TSTP Solution File: SYO446^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO446^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n022.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 : Mon Jun 24 21:02:13 EDT 2024
% Result : Theorem 0.24s 0.49s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYO446^1 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.14 % Command : run_vampire %s %d THM
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Jun 23 10:15:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.38 This is a TH0_THM_EQU_NAR problem
% 0.15/0.38 Running higher-order theorem proving
% 0.15/0.38 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.15/0.40 % (9745)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40 % (9745)Instruction limit reached!
% 0.15/0.40 % (9745)------------------------------
% 0.15/0.40 % (9745)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.40 % (9745)Termination reason: Unknown
% 0.15/0.40 % (9745)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (9745)Memory used [KB]: 1023
% 0.15/0.40 % (9745)Time elapsed: 0.004 s
% 0.15/0.40 % (9745)Instructions burned: 3 (million)
% 0.15/0.40 % (9745)------------------------------
% 0.15/0.40 % (9745)------------------------------
% 0.15/0.40 % (9742)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.40 % (9744)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)
% 0.15/0.40 % (9746)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)
% 0.15/0.40 % (9747)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)
% 0.15/0.40 % (9748)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.40 % (9743)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)
% 0.15/0.40 % (9746)Instruction limit reached!
% 0.15/0.40 % (9746)------------------------------
% 0.15/0.40 % (9746)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.40 % (9746)Termination reason: Unknown
% 0.15/0.40 % (9746)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (9746)Memory used [KB]: 1023
% 0.15/0.40 % (9746)Time elapsed: 0.004 s
% 0.15/0.40 % (9746)Instructions burned: 3 (million)
% 0.15/0.40 % (9746)------------------------------
% 0.15/0.40 % (9746)------------------------------
% 0.24/0.40 % (9743)Instruction limit reached!
% 0.24/0.40 % (9743)------------------------------
% 0.24/0.40 % (9743)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.41 % (9743)Termination reason: Unknown
% 0.24/0.41 % (9743)Termination phase: Property scanning
% 0.24/0.41
% 0.24/0.41 % (9743)Memory used [KB]: 1023
% 0.24/0.41 % (9743)Time elapsed: 0.004 s
% 0.24/0.41 % (9743)Instructions burned: 4 (million)
% 0.24/0.41 % (9743)------------------------------
% 0.24/0.41 % (9743)------------------------------
% 0.24/0.41 % (9747)Refutation not found, incomplete strategy
% 0.24/0.41 % (9747)------------------------------
% 0.24/0.41 % (9747)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.41 % (9747)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.41
% 0.24/0.41
% 0.24/0.41 % (9747)Memory used [KB]: 5628
% 0.24/0.41 % (9747)Time elapsed: 0.007 s
% 0.24/0.41 % (9747)Instructions burned: 8 (million)
% 0.24/0.41 % (9747)------------------------------
% 0.24/0.41 % (9747)------------------------------
% 0.24/0.41 % (9748)Instruction limit reached!
% 0.24/0.41 % (9748)------------------------------
% 0.24/0.41 % (9748)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.41 % (9748)Termination reason: Unknown
% 0.24/0.41 % (9748)Termination phase: Saturation
% 0.24/0.41
% 0.24/0.41 % (9748)Memory used [KB]: 5628
% 0.24/0.41 % (9748)Time elapsed: 0.012 s
% 0.24/0.41 % (9748)Instructions burned: 19 (million)
% 0.24/0.41 % (9748)------------------------------
% 0.24/0.41 % (9748)------------------------------
% 0.24/0.42 % (9749)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)
% 0.24/0.42 % (9744)Instruction limit reached!
% 0.24/0.42 % (9744)------------------------------
% 0.24/0.42 % (9744)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.42 % (9744)Termination reason: Unknown
% 0.24/0.42 % (9744)Termination phase: Saturation
% 0.24/0.42
% 0.24/0.42 % (9744)Memory used [KB]: 5756
% 0.24/0.42 % (9744)Time elapsed: 0.017 s
% 0.24/0.42 % (9744)Instructions burned: 27 (million)
% 0.24/0.42 % (9744)------------------------------
% 0.24/0.42 % (9744)------------------------------
% 0.24/0.42 % (9749)Instruction limit reached!
% 0.24/0.42 % (9749)------------------------------
% 0.24/0.42 % (9749)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.42 % (9749)Termination reason: Unknown
% 0.24/0.42 % (9749)Termination phase: shuffling
% 0.24/0.42
% 0.24/0.42 % (9749)Memory used [KB]: 1023
% 0.24/0.42 % (9749)Time elapsed: 0.004 s
% 0.24/0.42 % (9749)Instructions burned: 3 (million)
% 0.24/0.42 % (9749)------------------------------
% 0.24/0.42 % (9749)------------------------------
% 0.24/0.42 % (9750)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)
% 0.24/0.42 % (9751)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)
% 0.24/0.42 % (9752)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)
% 0.24/0.43 % (9752)Instruction limit reached!
% 0.24/0.43 % (9752)------------------------------
% 0.24/0.43 % (9752)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.43 % (9752)Termination reason: Unknown
% 0.24/0.43 % (9752)Termination phase: shuffling
% 0.24/0.43
% 0.24/0.43 % (9752)Memory used [KB]: 1023
% 0.24/0.43 % (9752)Time elapsed: 0.004 s
% 0.24/0.43 % (9752)Instructions burned: 4 (million)
% 0.24/0.43 % (9752)------------------------------
% 0.24/0.43 % (9752)------------------------------
% 0.24/0.43 % (9753)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)
% 0.24/0.43 % (9751)Instruction limit reached!
% 0.24/0.43 % (9751)------------------------------
% 0.24/0.43 % (9751)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.43 % (9751)Termination reason: Unknown
% 0.24/0.43 % (9751)Termination phase: Saturation
% 0.24/0.43
% 0.24/0.43 % (9751)Memory used [KB]: 5628
% 0.24/0.43 % (9751)Time elapsed: 0.010 s
% 0.24/0.43 % (9751)Instructions burned: 15 (million)
% 0.24/0.43 % (9751)------------------------------
% 0.24/0.43 % (9751)------------------------------
% 0.24/0.43 % (9754)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.24/0.43 % (9755)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.24/0.44 % (9754)Instruction limit reached!
