0)) => (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ (sK6 @ X0)) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (sK1 @ Y0 @ Y1))))))))) | ($false = (sK1 @ X0 @ sK3))) )),
% 0.21/0.53 inference(beta_eta_normalization,[],[f81])).
% 0.21/0.53 thf(f81,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = (sK1 @ X0 @ sK3)) | ($false = ((^[Y0 : $i]: ((X0 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))))) @ (sK6 @ X0)))) )),
% 0.21/0.53 inference(sigma_clausification,[],[f78])).
% 0.21/0.53 thf(f78,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2))))))))))) | ($false = (sK1 @ X0 @ sK3))) )),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f60])).
% 0.21/0.53 thf(f60,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = $true) | ($false = (sK1 @ X0 @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X0 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))))))))))) )),
% 0.21/0.53 inference(superposition,[],[f34,f52])).
% 0.21/0.53 thf(f52,plain,(
% 0.21/0.53 ( ! [X2 : $i,X1 : $i > $o] : (((sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X2) = $true) | ($false = (sK1 @ X1 @ X2)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))))))))))) )),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f51])).
% 0.21/0.53 thf(f51,plain,(
% 0.21/0.53 ( ! [X2 : $i,X1 : $i > $o] : (($true = ((sK1 @ X1 @ X2) => (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))))))))))) )),
% 0.21/0.53 inference(beta_eta_normalization,[],[f50])).
% 0.21/0.53 thf(f50,plain,(
% 0.21/0.53 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((sK1 @ X1 @ Y0) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))) @ X2) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))))))))))) )),
% 0.21/0.53 inference(pi_clausification,[],[f49])).
% 0.21/0.53 thf(f49,plain,(
% 0.21/0.53 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ X1 @ Y0) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0)))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))))))))))) )),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f48])).
% 0.21/0.53 thf(f48,plain,(
% 0.21/0.53 ( ! [X1 : $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) & (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))))))))) => (!! @ $i @ (^[Y0 : $i]: ((sK1 @ X1 @ Y0) => (sK1 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))) & (Y2 @ Y1))))) @ Y0))))) = $true)) )),
% 0.21/0.53 inference(beta_eta_normalization,[],[f47])).
% 0.21/0.53 thf(f47,plain,(
% 0.21/0.53 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))))))))) => (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1)))))) @ X1) = $true)) )),
% 0.21/0.53 inference(pi_clausification,[],[f12])).
% 0.21/0.53 thf(f12,plain,(
% 0.21/0.53 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((Y2 @ Y1) & (!! @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) => (sK1 @ Y2 @ Y3)))))))))) => (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK1 @ (^[Y2 : $i]: (?? @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) => (sK1 @ Y3 @ Y4)))) & (Y3 @ Y2))))) @ Y1))))))) = $true)),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f11])).
% 0.21/0.53 thf(f34,plain,(
% 0.21/0.53 ($false = (sK1 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) => (sK1 @ Y1 @ Y2)))) & (Y1 @ Y0))))) @ sK3))),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f33])).
% 0.21/0.53 thf(f100,plain,(
% 0.21/0.53 ((sK4 @ (sK6 @ sK4)) = $true)),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f99])).
% 0.21/0.53 thf(f99,plain,(
% 0.21/0.53 ($false = $true) | ((sK4 @ (sK6 @ sK4)) = $true)),
% 0.21/0.53 inference(forward_demodulation,[],[f97,f39])).
% 0.21/0.53 thf(f97,plain,(
% 0.21/0.53 ($false = (sK4 @ sK3)) | ((sK4 @ (sK6 @ sK4)) = $true)),
% 0.21/0.53 inference(trivial_inequality_removal,[],[f86])).
% 0.21/0.53 thf(f86,plain,(
% 0.21/0.53 ($false = (sK4 @ sK3)) | ($false = $true) | ((sK4 @ (sK6 @ sK4)) = $true)),
% 0.21/0.53 inference(superposition,[],[f84,f42])).
% 0.21/0.53 thf(f84,plain,(
% 0.21/0.53 ( ! [X0 : $i > $o] : (($false = (sK1 @ X0 @ sK3)) | ((X0 @ (sK6 @ X0)) = $true)) )),
% 0.21/0.53 inference(binary_proxy_clausification,[],[f82])).
% 0.21/0.53 % SZS output end Proof for theBenchmark
% 0.21/0.53 % (27929)------------------------------
% 0.21/0.53 % (27929)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.53 % (27929)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (27929)Memory used [KB]: 1279
% 0.21/0.53 % (27929)Time elapsed: 0.019 s
% 0.21/0.53 % (27929)Instructions burned: 42 (million)
% 0.21/0.53 % (27929)------------------------------
% 0.21/0.53 % (27929)------------------------------
% 0.21/0.53 % (27885)Success in time 0.181 s
% 0.21/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------