TSTP Solution File: SYN052^7 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYN052^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% 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 : Mon Jun 24 20:00:59 EDT 2024
% Result : Theorem 3.01s 0.80s
% Output : Refutation 3.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN052^7 : TPTP v8.2.0. Released v5.5.0.
% 0.11/0.12 % Command : run_vampire %s %d THM
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Jun 23 20:44:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 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
% 0.12/0.37 % (12788)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)
% 0.12/0.37 % (12787)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (12790)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)
% 0.12/0.37 % (12788)Instruction limit reached!
% 0.12/0.37 % (12788)------------------------------
% 0.12/0.37 % (12788)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12788)Termination reason: Unknown
% 0.12/0.37 % (12788)Termination phase: Property scanning
% 0.12/0.37
% 0.12/0.37 % (12788)Memory used [KB]: 1023
% 0.12/0.37 % (12788)Time elapsed: 0.004 s
% 0.12/0.37 % (12788)Instructions burned: 5 (million)
% 0.12/0.37 % (12788)------------------------------
% 0.12/0.37 % (12788)------------------------------
% 0.12/0.37 % (12795)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (12793)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)
% 0.12/0.37 % (12793)Instruction limit reached!
% 0.12/0.37 % (12793)------------------------------
% 0.12/0.37 % (12793)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12793)Termination reason: Unknown
% 0.12/0.37 % (12793)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (12793)Memory used [KB]: 1023
% 0.12/0.37 % (12793)Time elapsed: 0.003 s
% 0.12/0.37 % (12793)Instructions burned: 2 (million)
% 0.12/0.37 % (12793)------------------------------
% 0.12/0.37 % (12793)------------------------------
% 0.12/0.37 % (12791)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (12794)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)
% 0.12/0.37 % (12791)Instruction limit reached!
% 0.12/0.37 % (12791)------------------------------
% 0.12/0.37 % (12791)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (12791)Termination reason: Unknown
% 0.12/0.37 % (12791)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (12791)Memory used [KB]: 1023
% 0.12/0.37 % (12791)Time elapsed: 0.005 s
% 0.12/0.37 % (12791)Instructions burned: 2 (million)
% 0.12/0.37 % (12791)------------------------------
% 0.12/0.37 % (12791)------------------------------
% 0.12/0.38 % (12795)Instruction limit reached!
% 0.12/0.38 % (12795)------------------------------
% 0.12/0.38 % (12795)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (12795)Termination reason: Unknown
% 0.12/0.38 % (12795)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (12795)Memory used [KB]: 5628
% 0.12/0.38 % (12795)Time elapsed: 0.012 s
% 0.12/0.38 % (12795)Instructions burned: 18 (million)
% 0.12/0.38 % (12795)------------------------------
% 0.12/0.38 % (12795)------------------------------
% 0.12/0.38 % (12803)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)
% 0.12/0.39 % (12790)Instruction limit reached!
% 0.12/0.39 % (12790)------------------------------
% 0.12/0.39 % (12790)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (12790)Termination reason: Unknown
% 0.12/0.39 % (12790)Termination phase: Saturation
% 0.12/0.39
% 0.12/0.39 % (12790)Memory used [KB]: 5628
% 0.12/0.39 % (12790)Time elapsed: 0.017 s
% 0.12/0.39 % (12790)Instructions burned: 28 (million)
% 0.12/0.39 % (12790)------------------------------
% 0.12/0.39 % (12790)------------------------------
% 0.12/0.39 % (12803)Instruction limit reached!
% 0.12/0.39 % (12803)------------------------------
% 0.12/0.39 % (12803)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (12803)Termination reason: Unknown
% 0.12/0.39 % (12803)Termination phase: shuffling
% 0.12/0.39
% 0.12/0.39 % (12803)Memory used [KB]: 1023
% 0.12/0.39 % (12803)Time elapsed: 0.003 s
% 0.12/0.39 % (12803)Instructions burned: 4 (million)
% 0.12/0.39 % (12803)------------------------------
% 0.12/0.39 % (12803)------------------------------
% 0.12/0.39 % (12804)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)
% 0.12/0.39 % (12805)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)
% 0.12/0.40 % (12808)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)
% 0.12/0.40 % (12808)Instruction limit reached!
% 0.12/0.40 % (12808)------------------------------
% 0.12/0.40 % (12808)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (12808)Termination reason: Unknown
% 0.12/0.40 % (12808)Termination phase: shuffling
% 0.12/0.40
% 0.12/0.40 % (12808)Memory used [KB]: 1023
% 0.12/0.40 % (12808)Time elapsed: 0.004 s
% 0.12/0.40 % (12808)Instructions burned: 3 (million)
% 0.12/0.40 % (12808)------------------------------
% 0.12/0.40 % (12808)------------------------------
% 0.12/0.40 % (12813)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.12/0.40 % (12805)Instruction limit reached!
% 0.12/0.40 % (12805)------------------------------
% 0.12/0.40 % (12805)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (12805)Termination reason: Unknown
% 0.12/0.40 % (12805)Termination phase: Saturation
% 0.12/0.40
% 0.12/0.40 % (12805)Memory used [KB]: 5628
% 0.12/0.40 % (12805)Time elapsed: 0.011 s
% 0.12/0.40 % (12805)Instructions burned: 16 (million)
% 0.12/0.40 % (12805)------------------------------
% 0.12/0.40 % (12805)------------------------------
% 0.12/0.40 % (12811)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)
% 0.12/0.40 % (12813)Instruction limit reached!
% 0.12/0.40 % (12813)------------------------------
% 0.12/0.40 % (12813)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.40 % (12813)Termination reason: Unknown
% 0.12/0.40 % (12813)Termination phase: Function definition elimination
% 0.12/0.40
% 0.12/0.40 % (12813)Memory used [KB]: 1023
% 0.12/0.40 % (12813)Time elapsed: 0.005 s
% 0.12/0.40 % (12813)Instructions burned: 9 (million)
% 0.12/0.40 % (12813)------------------------------
% 0.12/0.40 % (12813)------------------------------
% 0.12/0.41 % (12804)Instruction limit reached!
% 0.12/0.41 % (12804)------------------------------
% 0.12/0.41 % (12804)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.41 % (12804)Termination reason: Unknown
% 0.12/0.41 % (12804)Termination phase: Saturation
% 0.12/0.41
% 0.12/0.41 % (12804)Memory used [KB]: 5756
% 0.12/0.41 % (12804)Time elapsed: 0.024 s
% 0.12/0.41 % (12804)Instructions burned: 37 (million)
% 0.12/0.41 % (12804)------------------------------
% 0.12/0.41 % (12804)------------------------------
% 0.21/0.41 % (12816)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (12818)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)
% 0.21/0.42 % (12821)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)
% 0.21/0.42 % (12818)Instruction limit reached!
% 0.21/0.42 % (12818)------------------------------
% 0.21/0.42 % (12818)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (12818)Termination reason: Unknown
% 0.21/0.42 % (12818)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (12818)Memory used [KB]: 1023
% 0.21/0.42 % (12818)Time elapsed: 0.004 s
% 0.21/0.42 % (12818)Instructions burned: 3 (million)
% 0.21/0.42 % (12818)------------------------------
% 0.21/0.42 % (12818)------------------------------
% 0.21/0.42 % (12821)Instruction limit reached!