% 0.24/0.44 % (9754)------------------------------
% 0.24/0.44 % (9754)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.44 % (9754)Termination reason: Unknown
% 0.24/0.44 % (9754)Termination phase: Property scanning
% 0.24/0.44
% 0.24/0.44 % (9754)Memory used [KB]: 1023
% 0.24/0.44 % (9754)Time elapsed: 0.006 s
% 0.24/0.44 % (9754)Instructions burned: 7 (million)
% 0.24/0.44 % (9754)------------------------------
% 0.24/0.44 % (9754)------------------------------
% 0.24/0.44 % (9750)Instruction limit reached!
% 0.24/0.44 % (9750)------------------------------
% 0.24/0.44 % (9750)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.44 % (9750)Termination reason: Unknown
% 0.24/0.44 % (9750)Termination phase: Saturation
% 0.24/0.44
% 0.24/0.44 % (9750)Memory used [KB]: 5756
% 0.24/0.44 % (9750)Time elapsed: 0.022 s
% 0.24/0.44 % (9750)Instructions burned: 37 (million)
% 0.24/0.44 % (9750)------------------------------
% 0.24/0.44 % (9750)------------------------------
% 0.24/0.44 % (9756)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)
% 0.24/0.44 % (9756)Instruction limit reached!
% 0.24/0.44 % (9756)------------------------------
% 0.24/0.44 % (9756)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.44 % (9756)Termination reason: Unknown
% 0.24/0.44 % (9756)Termination phase: shuffling
% 0.24/0.44
% 0.24/0.44 % (9756)Memory used [KB]: 1023
% 0.24/0.44 % (9756)Time elapsed: 0.004 s
% 0.24/0.44 % (9756)Instructions burned: 4 (million)
% 0.24/0.44 % (9756)------------------------------
% 0.24/0.44 % (9756)------------------------------
% 0.24/0.44 % (9755)Instruction limit reached!
% 0.24/0.44 % (9755)------------------------------
% 0.24/0.44 % (9755)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.44 % (9755)Termination reason: Unknown
% 0.24/0.44 % (9755)Termination phase: Saturation
% 0.24/0.44
% 0.24/0.44 % (9755)Memory used [KB]: 5884
% 0.24/0.44 % (9755)Time elapsed: 0.012 s
% 0.24/0.44 % (9755)Instructions burned: 16 (million)
% 0.24/0.44 % (9755)------------------------------
% 0.24/0.44 % (9755)------------------------------
% 0.24/0.45 % (9757)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)
% 0.24/0.45 % (9757)Instruction limit reached!
% 0.24/0.45 % (9757)------------------------------
% 0.24/0.45 % (9757)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.45 % (9757)Termination reason: Unknown
% 0.24/0.45 % (9757)Termination phase: shuffling
% 0.24/0.45
% 0.24/0.45 % (9757)Memory used [KB]: 1023
% 0.24/0.45 % (9757)Time elapsed: 0.004 s
% 0.24/0.45 % (9757)Instructions burned: 4 (million)
% 0.24/0.45 % (9757)------------------------------
% 0.24/0.45 % (9757)------------------------------
% 0.24/0.45 % (9758)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)
% 0.24/0.46 % (9759)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)
% 0.24/0.46 % (9758)Instruction limit reached!
% 0.24/0.46 % (9758)------------------------------
% 0.24/0.46 % (9758)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.46 % (9758)Termination reason: Unknown
% 0.24/0.46 % (9758)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (9758)Memory used [KB]: 1151
% 0.24/0.46 % (9758)Time elapsed: 0.006 s
% 0.24/0.46 % (9758)Instructions burned: 8 (million)
% 0.24/0.46 % (9758)------------------------------
% 0.24/0.46 % (9758)------------------------------
% 0.24/0.46 % (9759)Instruction limit reached!
% 0.24/0.46 % (9759)------------------------------
% 0.24/0.46 % (9759)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.46 % (9759)Termination reason: Unknown
% 0.24/0.46 % (9759)Termination phase: Property scanning
% 0.24/0.46
% 0.24/0.46 % (9759)Memory used [KB]: 1023
% 0.24/0.46 % (9759)Time elapsed: 0.004 s
% 0.24/0.46 % (9759)Instructions burned: 4 (million)
% 0.24/0.46 % (9759)------------------------------
% 0.24/0.46 % (9759)------------------------------
% 0.24/0.46 % (9760)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.24/0.46 % (9761)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)
% 0.24/0.46 % (9760)Instruction limit reached!
% 0.24/0.46 % (9760)------------------------------
% 0.24/0.46 % (9760)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.46 % (9760)Termination reason: Unknown
% 0.24/0.46 % (9760)Termination phase: shuffling
% 0.24/0.46
% 0.24/0.46 % (9760)Memory used [KB]: 1023
% 0.24/0.46 % (9760)Time elapsed: 0.004 s
% 0.24/0.46 % (9760)Instructions burned: 4 (million)
% 0.24/0.46 % (9760)------------------------------
% 0.24/0.46 % (9760)------------------------------
% 0.24/0.46 % (9762)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.24/0.47 % (9762)Refutation not found, incomplete strategy
% 0.24/0.47 % (9762)------------------------------
% 0.24/0.47 % (9762)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.47 % (9762)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.47
% 0.24/0.47
% 0.24/0.47 % (9762)Memory used [KB]: 5628
% 0.24/0.47 % (9762)Time elapsed: 0.007 s
% 0.24/0.47 % (9762)Instructions burned: 8 (million)
% 0.24/0.47 % (9762)------------------------------
% 0.24/0.47 % (9762)------------------------------
% 0.24/0.47 % (9761)Instruction limit reached!
% 0.24/0.47 % (9761)------------------------------
% 0.24/0.47 % (9761)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.47 % (9761)Termination reason: Unknown
% 0.24/0.47 % (9761)Termination phase: Saturation
% 0.24/0.47
% 0.24/0.47 % (9761)Memory used [KB]: 5628
% 0.24/0.47 % (9761)Time elapsed: 0.014 s
% 0.24/0.47 % (9761)Instructions burned: 18 (million)
% 0.24/0.47 % (9761)------------------------------
% 0.24/0.47 % (9761)------------------------------
% 0.24/0.47 % (9763)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.24/0.47 % (9764)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)
% 0.24/0.48 % (9763)Instruction limit reached!
% 0.24/0.48 % (9763)------------------------------
% 0.24/0.48 % (9763)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.48 % (9763)Termination reason: Unknown
% 0.24/0.48 % (9763)Termination phase: Function definition elimination
% 0.24/0.48
% 0.24/0.48 % (9763)Memory used [KB]: 1023
% 0.24/0.48 % (9763)Time elapsed: 0.006 s
% 0.24/0.48 % (9763)Instructions burned: 8 (million)
% 0.24/0.48 % (9763)------------------------------
% 0.24/0.48 % (9763)------------------------------
% 0.24/0.48 % (9765)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)
% 0.24/0.48 % (9753)First to succeed.
% 0.24/0.48 % (9764)Refutation not found, incomplete strategy
% 0.24/0.48 % (9764)------------------------------
% 0.24/0.48 % (9764)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.48 % (9764)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.48
% 0.24/0.48
% 0.24/0.48 % (9764)Memory used [KB]: 5628
% 0.24/0.48 % (9764)Time elapsed: 0.007 s
% 0.24/0.48 % (9764)Instructions burned: 9 (million)
% 0.24/0.48 % (9764)------------------------------
% 0.24/0.48 % (9764)------------------------------
% 0.24/0.49 % (9766)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.24/0.49 % (9753)Refutation found. Thanks to Tanya!
% 0.24/0.49 % SZS status Theorem for theBenchmark
% 0.24/0.49 % SZS output start Proof for theBenchmark
% 0.24/0.49 thf(type_def_5, type, mu: $tType).
% 0.24/0.49 thf(func_def_0, type, mu: $tType).
% 0.24/0.49 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.24/0.49 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_15, type, mtrue: $i > $o).
% 0.24/0.49 thf(func_def_16, type, mfalse: $i > $o).
% 0.24/0.49 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.24/0.49 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.24/0.49 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.24/0.49 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.24/0.49 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.24/0.49 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.24/0.49 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.24/0.49 thf(func_def_36, type, p: $i > $o).
% 0.24/0.49 thf(func_def_37, type, q: $i > $o).
% 0.24/0.49 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 0.24/0.49 thf(f679,plain,(
% 0.24/0.49 $false),
% 0.24/0.49 inference(avatar_sat_refutation,[],[f212,f238,f366,f419,f678])).
% 0.24/0.49 thf(f678,plain,(
% 0.24/0.49 ~spl0_1),
% 0.24/0.49 inference(avatar_contradiction_clause,[],[f677])).
% 0.24/0.49 thf(f677,plain,(
% 0.24/0.49 $false | ~spl0_1),
% 0.24/0.49 inference(trivial_inequality_removal,[],[f676])).
% 0.24/0.49 thf(f676,plain,(
% 0.24/0.49 ($true = $false) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f675])).
% 0.24/0.49 thf(f675,plain,(
% 0.24/0.49 ((~ $true) = $true) | ~spl0_1),
% 0.24/0.49 inference(forward_demodulation,[],[f662,f519])).
% 0.24/0.49 thf(f519,plain,(
% 0.24/0.49 ((q @ sK6) = $true) | ~spl0_1),
% 0.24/0.49 inference(not_proxy_clausification,[],[f518])).
% 0.24/0.49 thf(f518,plain,(
% 0.24/0.49 ($false = (~ (q @ sK6))) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f517])).
% 0.24/0.49 thf(f517,plain,(
% 0.24/0.49 (((~ (q @ sK6)) | $false) = $false) | ~spl0_1),
% 0.24/0.49 inference(backward_demodulation,[],[f505,f515])).
% 0.24/0.49 thf(f515,plain,(
% 0.24/0.49 ($false = (~ (rel_s5 @ sK2 @ sK6))) | ~spl0_1),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f505])).
% 0.24/0.49 thf(f505,plain,(
% 0.24/0.49 ($false = ((~ (q @ sK6)) | (~ (rel_s5 @ sK2 @ sK6)))) | ~spl0_1),
% 0.24/0.49 inference(beta_eta_normalization,[],[f504])).
% 0.24/0.49 thf(f504,plain,(
% 0.24/0.49 (((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK6) = $false) | ~spl0_1),
% 0.24/0.49 inference(sigma_clausification,[],[f441])).
% 0.24/0.49 thf(f441,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $false) | ~spl0_1),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f440])).
% 0.24/0.49 thf(f440,plain,(
% 0.24/0.49 (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) = $false) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f439])).
% 0.24/0.49 thf(f439,plain,(
% 0.24/0.49 ((((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | $false) = $false) | ~spl0_1),
% 0.24/0.49 inference(backward_demodulation,[],[f434,f437])).
% 0.24/0.49 thf(f437,plain,(
% 0.24/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))) = $false) | ~spl0_1),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f434])).
% 0.24/0.49 thf(f434,plain,(
% 0.24/0.49 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) | ~spl0_1),
% 0.24/0.49 inference(not_proxy_clausification,[],[f208])).
% 0.24/0.49 thf(f208,plain,(
% 0.24/0.49 ((~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $true) | ~spl0_1),
% 0.24/0.49 inference(avatar_component_clause,[],[f207])).
% 0.24/0.49 thf(f207,plain,(
% 0.24/0.49 spl0_1 <=> ((~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $true)),
% 0.24/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.24/0.49 thf(f662,plain,(
% 0.24/0.49 ($true = (~ (q @ sK6))) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f661])).