% 0.21/0.42 % (12821)------------------------------
% 0.21/0.42 % (12821)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (12821)Termination reason: Unknown
% 0.21/0.42 % (12821)Termination phase: shuffling
% 0.21/0.42
% 0.21/0.42 % (12821)Memory used [KB]: 1023
% 0.21/0.42 % (12821)Time elapsed: 0.004 s
% 0.21/0.42 % (12821)Instructions burned: 4 (million)
% 0.21/0.42 % (12821)------------------------------
% 0.21/0.42 % (12821)------------------------------
% 0.21/0.42 % (12816)Instruction limit reached!
% 0.21/0.42 % (12816)------------------------------
% 0.21/0.42 % (12816)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.42 % (12816)Termination reason: Unknown
% 0.21/0.42 % (12816)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (12816)Memory used [KB]: 5884
% 0.21/0.42 % (12816)Time elapsed: 0.012 s
% 0.21/0.42 % (12816)Instructions burned: 16 (million)
% 0.21/0.42 % (12816)------------------------------
% 0.21/0.42 % (12816)------------------------------
% 0.21/0.43 % (12825)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)
% 0.21/0.43 % (12825)Instruction limit reached!
% 0.21/0.43 % (12825)------------------------------
% 0.21/0.43 % (12825)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (12825)Termination reason: Unknown
% 0.21/0.43 % (12825)Termination phase: Function definition elimination
% 0.21/0.43
% 0.21/0.43 % (12825)Memory used [KB]: 1023
% 0.21/0.43 % (12825)Time elapsed: 0.006 s
% 0.21/0.43 % (12825)Instructions burned: 8 (million)
% 0.21/0.43 % (12825)------------------------------
% 0.21/0.43 % (12825)------------------------------
% 0.21/0.43 % (12827)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)
% 0.21/0.43 % (12827)Instruction limit reached!
% 0.21/0.43 % (12827)------------------------------
% 0.21/0.43 % (12827)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.43 % (12827)Termination reason: Unknown
% 0.21/0.43 % (12827)Termination phase: shuffling
% 0.21/0.43
% 0.21/0.43 % (12827)Memory used [KB]: 1023
% 0.21/0.43 % (12827)Time elapsed: 0.004 s
% 0.21/0.43 % (12827)Instructions burned: 3 (million)
% 0.21/0.43 % (12827)------------------------------
% 0.21/0.43 % (12827)------------------------------
% 0.21/0.44 % (12828)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.44 % (12832)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)
% 0.21/0.44 % (12828)Instruction limit reached!
% 0.21/0.44 % (12828)------------------------------
% 0.21/0.44 % (12828)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.44 % (12828)Termination reason: Unknown
% 0.21/0.44 % (12828)Termination phase: Property scanning
% 0.21/0.44
% 0.21/0.44 % (12828)Memory used [KB]: 1023
% 0.21/0.44 % (12828)Time elapsed: 0.004 s
% 0.21/0.44 % (12828)Instructions burned: 4 (million)
% 0.21/0.44 % (12828)------------------------------
% 0.21/0.44 % (12828)------------------------------
% 0.21/0.45 % (12833)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.21/0.45 % (12832)Instruction limit reached!
% 0.21/0.45 % (12832)------------------------------
% 0.21/0.45 % (12832)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.45 % (12832)Termination reason: Unknown
% 0.21/0.45 % (12832)Termination phase: Saturation
% 0.21/0.45
% 0.21/0.45 % (12832)Memory used [KB]: 5628
% 0.21/0.45 % (12832)Time elapsed: 0.014 s
% 0.21/0.45 % (12832)Instructions burned: 18 (million)
% 0.21/0.45 % (12832)------------------------------
% 0.21/0.45 % (12832)------------------------------
% 0.21/0.45 % (12835)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.21/0.46 % (12835)Instruction limit reached!
% 0.21/0.46 % (12835)------------------------------
% 0.21/0.46 % (12835)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.46 % (12835)Termination reason: Unknown
% 0.21/0.46 % (12835)Termination phase: Property scanning
% 0.21/0.46
% 0.21/0.46 % (12835)Memory used [KB]: 1023
% 0.21/0.46 % (12835)Time elapsed: 0.006 s
% 0.21/0.46 % (12835)Instructions burned: 6 (million)
% 0.21/0.46 % (12835)------------------------------
% 0.21/0.46 % (12835)------------------------------
% 0.21/0.46 % (12838)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)
% 0.21/0.46 % (12833)Refutation not found, incomplete strategy
% 0.21/0.46 % (12833)------------------------------
% 0.21/0.46 % (12833)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.46 % (12833)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % (12833)Memory used [KB]: 5628
% 0.21/0.46 % (12833)Time elapsed: 0.012 s
% 0.21/0.46 % (12833)Instructions burned: 17 (million)
% 0.21/0.46 % (12833)------------------------------
% 0.21/0.46 % (12833)------------------------------
% 0.21/0.46 % (12838)Refutation not found, incomplete strategy
% 0.21/0.46 % (12838)------------------------------
% 0.21/0.46 % (12838)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.46 % (12838)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.46
% 0.21/0.46
% 0.21/0.46 % (12838)Memory used [KB]: 5628
% 0.21/0.46 % (12838)Time elapsed: 0.008 s
% 0.21/0.46 % (12838)Instructions burned: 10 (million)
% 0.21/0.46 % (12838)------------------------------
% 0.21/0.46 % (12838)------------------------------
% 0.21/0.47 % (12842)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)
% 0.21/0.47 % (12843)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.21/0.47 % (12843)Instruction limit reached!
% 0.21/0.47 % (12843)------------------------------
% 0.21/0.47 % (12843)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.47 % (12843)Termination reason: Unknown
% 0.21/0.47 % (12843)Termination phase: Preprocessing 1
% 0.21/0.47
% 0.21/0.47 % (12843)Memory used [KB]: 1023
% 0.21/0.47 % (12843)Time elapsed: 0.005 s
% 0.21/0.47 % (12843)Instructions burned: 6 (million)
% 0.21/0.47 % (12843)------------------------------
% 0.21/0.47 % (12843)------------------------------
% 0.21/0.47 % (12844)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)
% 0.21/0.48 % (12844)Instruction limit reached!
% 0.21/0.48 % (12844)------------------------------
% 0.21/0.48 % (12844)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.48 % (12844)Termination reason: Unknown
% 0.21/0.48 % (12844)Termination phase: SInE selection
% 0.21/0.48
% 0.21/0.48 % (12844)Memory used [KB]: 1023
% 0.21/0.48 % (12844)Time elapsed: 0.005 s
% 0.21/0.48 % (12844)Instructions burned: 6 (million)
% 0.21/0.48 % (12844)------------------------------
% 0.21/0.48 % (12844)------------------------------
% 0.21/0.48 % (12845)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.21/0.48 % (12842)Instruction limit reached!
% 0.21/0.48 % (12842)------------------------------
% 0.21/0.48 % (12842)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.48 % (12842)Termination reason: Unknown
% 0.21/0.48 % (12842)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (12842)Memory used [KB]: 5756
% 0.21/0.48 % (12842)Time elapsed: 0.015 s
% 0.21/0.48 % (12842)Instructions burned: 22 (million)
% 0.21/0.48 % (12842)------------------------------
% 0.21/0.48 % (12842)------------------------------
% 0.21/0.48 % (12787)Instruction limit reached!