% 0.24/0.49 thf(f661,plain,(
% 0.24/0.49 ($true = ((~ (q @ sK6)) | $false)) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f659])).
% 0.24/0.49 thf(f659,plain,(
% 0.24/0.49 (((~ (q @ sK6)) | (~ $true)) = $true) | ~spl0_1),
% 0.24/0.49 inference(superposition,[],[f638,f563])).
% 0.24/0.49 thf(f563,plain,(
% 0.24/0.49 ((rel_s5 @ sK5 @ sK6) = $true) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f555])).
% 0.24/0.49 thf(f555,plain,(
% 0.24/0.49 (($true => (rel_s5 @ sK5 @ sK6)) = $true) | ~spl0_1),
% 0.24/0.49 inference(superposition,[],[f475,f522])).
% 0.24/0.49 thf(f522,plain,(
% 0.24/0.49 ((rel_s5 @ sK2 @ sK6) = $true) | ~spl0_1),
% 0.24/0.49 inference(not_proxy_clausification,[],[f515])).
% 0.24/0.49 thf(f475,plain,(
% 0.24/0.49 ( ! [X0 : $i] : ((((rel_s5 @ sK2 @ X0) => (rel_s5 @ sK5 @ X0)) = $true)) ) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f467])).
% 0.24/0.49 thf(f467,plain,(
% 0.24/0.49 ( ! [X0 : $i] : (((($true & (rel_s5 @ sK2 @ X0)) => (rel_s5 @ sK5 @ X0)) = $true)) ) | ~spl0_1),
% 0.24/0.49 inference(superposition,[],[f187,f466])).
% 0.24/0.49 thf(f466,plain,(
% 0.24/0.49 ((rel_s5 @ sK5 @ sK2) = $true) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f460])).
% 0.24/0.49 thf(f460,plain,(
% 0.24/0.49 (($true => (rel_s5 @ sK5 @ sK2)) = $true) | ~spl0_1),
% 0.24/0.49 inference(superposition,[],[f176,f451])).
% 0.24/0.49 thf(f451,plain,(
% 0.24/0.49 ((rel_s5 @ sK2 @ sK5) = $true) | ~spl0_1),
% 0.24/0.49 inference(not_proxy_clausification,[],[f450])).
% 0.24/0.49 thf(f450,plain,(
% 0.24/0.49 ((~ (rel_s5 @ sK2 @ sK5)) = $false) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f449])).
% 0.24/0.49 thf(f449,plain,(
% 0.24/0.49 (($false | (~ (rel_s5 @ sK2 @ sK5))) = $false) | ~spl0_1),
% 0.24/0.49 inference(backward_demodulation,[],[f446,f448])).
% 0.24/0.49 thf(f448,plain,(
% 0.24/0.49 ((~ (p @ sK5)) = $false) | ~spl0_1),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f446])).
% 0.24/0.49 thf(f446,plain,(
% 0.24/0.49 (((~ (p @ sK5)) | (~ (rel_s5 @ sK2 @ sK5))) = $false) | ~spl0_1),
% 0.24/0.49 inference(beta_eta_normalization,[],[f445])).
% 0.24/0.49 thf(f445,plain,(
% 0.24/0.49 (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK5) = $false) | ~spl0_1),
% 0.24/0.49 inference(sigma_clausification,[],[f444])).
% 0.24/0.49 thf(f444,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $false) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f443])).
% 0.24/0.49 thf(f443,plain,(
% 0.24/0.49 (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | $false) = $false) | ~spl0_1),
% 0.24/0.49 inference(backward_demodulation,[],[f440,f441])).
% 0.24/0.49 thf(f176,plain,(
% 0.24/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)))) )),
% 0.24/0.49 inference(beta_eta_normalization,[],[f175])).
% 0.24/0.49 thf(f175,plain,(
% 0.24/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2) = $true)) )),
% 0.24/0.49 inference(pi_clausification,[],[f174])).
% 0.24/0.49 thf(f174,plain,(
% 0.24/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))) = $true)) )),
% 0.24/0.49 inference(beta_eta_normalization,[],[f173])).
% 0.24/0.49 thf(f173,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.24/0.49 inference(pi_clausification,[],[f162])).
% 0.24/0.49 thf(f162,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))) = $true)),
% 0.24/0.49 inference(beta_eta_normalization,[],[f158])).
% 0.24/0.49 thf(f158,plain,(
% 0.24/0.49 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5))),
% 0.24/0.49 inference(definition_unfolding,[],[f115,f144])).
% 0.24/0.49 thf(f144,plain,(
% 0.24/0.49 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f77])).
% 0.24/0.49 thf(f77,plain,(
% 0.24/0.49 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.24/0.49 inference(fool_elimination,[],[f76])).
% 0.24/0.49 thf(f76,plain,(
% 0.24/0.49 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))) = msymmetric)),
% 0.24/0.49 inference(rectify,[],[f19])).
% 0.24/0.49 thf(f19,axiom,(
% 0.24/0.49 ((^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.24/0.49 thf(f115,plain,(
% 0.24/0.49 ((msymmetric @ rel_s5) = $true)),
% 0.24/0.49 inference(cnf_transformation,[],[f107])).
% 0.24/0.49 thf(f107,plain,(
% 0.24/0.49 ((msymmetric @ rel_s5) = $true)),
% 0.24/0.49 inference(fool_elimination,[],[f106])).
% 0.24/0.49 thf(f106,plain,(
% 0.24/0.49 (msymmetric @ rel_s5)),
% 0.24/0.49 inference(rectify,[],[f36])).
% 0.24/0.49 thf(f36,axiom,(
% 0.24/0.49 (msymmetric @ rel_s5)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.24/0.49 thf(f187,plain,(
% 0.24/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X3 @ X1) & (rel_s5 @ X1 @ X2)) => (rel_s5 @ X3 @ X2)) = $true)) )),
% 0.24/0.49 inference(beta_eta_normalization,[],[f186])).
% 0.24/0.49 thf(f186,plain,(
% 0.24/0.49 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s5 @ Y0 @ X1) & (rel_s5 @ X1 @ X2)) => (rel_s5 @ Y0 @ X2))) @ X3) = $true)) )),
% 0.24/0.49 inference(pi_clausification,[],[f185])).
% 0.24/0.49 thf(f185,plain,(
% 0.24/0.49 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ Y0 @ X1) & (rel_s5 @ X1 @ X2)) => (rel_s5 @ Y0 @ X2)))) = $true)) )),
% 0.24/0.49 inference(beta_eta_normalization,[],[f184])).
% 0.24/0.49 thf(f184,plain,(
% 0.24/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ X1) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ Y1 @ Y0))))) @ X2))) )),
% 0.24/0.49 inference(pi_clausification,[],[f183])).
% 0.24/0.49 thf(f183,plain,(
% 0.24/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ X1) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ Y1 @ Y0)))))) = $true)) )),
% 0.24/0.49 inference(beta_eta_normalization,[],[f182])).
% 0.24/0.49 thf(f182,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y0) & (rel_s5 @ Y0 @ Y1)) => (rel_s5 @ Y2 @ Y1))))))) @ X1) = $true)) )),
% 0.24/0.49 inference(pi_clausification,[],[f163])).
% 0.24/0.49 thf(f163,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y0) & (rel_s5 @ Y0 @ Y1)) => (rel_s5 @ Y2 @ Y1)))))))) = $true)),
% 0.24/0.49 inference(beta_eta_normalization,[],[f161])).
% 0.24/0.49 thf(f161,plain,(
% 0.24/0.49 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) @ rel_s5) = $true)),
% 0.24/0.49 inference(definition_unfolding,[],[f127,f120])).
% 0.24/0.49 thf(f120,plain,(
% 0.24/0.49 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f59])).
% 0.24/0.49 thf(f59,plain,(
% 0.24/0.49 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.24/0.49 inference(fool_elimination,[],[f58])).
% 0.24/0.49 thf(f58,plain,(
% 0.24/0.49 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X1 @ X3)) => (X0 @ X1 @ X2)))) = mtransitive)),
% 0.24/0.49 inference(rectify,[],[f21])).
% 0.24/0.49 thf(f21,axiom,(
% 0.24/0.49 ((^[X6 : $i > $i > $o] : (! [X8,X10,X9] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.24/0.49 thf(f127,plain,(
% 0.24/0.49 ((mtransitive @ rel_s5) = $true)),
% 0.24/0.49 inference(cnf_transformation,[],[f105])).
% 0.24/0.49 thf(f105,plain,(
% 0.24/0.49 ((mtransitive @ rel_s5) = $true)),
% 0.24/0.49 inference(fool_elimination,[],[f104])).
% 0.24/0.49 thf(f104,plain,(
% 0.24/0.49 (mtransitive @ rel_s5)),
% 0.24/0.49 inference(rectify,[],[f35])).
% 0.24/0.49 thf(f35,axiom,(
% 0.24/0.49 (mtransitive @ rel_s5)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.24/0.49 thf(f638,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((~ (q @ X1)) | (~ (rel_s5 @ sK5 @ X1))) = $true)) ) | ~spl0_1),
% 0.24/0.49 inference(beta_eta_normalization,[],[f636])).
% 0.24/0.49 thf(f636,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))) @ X1) = $true)) ) | ~spl0_1),
% 0.24/0.49 inference(pi_clausification,[],[f609])).
% 0.24/0.49 thf(f609,plain,(
% 0.24/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f608])).
% 0.24/0.49 thf(f608,plain,(
% 0.24/0.49 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) = $true) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f607])).
% 0.24/0.49 thf(f607,plain,(
% 0.24/0.49 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) = $true) | ~spl0_1),
% 0.24/0.49 inference(forward_demodulation,[],[f597,f454])).
% 0.24/0.49 thf(f454,plain,(
% 0.24/0.49 ($true = (p @ sK5)) | ~spl0_1),
% 0.24/0.49 inference(not_proxy_clausification,[],[f448])).
% 0.24/0.49 thf(f597,plain,(
% 0.24/0.49 ($true = ((~ (p @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0))))))) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f596])).
% 0.24/0.49 thf(f596,plain,(
% 0.24/0.49 ((((~ (p @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) | $false) = $true) | ~spl0_1),
% 0.24/0.49 inference(boolean_simplification,[],[f588])).
% 0.24/0.49 thf(f588,plain,(
% 0.24/0.49 ((((~ (p @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) | (~ $true)) = $true) | ~spl0_1),
% 0.24/0.49 inference(superposition,[],[f570,f451])).
% 0.24/0.49 thf(f570,plain,(
% 0.24/0.49 ( ! [X1 : $i] : (($true = (((~ (p @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ X1 @ Y0)))))) | (~ (rel_s5 @ sK2 @ X1))))) ) | ~spl0_1),
% 0.24/0.49 inference(beta_eta_normalization,[],[f569])).
% 0.24/0.49 thf(f569,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1) = $true)) ) | ~spl0_1),
% 0.24/0.49 inference(pi_clausification,[],[f525])).
% 0.24/0.49 thf(f525,plain,(
% 0.24/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_1),
% 0.24/0.49 inference(not_proxy_clausification,[],[f437])).
% 0.24/0.49 thf(f419,plain,(
% 0.24/0.49 ~spl0_2 | ~spl0_4),
% 0.24/0.49 inference(avatar_contradiction_clause,[],[f418])).
% 0.24/0.49 thf(f418,plain,(
% 0.24/0.49 $false | (~spl0_2 | ~spl0_4)),
% 0.24/0.49 inference(trivial_inequality_removal,[],[f417])).
% 0.24/0.49 thf(f417,plain,(
% 0.24/0.49 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.24/0.49 inference(boolean_simplification,[],[f416])).