% 0.21/0.48 % (12787)------------------------------
% 0.21/0.48 % (12787)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.48 % (12787)Termination reason: Unknown
% 0.21/0.48 % (12787)Termination phase: Saturation
% 0.21/0.48
% 0.21/0.48 % (12787)Memory used [KB]: 6396
% 0.21/0.48 % (12787)Time elapsed: 0.113 s
% 0.21/0.48 % (12787)Instructions burned: 184 (million)
% 0.21/0.48 % (12787)------------------------------
% 0.21/0.48 % (12787)------------------------------
% 0.21/0.49 % (12846)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 (2998ds/779Mi)
% 0.21/0.49 % (12847)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 (2998ds/19Mi)
% 0.21/0.49 % (12848)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.21/0.50 % (12849)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.21/0.50 % (12847)Instruction limit reached!
% 0.21/0.50 % (12847)------------------------------
% 0.21/0.50 % (12847)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.50 % (12847)Termination reason: Unknown
% 0.21/0.50 % (12847)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (12847)Memory used [KB]: 5628
% 0.21/0.50 % (12847)Time elapsed: 0.010 s
% 0.21/0.50 % (12847)Instructions burned: 20 (million)
% 0.21/0.50 % (12847)------------------------------
% 0.21/0.50 % (12847)------------------------------
% 0.21/0.50 % (12849)Instruction limit reached!
% 0.21/0.50 % (12849)------------------------------
% 0.21/0.50 % (12849)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.50 % (12849)Termination reason: Unknown
% 0.21/0.50 % (12849)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (12849)Memory used [KB]: 5628
% 0.21/0.50 % (12849)Time elapsed: 0.008 s
% 0.21/0.50 % (12849)Instructions burned: 17 (million)
% 0.21/0.50 % (12849)------------------------------
% 0.21/0.50 % (12849)------------------------------
% 0.21/0.51 % (12850)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.21/0.51 % (12850)Instruction limit reached!
% 0.21/0.51 % (12850)------------------------------
% 0.21/0.51 % (12850)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.51 % (12850)Termination reason: Unknown
% 0.21/0.51 % (12850)Termination phase: shuffling
% 0.21/0.51
% 0.21/0.51 % (12850)Memory used [KB]: 1023
% 0.21/0.51 % (12850)Time elapsed: 0.002 s
% 0.21/0.51 % (12850)Instructions burned: 3 (million)
% 0.21/0.51 % (12850)------------------------------
% 0.21/0.51 % (12850)------------------------------
% 0.21/0.51 % (12851)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.21/0.52 % (12852)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 (2998ds/127Mi)
% 0.21/0.52 % (12794)Refutation not found, non-redundant clauses discarded% (12794)------------------------------
% 0.21/0.52 % (12794)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.52 % (12794)Termination reason: Refutation not found, non-redundant clauses discarded
% 0.21/0.52
% 0.21/0.52 % (12794)Memory used [KB]: 6524
% 0.21/0.52 % (12794)Time elapsed: 0.151 s
% 0.21/0.52 % (12794)Instructions burned: 273 (million)
% 0.21/0.52 % (12794)------------------------------
% 0.21/0.52 % (12794)------------------------------
% 0.21/0.52 % (12851)Instruction limit reached!
% 0.21/0.52 % (12851)------------------------------
% 0.21/0.52 % (12851)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.52 % (12851)Termination reason: Unknown
% 0.21/0.52 % (12851)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (12851)Memory used [KB]: 5756
% 0.21/0.52 % (12851)Time elapsed: 0.011 s
% 0.21/0.52 % (12851)Instructions burned: 31 (million)
% 0.21/0.52 % (12851)------------------------------
% 0.21/0.52 % (12851)------------------------------
% 0.21/0.53 % (12853)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 (2998ds/100Mi)
% 0.21/0.53 % (12854)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 (2998ds/3Mi)
% 0.21/0.53 % (12854)Instruction limit reached!
% 0.21/0.53 % (12854)------------------------------
% 0.21/0.53 % (12854)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.53 % (12854)Termination reason: Unknown
% 0.21/0.53 % (12854)Termination phase: Property scanning
% 0.21/0.53
% 0.21/0.53 % (12854)Memory used [KB]: 1023
% 0.21/0.53 % (12854)Time elapsed: 0.003 s
% 0.21/0.53 % (12854)Instructions burned: 4 (million)
% 0.21/0.53 % (12854)------------------------------
% 0.21/0.53 % (12854)------------------------------
% 0.21/0.54 % (12855)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)
% 0.21/0.55 % (12855)Refutation not found, incomplete strategy
% 0.21/0.55 % (12855)------------------------------
% 0.21/0.55 % (12855)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.55 % (12855)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.55
% 0.21/0.55
% 0.21/0.55 % (12855)Memory used [KB]: 5628
% 0.21/0.55 % (12855)Time elapsed: 0.007 s
% 0.21/0.55 % (12855)Instructions burned: 17 (million)
% 0.21/0.55 % (12855)------------------------------
% 0.21/0.55 % (12855)------------------------------
% 0.21/0.56 % (12856)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 (2997ds/86Mi)
% 0.21/0.56 % (12853)Instruction limit reached!
% 0.21/0.56 % (12853)------------------------------
% 0.21/0.56 % (12853)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.56 % (12853)Termination reason: Unknown
% 0.21/0.56 % (12853)Termination phase: Saturation
% 0.21/0.56
% 0.21/0.56 % (12853)Memory used [KB]: 5884
% 0.21/0.56 % (12853)Time elapsed: 0.035 s
% 0.21/0.56 % (12853)Instructions burned: 100 (million)
% 0.21/0.56 % (12853)------------------------------
% 0.21/0.56 % (12853)------------------------------
% 0.21/0.57 % (12852)Instruction limit reached!
% 0.21/0.57 % (12852)------------------------------
% 0.21/0.57 % (12852)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.57 % (12852)Termination reason: Unknown
% 0.21/0.57 % (12852)Termination phase: Saturation
% 0.21/0.57
% 0.21/0.57 % (12852)Memory used [KB]: 6268
% 0.21/0.57 % (12852)Time elapsed: 0.048 s
% 0.21/0.57 % (12852)Instructions burned: 129 (million)
% 0.21/0.57 % (12852)------------------------------
% 0.21/0.57 % (12852)------------------------------
% 0.21/0.57 % (12857)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 (2997ds/107Mi)
% 0.21/0.57 % (12858)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 (2997ds/39Mi)
% 0.21/0.59 % (12856)Instruction limit reached!
% 0.21/0.59 % (12856)------------------------------
% 0.21/0.59 % (12856)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.59 % (12856)Termination reason: Unknown
% 0.21/0.59 % (12856)Termination phase: Saturation
% 0.21/0.59
% 0.21/0.59 % (12856)Memory used [KB]: 6140
% 0.21/0.59 % (12856)Time elapsed: 0.032 s
% 0.21/0.59 % (12856)Instructions burned: 86 (million)
% 0.21/0.59 % (12856)------------------------------
% 0.21/0.59 % (12856)------------------------------
% 0.21/0.59 % (12858)Instruction limit reached!