% 0.24/0.49 thf(f416,plain,(
% 0.24/0.49 ((~ $true) = $true) | (~spl0_2 | ~spl0_4)),
% 0.24/0.49 inference(forward_demodulation,[],[f407,f241])).
% 0.24/0.49 thf(f241,plain,(
% 0.24/0.49 ((rel_s5 @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.24/0.49 inference(not_proxy_clausification,[],[f230])).
% 0.24/0.49 thf(f230,plain,(
% 0.24/0.49 ((~ (rel_s5 @ sK2 @ sK3)) = $false) | ~spl0_2),
% 0.24/0.49 inference(boolean_simplification,[],[f229])).
% 0.24/0.49 thf(f229,plain,(
% 0.24/0.49 (($false | (~ (rel_s5 @ sK2 @ sK3))) = $false) | ~spl0_2),
% 0.24/0.49 inference(backward_demodulation,[],[f223,f228])).
% 0.24/0.49 thf(f228,plain,(
% 0.24/0.49 (((~ (p @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))))) = $false) | ~spl0_2),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f223])).
% 0.24/0.49 thf(f223,plain,(
% 0.24/0.49 ($false = (((~ (p @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))))) | (~ (rel_s5 @ sK2 @ sK3)))) | ~spl0_2),
% 0.24/0.49 inference(beta_eta_normalization,[],[f222])).
% 0.24/0.49 thf(f222,plain,(
% 0.24/0.49 ($false = ((^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK3)) | ~spl0_2),
% 0.24/0.49 inference(sigma_clausification,[],[f219])).
% 0.24/0.49 thf(f219,plain,(
% 0.24/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_2),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f215])).
% 0.24/0.49 thf(f215,plain,(
% 0.24/0.49 (((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $false) | ~spl0_2),
% 0.24/0.49 inference(not_proxy_clausification,[],[f211])).
% 0.24/0.49 thf(f211,plain,(
% 0.24/0.49 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))))) | ~spl0_2),
% 0.24/0.49 inference(avatar_component_clause,[],[f210])).
% 0.24/0.49 thf(f210,plain,(
% 0.24/0.49 spl0_2 <=> ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))))))),
% 0.24/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.24/0.49 thf(f407,plain,(
% 0.24/0.49 ((~ (rel_s5 @ sK2 @ sK3)) = $true) | (~spl0_2 | ~spl0_4)),
% 0.24/0.49 inference(boolean_simplification,[],[f406])).
% 0.24/0.49 thf(f406,plain,(
% 0.24/0.49 (($false | (~ (rel_s5 @ sK2 @ sK3))) = $true) | (~spl0_2 | ~spl0_4)),
% 0.24/0.49 inference(boolean_simplification,[],[f403])).
% 0.24/0.49 thf(f403,plain,(
% 0.24/0.49 (((~ $true) | (~ (rel_s5 @ sK2 @ sK3))) = $true) | (~spl0_2 | ~spl0_4)),
% 0.24/0.49 inference(superposition,[],[f384,f311])).
% 0.24/0.49 thf(f311,plain,(
% 0.24/0.49 ((p @ sK3) = $true) | ~spl0_2),
% 0.24/0.49 inference(not_proxy_clausification,[],[f310])).
% 0.24/0.49 thf(f310,plain,(
% 0.24/0.49 ((~ (p @ sK3)) = $false) | ~spl0_2),
% 0.24/0.49 inference(boolean_simplification,[],[f309])).
% 0.24/0.49 thf(f309,plain,(
% 0.24/0.49 (((~ (p @ sK3)) | $false) = $false) | ~spl0_2),
% 0.24/0.49 inference(backward_demodulation,[],[f228,f307])).
% 0.24/0.49 thf(f307,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0))))) = $false) | ~spl0_2),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f228])).
% 0.24/0.49 thf(f384,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((~ (p @ X1)) | (~ (rel_s5 @ sK2 @ X1))) = $true)) ) | ~spl0_4),
% 0.24/0.49 inference(beta_eta_normalization,[],[f383])).
% 0.24/0.49 thf(f383,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1) = $true)) ) | ~spl0_4),
% 0.24/0.49 inference(pi_clausification,[],[f237])).
% 0.24/0.49 thf(f237,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $true) | ~spl0_4),
% 0.24/0.49 inference(avatar_component_clause,[],[f236])).
% 0.24/0.49 thf(f236,plain,(
% 0.24/0.49 spl0_4 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $true)),
% 0.24/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.24/0.49 thf(f366,plain,(
% 0.24/0.49 ~spl0_2 | ~spl0_3),
% 0.24/0.49 inference(avatar_contradiction_clause,[],[f365])).
% 0.24/0.49 thf(f365,plain,(
% 0.24/0.49 $false | (~spl0_2 | ~spl0_3)),
% 0.24/0.49 inference(trivial_inequality_removal,[],[f364])).
% 0.24/0.49 thf(f364,plain,(
% 0.24/0.49 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 0.24/0.49 inference(boolean_simplification,[],[f363])).
% 0.24/0.49 thf(f363,plain,(
% 0.24/0.49 ((~ $true) = $true) | (~spl0_2 | ~spl0_3)),
% 0.24/0.49 inference(backward_demodulation,[],[f340,f361])).
% 0.24/0.49 thf(f361,plain,(
% 0.24/0.49 ((rel_s5 @ sK2 @ sK4) = $true) | ~spl0_2),
% 0.24/0.49 inference(boolean_simplification,[],[f350])).
% 0.24/0.49 thf(f350,plain,(
% 0.24/0.49 (($true => (rel_s5 @ sK2 @ sK4)) = $true) | ~spl0_2),
% 0.24/0.49 inference(superposition,[],[f253,f346])).
% 0.24/0.49 thf(f346,plain,(
% 0.24/0.49 ((rel_s5 @ sK3 @ sK4) = $true) | ~spl0_2),
% 0.24/0.49 inference(not_proxy_clausification,[],[f334])).