% 0.21/0.59 % (12858)------------------------------
% 0.21/0.59 % (12858)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.59 % (12858)Termination reason: Unknown
% 0.21/0.59 % (12858)Termination phase: Saturation
% 0.21/0.59
% 0.21/0.59 % (12858)Memory used [KB]: 5884
% 0.21/0.59 % (12858)Time elapsed: 0.015 s
% 0.21/0.59 % (12858)Instructions burned: 40 (million)
% 0.21/0.59 % (12858)------------------------------
% 0.21/0.59 % (12858)------------------------------
% 1.79/0.60 % (12859)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 (2997ds/448Mi)
% 1.79/0.60 % (12860)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 (2997ds/46Mi)
% 1.92/0.62 % (12860)Instruction limit reached!
% 1.92/0.62 % (12860)------------------------------
% 1.92/0.62 % (12860)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.92/0.62 % (12860)Termination reason: Unknown
% 1.92/0.62 % (12860)Termination phase: Saturation
% 1.92/0.62
% 1.92/0.62 % (12860)Memory used [KB]: 5884
% 1.92/0.62 % (12860)Time elapsed: 0.020 s
% 1.92/0.62 % (12860)Instructions burned: 47 (million)
% 1.92/0.62 % (12860)------------------------------
% 1.92/0.62 % (12860)------------------------------
% 1.92/0.62 % (12867)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 (2997ds/98Mi)
% 1.92/0.63 % (12845)Instruction limit reached!
% 1.92/0.63 % (12845)------------------------------
% 1.92/0.63 % (12845)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 1.92/0.63 % (12845)Termination reason: Unknown
% 1.92/0.63 % (12845)Termination phase: Saturation
% 1.92/0.63
% 1.92/0.63 % (12845)Memory used [KB]: 6524
% 1.92/0.63 % (12845)Time elapsed: 0.149 s
% 1.92/0.63 % (12845)Instructions burned: 378 (million)
% 1.92/0.63 % (12845)------------------------------
% 1.92/0.63 % (12845)------------------------------
% 2.03/0.64 % (12868)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 (2997ds/507Mi)
% 2.03/0.64 % (12857)Instruction limit reached!
% 2.03/0.64 % (12857)------------------------------
% 2.03/0.64 % (12857)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.64 % (12857)Termination reason: Unknown
% 2.03/0.64 % (12857)Termination phase: Saturation
% 2.03/0.64
% 2.03/0.64 % (12857)Memory used [KB]: 6140
% 2.03/0.64 % (12857)Time elapsed: 0.066 s
% 2.03/0.64 % (12857)Instructions burned: 107 (million)
% 2.03/0.64 % (12857)------------------------------
% 2.03/0.64 % (12857)------------------------------
% 2.03/0.64 % (12868)Refutation not found, incomplete strategy
% 2.03/0.64 % (12868)------------------------------
% 2.03/0.64 % (12868)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.64 % (12868)Termination reason: Refutation not found, incomplete strategy
% 2.03/0.64
% 2.03/0.64
% 2.03/0.64 % (12868)Memory used [KB]: 5628
% 2.03/0.64 % (12868)Time elapsed: 0.007 s
% 2.03/0.64 % (12868)Instructions burned: 17 (million)
% 2.03/0.64 % (12868)------------------------------
% 2.03/0.64 % (12868)------------------------------
% 2.03/0.65 % (12872)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 2.03/0.65 % (12869)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 (2997ds/149Mi)
% 2.03/0.66 % (12867)Instruction limit reached!
% 2.03/0.66 % (12867)------------------------------
% 2.03/0.66 % (12867)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.66 % (12867)Termination reason: Unknown
% 2.03/0.66 % (12867)Termination phase: Saturation
% 2.03/0.66
% 2.03/0.66 % (12867)Memory used [KB]: 1279
% 2.03/0.66 % (12867)Time elapsed: 0.034 s
% 2.03/0.66 % (12867)Instructions burned: 98 (million)
% 2.03/0.66 % (12867)------------------------------
% 2.03/0.66 % (12867)------------------------------
% 2.03/0.66 % (12872)Instruction limit reached!
% 2.03/0.66 % (12872)------------------------------
% 2.03/0.66 % (12872)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.66 % (12872)Termination reason: Unknown
% 2.03/0.66 % (12872)Termination phase: Saturation
% 2.03/0.66
% 2.03/0.66 % (12872)Memory used [KB]: 5756
% 2.03/0.66 % (12872)Time elapsed: 0.014 s
% 2.03/0.66 % (12872)Instructions burned: 40 (million)
% 2.03/0.66 % (12872)------------------------------
% 2.03/0.66 % (12872)------------------------------
% 2.03/0.67 % (12879)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2996ds/6Mi)
% 2.03/0.67 % (12879)Instruction limit reached!
% 2.03/0.67 % (12879)------------------------------
% 2.03/0.67 % (12879)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.67 % (12879)Termination reason: Unknown
% 2.03/0.67 % (12879)Termination phase: Function definition elimination
% 2.03/0.67
% 2.03/0.67 % (12879)Memory used [KB]: 1151
% 2.03/0.67 % (12879)Time elapsed: 0.004 s
% 2.03/0.67 % (12879)Instructions burned: 8 (million)
% 2.03/0.67 % (12879)------------------------------
% 2.03/0.67 % (12879)------------------------------
% 2.03/0.67 % (12883)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on theBenchmark for (2996ds/1087Mi)
% 2.03/0.68 % (12886)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2996ds/47Mi)
% 2.03/0.68 % (12883)Refutation not found, incomplete strategy
% 2.03/0.68 % (12883)------------------------------
% 2.03/0.68 % (12883)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.68 % (12883)Termination reason: Refutation not found, incomplete strategy
% 2.03/0.68
% 2.03/0.68
% 2.03/0.68 % (12883)Memory used [KB]: 5628
% 2.03/0.68 % (12883)Time elapsed: 0.007 s
% 2.03/0.68 % (12883)Instructions burned: 17 (million)
% 2.03/0.68 % (12883)------------------------------
% 2.03/0.68 % (12883)------------------------------
% 2.03/0.69 % (12891)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on theBenchmark for (2996ds/44Mi)
% 2.03/0.69 % (12886)Instruction limit reached!
% 2.03/0.69 % (12886)------------------------------
% 2.03/0.69 % (12886)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.69 % (12886)Termination reason: Unknown
% 2.03/0.69 % (12886)Termination phase: Saturation
% 2.03/0.69
% 2.03/0.69 % (12886)Memory used [KB]: 5756
% 2.03/0.69 % (12886)Time elapsed: 0.015 s
% 2.03/0.69 % (12886)Instructions burned: 48 (million)
% 2.03/0.69 % (12886)------------------------------
% 2.03/0.69 % (12886)------------------------------
% 2.03/0.70 % (12898)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on theBenchmark for (2996ds/432Mi)
% 2.03/0.70 % (12891)Instruction limit reached!
% 2.03/0.70 % (12891)------------------------------
% 2.03/0.70 % (12891)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.03/0.70 % (12891)Termination reason: Unknown
% 2.03/0.70 % (12891)Termination phase: Saturation
% 2.03/0.70
% 2.03/0.70 % (12891)Memory used [KB]: 1279
% 2.03/0.70 % (12891)Time elapsed: 0.016 s
% 2.03/0.70 % (12891)Instructions burned: 46 (million)
% 2.03/0.70 % (12891)------------------------------
% 2.03/0.70 % (12891)------------------------------
% 2.03/0.71 % (12903)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2996ds/62Mi)
% 2.45/0.72 % (12869)Instruction limit reached!
% 2.45/0.72 % (12869)------------------------------
% 2.45/0.72 % (12869)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.45/0.72 % (12869)Termination reason: Unknown
% 2.45/0.72 % (12869)Termination phase: Saturation
% 2.45/0.72
% 2.45/0.72 % (12869)Memory used [KB]: 6140
% 2.45/0.72 % (12869)Time elapsed: 0.070 s
% 2.45/0.72 % (12869)Instructions burned: 150 (million)
% 2.45/0.72 % (12869)------------------------------
% 2.45/0.72 % (12869)------------------------------
% 2.45/0.73 % (12915)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2996ds/31Mi)
% 2.45/0.73 % (12903)Instruction limit reached!
% 2.45/0.73 % (12903)------------------------------
% 2.45/0.73 % (12903)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.45/0.73 % (12903)Termination reason: Unknown
% 2.45/0.73 % (12903)Termination phase: Saturation
% 2.45/0.73
% 2.45/0.73 % (12903)Memory used [KB]: 5884
% 2.45/0.73 % (12903)Time elapsed: 0.023 s
% 2.45/0.73 % (12903)Instructions burned: 63 (million)
% 2.45/0.73 % (12903)------------------------------
% 2.45/0.73 % (12903)------------------------------
% 2.45/0.74 % (12919)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2996ds/96Mi)
% 2.45/0.74 % (12915)Instruction limit reached!
% 2.45/0.74 % (12915)------------------------------
% 2.45/0.74 % (12915)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.45/0.74 % (12915)Termination reason: Unknown
% 2.45/0.74 % (12915)Termination phase: Saturation
% 2.45/0.74
% 2.45/0.74 % (12915)Memory used [KB]: 5756
% 2.45/0.74 % (12915)Time elapsed: 0.012 s
% 2.45/0.74 % (12915)Instructions burned: 31 (million)
% 2.45/0.74 % (12915)------------------------------
% 2.45/0.74 % (12915)------------------------------
% 2.45/0.75 % (12923)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on theBenchmark for (2996ds/453Mi)
% 2.45/0.76 % (12859)Instruction limit reached!
% 2.45/0.76 % (12859)------------------------------
% 2.45/0.76 % (12859)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.45/0.76 % (12859)Termination reason: Unknown
% 2.45/0.76 % (12859)Termination phase: Saturation
% 2.45/0.76
% 2.45/0.76 % (12859)Memory used [KB]: 6652
% 2.45/0.76 % (12859)Time elapsed: 0.161 s
% 2.45/0.76 % (12859)Instructions burned: 450 (million)
% 2.45/0.76 % (12859)------------------------------
% 2.45/0.76 % (12859)------------------------------
% 2.45/0.77 % (12930)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2995ds/71Mi)
% 2.45/0.77 % (12919)Instruction limit reached!
% 2.45/0.77 % (12919)------------------------------
% 2.45/0.77 % (12919)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.45/0.77 % (12919)Termination reason: Unknown
% 2.45/0.77 % (12919)Termination phase: Saturation
% 2.45/0.77
% 2.45/0.77 % (12919)Memory used [KB]: 6012
% 2.45/0.77 % (12919)Time elapsed: 0.035 s
% 2.45/0.77 % (12919)Instructions burned: 96 (million)
% 2.45/0.77 % (12919)------------------------------
% 2.45/0.77 % (12919)------------------------------
% 2.45/0.78 % (12846)Instruction limit reached!
% 2.45/0.78 % (12846)------------------------------
% 2.45/0.78 % (12846)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 2.45/0.78 % (12846)Termination reason: Unknown
% 2.45/0.78 % (12846)Termination phase: Saturation
% 2.45/0.78
% 2.45/0.78 % (12846)Memory used [KB]: 7291
% 2.45/0.78 % (12846)Time elapsed: 0.313 s
% 2.45/0.78 % (12846)Instructions burned: 781 (million)
% 2.45/0.78 % (12846)------------------------------
% 2.45/0.78 % (12846)------------------------------
% 3.01/0.78 % (12938)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2995ds/83Mi)
% 3.01/0.79 % (12811)First to succeed.
% 3.01/0.79 % (12930)Instruction limit reached!
% 3.01/0.79 % (12930)------------------------------
% 3.01/0.79 % (12930)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 3.01/0.79 % (12930)Termination reason: Unknown
% 3.01/0.79 % (12930)Termination phase: Saturation
% 3.01/0.79
% 3.01/0.79 % (12930)Memory used [KB]: 5884
% 3.01/0.79 % (12930)Time elapsed: 0.027 s
% 3.01/0.79 % (12930)Instructions burned: 72 (million)
% 3.01/0.79 % (12930)------------------------------
% 3.01/0.79 % (12930)------------------------------
% 3.01/0.80 % (12940)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2995ds/11Mi)
% 3.01/0.80 % (12811)Refutation found. Thanks to Tanya!
% 3.01/0.80 % SZS status Theorem for theBenchmark
% 3.01/0.80 % SZS output start Proof for theBenchmark
% 3.01/0.80 thf(type_def_5, type, mu: $tType).
% 3.01/0.80 thf(func_def_0, type, mu: $tType).
% 3.01/0.80 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 3.01/0.80 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_8, type, mtrue: $i > $o).
% 3.01/0.80 thf(func_def_9, type, mfalse: $i > $o).
% 3.01/0.80 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 3.01/0.80 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 3.01/0.80 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 3.01/0.80 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 3.01/0.80 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 3.01/0.80 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 3.01/0.80 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 3.01/0.80 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 3.01/0.80 thf(func_def_37, type, p: $i > $o).
% 3.01/0.80 thf(func_def_38, type, big_f: mu > $i > $o).
% 3.01/0.80 thf(func_def_55, type, ph1: !>[X0: $tType]:(X0)).
% 3.01/0.80 thf(func_def_56, type, sK2: $i > mu).
% 3.01/0.80 thf(func_def_61, type, sK7: mu).
% 3.01/0.80 thf(f7273,plain,(
% 3.01/0.80 $false),
% 3.01/0.80 inference(avatar_sat_refutation,[],[f243,f1435,f1872,f7088,f7272])).
% 3.01/0.80 thf(f7272,plain,(
% 3.01/0.80 ~spl0_2 | ~spl0_6),
% 3.01/0.80 inference(avatar_contradiction_clause,[],[f7271])).
% 3.01/0.80 thf(f7271,plain,(
% 3.01/0.80 $false | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(trivial_inequality_removal,[],[f7270])).
% 3.01/0.80 thf(f7270,plain,(
% 3.01/0.80 ($false = $true) | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(boolean_simplification,[],[f7269])).
% 3.01/0.80 thf(f7269,plain,(
% 3.01/0.80 ((~ $true) = $true) | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(backward_demodulation,[],[f7196,f7263])).
% 3.01/0.80 thf(f7263,plain,(
% 3.01/0.80 ((rel_s4 @ sK5 @ sK14) = $true) | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(boolean_simplification,[],[f7230])).
% 3.01/0.80 thf(f7230,plain,(
% 3.01/0.80 (($true => (rel_s4 @ sK5 @ sK14)) = $true) | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(superposition,[],[f2079,f7203])).