% 0.24/0.49 thf(f334,plain,(
% 0.24/0.49 ($false = (~ (rel_s5 @ sK3 @ sK4))) | ~spl0_2),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f333])).
% 0.24/0.49 thf(f333,plain,(
% 0.24/0.49 (((~ (q @ sK4)) | (~ (rel_s5 @ sK3 @ sK4))) = $false) | ~spl0_2),
% 0.24/0.49 inference(beta_eta_normalization,[],[f332])).
% 0.24/0.49 thf(f332,plain,(
% 0.24/0.49 (((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))) @ sK4) = $false) | ~spl0_2),
% 0.24/0.49 inference(sigma_clausification,[],[f307])).
% 0.24/0.49 thf(f253,plain,(
% 0.24/0.49 ( ! [X0 : $i] : ((((rel_s5 @ sK3 @ X0) => (rel_s5 @ sK2 @ X0)) = $true)) ) | ~spl0_2),
% 0.24/0.49 inference(boolean_simplification,[],[f246])).
% 0.24/0.49 thf(f246,plain,(
% 0.24/0.49 ( ! [X0 : $i] : (((($true & (rel_s5 @ sK3 @ X0)) => (rel_s5 @ sK2 @ X0)) = $true)) ) | ~spl0_2),
% 0.24/0.49 inference(superposition,[],[f187,f241])).
% 0.24/0.49 thf(f340,plain,(
% 0.24/0.49 ((~ (rel_s5 @ sK2 @ sK4)) = $true) | (~spl0_2 | ~spl0_3)),
% 0.24/0.49 inference(boolean_simplification,[],[f339])).
% 0.24/0.49 thf(f339,plain,(
% 0.24/0.49 (($false | (~ (rel_s5 @ sK2 @ sK4))) = $true) | (~spl0_2 | ~spl0_3)),
% 0.24/0.49 inference(superposition,[],[f245,f337])).
% 0.24/0.49 thf(f337,plain,(
% 0.24/0.49 ((~ (q @ sK4)) = $false) | ~spl0_2),
% 0.24/0.49 inference(boolean_simplification,[],[f336])).
% 0.24/0.49 thf(f336,plain,(
% 0.24/0.49 ($false = ((~ (q @ sK4)) | $false)) | ~spl0_2),
% 0.24/0.49 inference(backward_demodulation,[],[f333,f334])).
% 0.24/0.49 thf(f245,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((~ (q @ X1)) | (~ (rel_s5 @ sK2 @ X1))) = $true)) ) | ~spl0_3),
% 0.24/0.49 inference(beta_eta_normalization,[],[f244])).
% 0.24/0.49 thf(f244,plain,(
% 0.24/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1) = $true)) ) | ~spl0_3),
% 0.24/0.49 inference(pi_clausification,[],[f234])).
% 0.24/0.49 thf(f234,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $true) | ~spl0_3),
% 0.24/0.49 inference(avatar_component_clause,[],[f233])).
% 0.24/0.49 thf(f233,plain,(
% 0.24/0.49 spl0_3 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $true)),
% 0.24/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.24/0.49 thf(f238,plain,(
% 0.24/0.49 spl0_3 | spl0_4 | ~spl0_2),
% 0.24/0.49 inference(avatar_split_clause,[],[f231,f210,f236,f233])).
% 0.24/0.49 thf(f231,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $true) | ~spl0_2),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f224])).
% 0.24/0.49 thf(f224,plain,(
% 0.24/0.49 (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) = $true) | ~spl0_2),
% 0.24/0.49 inference(not_proxy_clausification,[],[f221])).
% 0.24/0.49 thf(f221,plain,(
% 0.24/0.49 ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))) = $false) | ~spl0_2),
% 0.24/0.49 inference(boolean_simplification,[],[f220])).
% 0.24/0.49 thf(f220,plain,(
% 0.24/0.49 (($false | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $false) | ~spl0_2),
% 0.24/0.49 inference(backward_demodulation,[],[f215,f219])).
% 0.24/0.49 thf(f212,plain,(
% 0.24/0.49 spl0_1 | spl0_2),
% 0.24/0.49 inference(avatar_split_clause,[],[f205,f210,f207])).
% 0.24/0.49 thf(f205,plain,(
% 0.24/0.49 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))))) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $true)),
% 0.24/0.49 inference(binary_proxy_clausification,[],[f202])).
% 0.24/0.49 thf(f202,plain,(
% 0.24/0.49 ($true = ((~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))))) | (~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))))))))),
% 0.24/0.49 inference(not_proxy_clausification,[],[f201])).
% 0.24/0.49 thf(f201,plain,(
% 0.24/0.49 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))))) | (~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))))) = $false)),
% 0.24/0.49 inference(beta_eta_normalization,[],[f200])).
% 0.24/0.49 thf(f200,plain,(
% 0.24/0.49 (((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))) @ sK2) = $false)),
% 0.24/0.49 inference(sigma_clausification,[],[f197])).
% 0.24/0.49 thf(f197,plain,(
% 0.24/0.49 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))) = $false)),
% 0.24/0.49 inference(not_proxy_clausification,[],[f170])).
% 0.24/0.49 thf(f170,plain,(
% 0.24/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))) = $true)),
% 0.24/0.49 inference(boolean_simplification,[],[f169])).
% 0.24/0.49 thf(f169,plain,(
% 0.24/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.24/0.49 inference(boolean_simplification,[],[f168])).
% 0.24/0.49 thf(f168,plain,(
% 0.24/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))) = $true)),
% 0.24/0.49 inference(boolean_simplification,[],[f167])).
% 0.24/0.49 thf(f167,plain,(
% 0.24/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ ((~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.24/0.49 inference(boolean_simplification,[],[f166])).
% 0.24/0.49 thf(f166,plain,(
% 0.24/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))))) | (~ ((~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))) = $true)),
% 0.24/0.49 inference(boolean_simplification,[],[f165])).
% 0.24/0.49 thf(f165,plain,(
% 0.24/0.49 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))))) | (~ ((~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.24/0.49 inference(beta_eta_normalization,[],[f160])).