% 3.01/0.80 thf(f7203,plain,(
% 3.01/0.80 ((rel_s4 @ sK6 @ sK14) = $true) | ~spl0_6),
% 3.01/0.80 inference(not_proxy_clausification,[],[f7186])).
% 3.01/0.80 thf(f7186,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK6 @ sK14))) | ~spl0_6),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f7162])).
% 3.01/0.80 thf(f7162,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK6 @ sK14)) | (big_f @ (sK2 @ sK4) @ sK14))) | ~spl0_6),
% 3.01/0.80 inference(beta_eta_normalization,[],[f7156])).
% 3.01/0.80 thf(f7156,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))) @ sK14)) | ~spl0_6),
% 3.01/0.80 inference(sigma_clausification,[],[f7143])).
% 3.01/0.80 thf(f7143,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) | ~spl0_6),
% 3.01/0.80 inference(not_proxy_clausification,[],[f1434])).
% 3.01/0.80 thf(f1434,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) = $true) | ~spl0_6),
% 3.01/0.80 inference(avatar_component_clause,[],[f1433])).
% 3.01/0.80 thf(f1433,plain,(
% 3.01/0.80 spl0_6 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) = $true)),
% 3.01/0.80 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 3.01/0.80 thf(f2079,plain,(
% 3.01/0.80 ( ! [X0 : $i] : ((((rel_s4 @ sK6 @ X0) => (rel_s4 @ sK5 @ X0)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2067])).
% 3.01/0.80 thf(f2067,plain,(
% 3.01/0.80 ( ! [X0 : $i] : (((($true & (rel_s4 @ sK6 @ X0)) => (rel_s4 @ sK5 @ X0)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f195,f2061])).
% 3.01/0.80 thf(f2061,plain,(
% 3.01/0.80 ((rel_s4 @ sK5 @ sK6) = $true) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f2060])).
% 3.01/0.80 thf(f2060,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK5 @ sK6))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2059])).
% 3.01/0.80 thf(f2059,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK5 @ sK6)) | $false)) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f2045,f2057])).
% 3.01/0.80 thf(f2057,plain,(
% 3.01/0.80 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (big_f @ Y0 @ Y1)))))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f2045])).
% 3.01/0.80 thf(f2045,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK5 @ sK6)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (big_f @ Y0 @ Y1))))))))) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f2044])).
% 3.01/0.80 thf(f2044,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))) @ sK6)) | ~spl0_2),
% 3.01/0.80 inference(sigma_clausification,[],[f2034])).
% 3.01/0.80 thf(f2034,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2033])).
% 3.01/0.80 thf(f2033,plain,(
% 3.01/0.80 ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2)))))))))))) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f1911,f2032])).
% 3.01/0.80 thf(f2032,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f1911])).
% 3.01/0.80 thf(f1911,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2)))))))))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f1901])).
% 3.01/0.80 thf(f1901,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))))) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f1900])).
% 3.01/0.80 thf(f1900,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))) @ sK5)) | ~spl0_2),
% 3.01/0.80 inference(sigma_clausification,[],[f1886])).
% 3.01/0.80 thf(f1886,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f242])).
% 3.01/0.80 thf(f242,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(avatar_component_clause,[],[f241])).
% 3.01/0.80 thf(f241,plain,(
% 3.01/0.80 spl0_2 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) = $true)),
% 3.01/0.80 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 3.01/0.80 thf(f195,plain,(
% 3.01/0.80 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s4 @ X2 @ X1) & (rel_s4 @ X1 @ X3)) => (rel_s4 @ X2 @ X3)) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f194])).
% 3.01/0.80 thf(f194,plain,(
% 3.01/0.80 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s4 @ X2 @ X1) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X2 @ Y0))) @ X3) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f193])).
% 3.01/0.80 thf(f193,plain,(
% 3.01/0.80 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ X2 @ X1) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X2 @ Y0)))))) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f192])).
% 3.01/0.80 thf(f192,plain,(
% 3.01/0.80 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X1 @ Y1)) => (rel_s4 @ Y0 @ Y1))))) @ X2) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f191])).
% 3.01/0.80 thf(f191,plain,(
% 3.01/0.80 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X1 @ Y1)) => (rel_s4 @ Y0 @ Y1)))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f190])).
% 3.01/0.80 thf(f190,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ Y0 @ Y2)) => (rel_s4 @ Y1 @ Y2))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f162])).
% 3.01/0.80 thf(f162,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ Y0 @ Y2)) => (rel_s4 @ Y1 @ Y2)))))))) = $true)),
% 3.01/0.80 inference(beta_eta_normalization,[],[f160])).
% 3.01/0.80 thf(f160,plain,(
% 3.01/0.80 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))) @ rel_s4) = $true)),
% 3.01/0.80 inference(definition_unfolding,[],[f132,f139])).
% 3.01/0.80 thf(f139,plain,(
% 3.01/0.80 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))))),
% 3.01/0.80 inference(cnf_transformation,[],[f47])).
% 3.01/0.80 thf(f47,plain,(
% 3.01/0.80 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y2 @ Y3))))))))))),
% 3.01/0.80 inference(fool_elimination,[],[f46])).
% 3.01/0.80 thf(f46,plain,(
% 3.01/0.80 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X2 @ X3)) => (X0 @ X2 @ X1)))))),
% 3.01/0.80 inference(rectify,[],[f21])).
% 3.01/0.80 thf(f21,axiom,(
% 3.01/0.80 (mtransitive = (^[X5 : $i > $i > $o] : (! [X10,X8,X9] : (((X5 @ X9 @ X10) & (X5 @ X8 @ X9)) => (X5 @ X8 @ X10)))))),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 3.01/0.80 thf(f132,plain,(
% 3.01/0.80 ((mtransitive @ rel_s4) = $true)),
% 3.01/0.80 inference(cnf_transformation,[],[f82])).
% 3.01/0.80 thf(f82,plain,(
% 3.01/0.80 ((mtransitive @ rel_s4) = $true)),
% 3.01/0.80 inference(fool_elimination,[],[f81])).
% 3.01/0.80 thf(f81,plain,(
% 3.01/0.80 (mtransitive @ rel_s4)),
% 3.01/0.80 inference(rectify,[],[f35])).
% 3.01/0.80 thf(f35,axiom,(
% 3.01/0.80 (mtransitive @ rel_s4)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 3.01/0.80 thf(f7196,plain,(
% 3.01/0.80 ((~ (rel_s4 @ sK5 @ sK14)) = $true) | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(boolean_simplification,[],[f7193])).
% 3.01/0.80 thf(f7193,plain,(
% 3.01/0.80 (((~ (rel_s4 @ sK5 @ sK14)) | $false) = $true) | (~spl0_2 | ~spl0_6)),
% 3.01/0.80 inference(superposition,[],[f4834,f7192])).
% 3.01/0.80 thf(f7192,plain,(
% 3.01/0.80 ((big_f @ (sK2 @ sK4) @ sK14) = $false) | ~spl0_6),
% 3.01/0.80 inference(boolean_simplification,[],[f7191])).
% 3.01/0.80 thf(f7191,plain,(
% 3.01/0.80 ($false = ($false | (big_f @ (sK2 @ sK4) @ sK14))) | ~spl0_6),
% 3.01/0.80 inference(backward_demodulation,[],[f7162,f7186])).
% 3.01/0.80 thf(f4834,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK5 @ X1)) | (big_f @ (sK2 @ sK4) @ X1)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f4826])).
% 3.01/0.80 thf(f4826,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))) @ X1) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(pi_clausification,[],[f3115])).
% 3.01/0.80 thf(f3115,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0)))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3114])).
% 3.01/0.80 thf(f3114,plain,(
% 3.01/0.80 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3113])).
% 3.01/0.80 thf(f3113,plain,(
% 3.01/0.80 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(forward_demodulation,[],[f3104,f2210])).
% 3.01/0.80 thf(f2210,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f2032])).
% 3.01/0.80 thf(f3104,plain,(
% 3.01/0.80 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3103])).
% 3.01/0.80 thf(f3103,plain,(
% 3.01/0.80 (($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0)))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3081])).
% 3.01/0.80 thf(f3081,plain,(
% 3.01/0.80 (((~ $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0)))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f2997,f1915])).
% 3.01/0.80 thf(f1915,plain,(
% 3.01/0.80 ((rel_s4 @ sK4 @ sK5) = $true) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f1914])).
% 3.01/0.80 thf(f1914,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK4 @ sK5))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f1913])).
% 3.01/0.80 thf(f1913,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | $false)) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f1901,f1911])).
% 3.01/0.80 thf(f2997,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0)))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f2992])).
% 3.01/0.80 thf(f2992,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f891])).
% 3.01/0.80 thf(f891,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1)))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f890])).
% 3.01/0.80 thf(f890,plain,(
% 3.01/0.80 (($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))) = $true)),
% 3.01/0.80 inference(forward_demodulation,[],[f889,f170])).
% 3.01/0.80 thf(f170,plain,(
% 3.01/0.80 ( ! [X1 : $i] : (((exists_in_world @ (sK2 @ X1) @ X1) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f169])).
% 3.01/0.80 thf(f169,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : mu]: (exists_in_world @ Y0 @ X1)) @ (sK2 @ X1)) = $true)) )),
% 3.01/0.80 inference(sigma_clausification,[],[f168])).
% 3.01/0.80 thf(f168,plain,(
% 3.01/0.80 ( ! [X1 : $i] : (((?? @ mu @ (^[Y0 : mu]: (exists_in_world @ Y0 @ X1))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f167])).
% 3.01/0.80 thf(f167,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0)))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f128])).
% 3.01/0.80 thf(f128,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0))))) = $true)),
% 3.01/0.80 inference(cnf_transformation,[],[f100])).
% 3.01/0.80 thf(f100,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0))))) = $true)),
% 3.01/0.80 inference(fool_elimination,[],[f99])).
% 3.01/0.80 thf(f99,plain,(
% 3.01/0.80 ! [X0] : ? [X1 : mu] : (exists_in_world @ X1 @ X0)),
% 3.01/0.80 inference(rectify,[],[f14])).
% 3.01/0.80 thf(f14,axiom,(
% 3.01/0.80 ! [X6] : ? [X0 : mu] : (exists_in_world @ X0 @ X6)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax)).
% 3.01/0.80 thf(f889,plain,(
% 3.01/0.80 (((exists_in_world @ (sK2 @ sK4) @ sK4) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f888])).
% 3.01/0.80 thf(f888,plain,(
% 3.01/0.80 (((exists_in_world @ (sK2 @ sK4) @ sK4) => (~ (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f887])).
% 3.01/0.80 thf(f887,plain,(
% 3.01/0.80 ($true = ((exists_in_world @ (sK2 @ sK4) @ sK4) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))) | $false))))),
% 3.01/0.80 inference(superposition,[],[f545,f866])).
% 3.01/0.80 thf(f866,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))),
% 3.01/0.80 inference(boolean_simplification,[],[f865])).
% 3.01/0.80 thf(f865,plain,(
% 3.01/0.80 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 3.01/0.80 inference(backward_demodulation,[],[f846,f861])).
% 3.01/0.80 thf(f861,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))))),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f846])).
% 3.01/0.80 thf(f846,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 3.01/0.80 inference(not_proxy_clausification,[],[f571])).
% 3.01/0.80 thf(f571,plain,(
% 3.01/0.80 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f570])).
% 3.01/0.80 thf(f570,plain,(
% 3.01/0.80 (($true => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 3.01/0.80 inference(superposition,[],[f545,f170])).
% 3.01/0.80 thf(f545,plain,(
% 3.01/0.80 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK4) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ X1 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f542])).
% 3.01/0.80 thf(f542,plain,(
% 3.01/0.80 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f417])).
% 3.01/0.80 thf(f417,plain,(
% 3.01/0.80 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f416])).
% 3.01/0.80 thf(f416,plain,(
% 3.01/0.80 (($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f413])).
% 3.01/0.80 thf(f413,plain,(
% 3.01/0.80 (((~ $true) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK4 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))) = $true)),
% 3.01/0.80 inference(superposition,[],[f405,f166])).
% 3.01/0.80 thf(f166,plain,(
% 3.01/0.80 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f165])).
% 3.01/0.80 thf(f165,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f163])).
% 3.01/0.80 thf(f163,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 3.01/0.80 inference(beta_eta_normalization,[],[f159])).
% 3.01/0.80 thf(f159,plain,(
% 3.01/0.80 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 3.01/0.80 inference(definition_unfolding,[],[f123,f114])).
% 3.01/0.80 thf(f114,plain,(
% 3.01/0.80 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 3.01/0.80 inference(cnf_transformation,[],[f63])).
% 3.01/0.80 thf(f63,plain,(
% 3.01/0.80 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 3.01/0.80 inference(fool_elimination,[],[f62])).
% 3.01/0.80 thf(f62,plain,(
% 3.01/0.80 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 3.01/0.80 inference(rectify,[],[f18])).
% 3.01/0.80 thf(f18,axiom,(
% 3.01/0.80 (mreflexive = (^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))))),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 3.01/0.80 thf(f123,plain,(
% 3.01/0.80 ((mreflexive @ rel_s4) = $true)),
% 3.01/0.80 inference(cnf_transformation,[],[f84])).
% 3.01/0.80 thf(f84,plain,(
% 3.01/0.80 ((mreflexive @ rel_s4) = $true)),
% 3.01/0.80 inference(fool_elimination,[],[f83])).
% 3.01/0.80 thf(f83,plain,(
% 3.01/0.80 (mreflexive @ rel_s4)),
% 3.01/0.80 inference(rectify,[],[f34])).
% 3.01/0.80 thf(f34,axiom,(
% 3.01/0.80 (mreflexive @ rel_s4)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 3.01/0.80 thf(f405,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f404])).
% 3.01/0.80 thf(f404,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f389])).
% 3.01/0.80 thf(f389,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))) = $true)),
% 3.01/0.80 inference(not_proxy_clausification,[],[f217])).
% 3.01/0.80 thf(f217,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))))),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f215])).
% 3.01/0.80 thf(f215,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))))),
% 3.01/0.80 inference(boolean_simplification,[],[f214])).
% 3.01/0.80 thf(f214,plain,(
% 3.01/0.80 ($false = ($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))))))),
% 3.01/0.80 inference(backward_demodulation,[],[f211,f213])).
% 3.01/0.80 thf(f213,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK3 @ sK4)))),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f211])).
% 3.01/0.80 thf(f211,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK3 @ sK4)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_f @ Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))))))),
% 3.01/0.80 inference(beta_eta_normalization,[],[f210])).