% 0.24/0.49 thf(f160,plain,(
% 0.24/0.49 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))))) = $true)),
% 0.24/0.49 inference(definition_unfolding,[],[f122,f134,f151,f157,f148,f157,f148,f157,f157])).
% 0.24/0.49 thf(f148,plain,(
% 0.24/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.24/0.49 inference(definition_unfolding,[],[f132,f113,f147,f113,f113])).
% 0.24/0.49 thf(f147,plain,(
% 0.24/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f67])).
% 0.24/0.49 thf(f67,plain,(
% 0.24/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.24/0.49 inference(fool_elimination,[],[f66])).
% 0.24/0.49 thf(f66,plain,(
% 0.24/0.49 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.24/0.49 inference(rectify,[],[f4])).
% 0.24/0.49 thf(f4,axiom,(
% 0.24/0.49 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.24/0.49 thf(f113,plain,(
% 0.24/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f110])).
% 0.24/0.49 thf(f110,plain,(
% 0.24/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.24/0.49 inference(fool_elimination,[],[f109])).
% 0.24/0.49 thf(f109,plain,(
% 0.24/0.49 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.24/0.49 inference(rectify,[],[f3])).
% 0.24/0.49 thf(f3,axiom,(
% 0.24/0.49 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.24/0.49 thf(f132,plain,(
% 0.24/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f57])).
% 0.24/0.49 thf(f57,plain,(
% 0.24/0.49 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.24/0.49 inference(fool_elimination,[],[f56])).
% 0.24/0.49 thf(f56,plain,(
% 0.24/0.49 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.24/0.49 inference(rectify,[],[f5])).
% 0.24/0.49 thf(f5,axiom,(
% 0.24/0.49 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.24/0.49 thf(f157,plain,(
% 0.24/0.49 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.24/0.49 inference(definition_unfolding,[],[f128,f113,f139,f113])).
% 0.24/0.49 thf(f139,plain,(
% 0.24/0.49 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f49])).
% 0.24/0.49 thf(f49,plain,(
% 0.24/0.49 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.24/0.49 inference(fool_elimination,[],[f48])).
% 0.24/0.49 thf(f48,plain,(
% 0.24/0.49 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))))),
% 0.24/0.49 inference(rectify,[],[f32])).
% 0.24/0.49 thf(f32,axiom,(
% 0.24/0.49 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.24/0.49 thf(f128,plain,(
% 0.24/0.49 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.24/0.49 inference(cnf_transformation,[],[f84])).
% 0.24/0.49 thf(f84,plain,(
% 0.24/0.49 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.24/0.49 inference(fool_elimination,[],[f83])).
% 0.24/0.49 thf(f83,plain,(
% 0.24/0.49 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.24/0.49 inference(rectify,[],[f33])).
% 0.24/0.49 thf(f33,axiom,(
% 0.24/0.49 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.24/0.49 thf(f151,plain,(
% 0.24/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.24/0.49 inference(definition_unfolding,[],[f146,f148,f149,f149])).
% 0.24/0.49 thf(f149,plain,(
% 0.24/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.24/0.49 inference(definition_unfolding,[],[f129,f147,f113])).
% 0.24/0.49 thf(f129,plain,(
% 0.24/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.24/0.49 inference(cnf_transformation,[],[f102])).
% 0.24/0.49 thf(f102,plain,(
% 0.24/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.24/0.49 inference(fool_elimination,[],[f101])).
% 0.24/0.49 thf(f101,plain,(
% 0.24/0.49 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.24/0.49 inference(rectify,[],[f6])).
% 0.24/0.49 thf(f6,axiom,(
% 0.24/0.49 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.24/0.49 thf(f146,plain,(
% 0.24/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f96])).
% 0.24/0.49 thf(f96,plain,(
% 0.24/0.49 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.24/0.49 inference(fool_elimination,[],[f95])).
% 0.24/0.49 thf(f95,plain,(
% 0.24/0.49 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.24/0.49 inference(rectify,[],[f8])).
% 0.24/0.49 thf(f8,axiom,(
% 0.24/0.49 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.24/0.49 thf(f134,plain,(
% 0.24/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.24/0.49 inference(cnf_transformation,[],[f55])).
% 0.24/0.49 thf(f55,plain,(
% 0.24/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.24/0.49 inference(fool_elimination,[],[f54])).
% 0.24/0.49 thf(f54,plain,(
% 0.24/0.49 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.24/0.49 inference(rectify,[],[f28])).
% 0.24/0.49 thf(f28,axiom,(
% 0.24/0.49 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.24/0.49 thf(f122,plain,(
% 0.24/0.49 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))))),
% 0.24/0.49 inference(cnf_transformation,[],[f69])).
% 0.24/0.49 thf(f69,plain,(
% 0.24/0.49 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))))),
% 0.24/0.49 inference(fool_elimination,[],[f68])).
% 0.24/0.49 thf(f68,plain,(
% 0.24/0.49 ~(mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))),
% 0.24/0.49 inference(rectify,[],[f38])).
% 0.24/0.49 thf(f38,negated_conjecture,(
% 0.24/0.49 ~(mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))),
% 0.24/0.49 inference(negated_conjecture,[],[f37])).
% 0.24/0.49 thf(f37,conjecture,(
% 0.24/0.49 (mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))),
% 0.24/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.24/0.49 % SZS output end Proof for theBenchmark
% 0.24/0.49 % (9753)------------------------------
% 0.24/0.49 % (9753)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.24/0.49 % (9753)Termination reason: Refutation
% 0.24/0.49
% 0.24/0.49 % (9753)Memory used [KB]: 6140
% 0.24/0.49 % (9753)Time elapsed: 0.080 s
% 0.24/0.49 % (9753)Instructions burned: 78 (million)
% 0.24/0.49 % (9753)------------------------------
% 0.24/0.49 % (9753)------------------------------
% 0.24/0.49 % (9741)Success in time 0.104 s
%------------------------------------------------------------------------------