% 3.01/0.80 thf(f210,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_f @ Y2 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_f @ Y2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_f @ Y3 @ Y4))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_f @ Y3 @ Y4))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) @ sK4))),
% 3.01/0.80 inference(sigma_clausification,[],[f209])).
% 3.01/0.80 thf(f209,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_f @ Y2 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_f @ Y2 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_f @ Y3 @ Y4))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | (big_f @ Y3 @ Y4))))))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))))),
% 3.01/0.80 inference(beta_eta_normalization,[],[f208])).
% 3.01/0.80 thf(f208,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_f @ Y3 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_f @ Y3 @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y3 @ Y5)) | (big_f @ Y4 @ Y5))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y3 @ Y5)) | (big_f @ Y4 @ Y5))))))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) @ sK3))),
% 3.01/0.80 inference(sigma_clausification,[],[f205])).
% 3.01/0.80 thf(f205,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_f @ Y3 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_f @ Y3 @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y3 @ Y5)) | (big_f @ Y4 @ Y5))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y3 @ Y5)) | (big_f @ Y4 @ Y5))))))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))),
% 3.01/0.80 inference(not_proxy_clausification,[],[f164])).
% 3.01/0.80 thf(f164,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_f @ Y3 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y2 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_f @ Y3 @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (p @ Y5)))))))))))))))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y3 @ Y5)) | (big_f @ Y4 @ Y5))))))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y3 @ Y5)) | (big_f @ Y4 @ Y5))))))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))))) = $true)),
% 3.01/0.80 inference(beta_eta_normalization,[],[f161])).
% 3.01/0.80 thf(f161,plain,(
% 3.01/0.80 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ p) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_f @ Y0)))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_f @ Y0)) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ p))))))) @ ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_f @ Y0))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ (big_f @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))))))) = $true)),
% 3.01/0.80 inference(definition_unfolding,[],[f138,f131,f117,f151,f117,f143,f150,f117,f151,f117,f117,f117,f151,f117,f117,f150,f117,f151,f117,f117,f143,f117,f117,f151,f117,f143,f117,f117])).
% 3.01/0.80 thf(f150,plain,(
% 3.01/0.80 (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)))))))),
% 3.01/0.80 inference(definition_unfolding,[],[f142,f147,f133,f147,f147])).
% 3.01/0.80 thf(f133,plain,(
% 3.01/0.80 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 3.01/0.80 inference(cnf_transformation,[],[f109])).
% 3.01/0.80 thf(f109,plain,(
% 3.01/0.80 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 3.01/0.80 inference(fool_elimination,[],[f108])).
% 3.01/0.80 thf(f108,plain,(
% 3.01/0.80 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 3.01/0.80 inference(rectify,[],[f3])).
% 3.01/0.80 thf(f3,axiom,(
% 3.01/0.80 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 3.01/0.80 thf(f147,plain,(
% 3.01/0.80 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 3.01/0.80 inference(cnf_transformation,[],[f96])).
% 3.01/0.80 thf(f96,plain,(
% 3.01/0.80 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 3.01/0.80 inference(fool_elimination,[],[f95])).
% 3.01/0.80 thf(f95,plain,(
% 3.01/0.80 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 3.01/0.80 inference(rectify,[],[f2])).
% 3.01/0.80 thf(f2,axiom,(
% 3.01/0.80 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 3.01/0.80 thf(f142,plain,(
% 3.01/0.80 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 3.01/0.80 inference(cnf_transformation,[],[f67])).
% 3.01/0.80 thf(f67,plain,(
% 3.01/0.80 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 3.01/0.80 inference(fool_elimination,[],[f66])).
% 3.01/0.80 thf(f66,plain,(
% 3.01/0.80 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 3.01/0.80 inference(rectify,[],[f8])).
% 3.01/0.80 thf(f8,axiom,(
% 3.01/0.80 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 3.01/0.80 thf(f143,plain,(
% 3.01/0.80 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 3.01/0.80 inference(cnf_transformation,[],[f49])).
% 3.01/0.80 thf(f49,plain,(
% 3.01/0.80 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 3.01/0.80 inference(fool_elimination,[],[f48])).
% 3.01/0.80 thf(f48,plain,(
% 3.01/0.80 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_ind)),
% 3.01/0.80 inference(rectify,[],[f15])).
% 3.01/0.80 thf(f15,axiom,(
% 3.01/0.80 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))) = mforall_ind)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 3.01/0.80 thf(f151,plain,(
% 3.01/0.80 (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)))))),
% 3.01/0.80 inference(definition_unfolding,[],[f122,f133,f147])).
% 3.01/0.80 thf(f122,plain,(
% 3.01/0.80 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 3.01/0.80 inference(cnf_transformation,[],[f92])).
% 3.01/0.80 thf(f92,plain,(
% 3.01/0.80 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 3.01/0.80 inference(fool_elimination,[],[f91])).
% 3.01/0.80 thf(f91,plain,(
% 3.01/0.80 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 3.01/0.80 inference(rectify,[],[f9])).
% 3.01/0.80 thf(f9,axiom,(
% 3.01/0.80 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 3.01/0.80 thf(f117,plain,(
% 3.01/0.80 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 3.01/0.80 inference(cnf_transformation,[],[f80])).
% 3.01/0.80 thf(f80,plain,(
% 3.01/0.80 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 3.01/0.80 inference(fool_elimination,[],[f79])).
% 3.01/0.80 thf(f79,plain,(
% 3.01/0.80 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 3.01/0.80 inference(rectify,[],[f32])).
% 3.01/0.80 thf(f32,axiom,(
% 3.01/0.80 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))))),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 3.01/0.80 thf(f131,plain,(
% 3.01/0.80 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 3.01/0.80 inference(cnf_transformation,[],[f55])).
% 3.01/0.80 thf(f55,plain,(
% 3.01/0.80 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 3.01/0.80 inference(fool_elimination,[],[f54])).
% 3.01/0.80 thf(f54,plain,(
% 3.01/0.80 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 3.01/0.80 inference(rectify,[],[f28])).
% 3.01/0.80 thf(f28,axiom,(
% 3.01/0.80 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 3.01/0.80 thf(f138,plain,(
% 3.01/0.80 ((~ (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (big_f @ Y0)))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_f @ Y0)) @ (mbox_s4 @ p))))))) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_f @ Y0))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_f @ Y0))))) @ (mbox_s4 @ p)))))))) = $true)),
% 3.01/0.80 inference(cnf_transformation,[],[f107])).
% 3.01/0.80 thf(f107,plain,(
% 3.01/0.80 ((~ (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (big_f @ Y0)))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_f @ Y0)) @ (mbox_s4 @ p))))))) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_f @ Y0))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mbox_s4 @ (big_f @ Y0))))) @ (mbox_s4 @ p)))))))) = $true)),
% 3.01/0.80 inference(fool_elimination,[],[f106])).
% 3.01/0.80 thf(f106,plain,(
% 3.01/0.80 ~(mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (big_f @ X0)))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_f @ X0)) @ (mbox_s4 @ p))))))) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : (mbox_s4 @ (big_f @ X1))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X2 : mu] : (mbox_s4 @ (big_f @ X2))))) @ (mbox_s4 @ p)))))))),
% 3.01/0.80 inference(rectify,[],[f38])).
% 3.01/0.80 thf(f38,negated_conjecture,(
% 3.01/0.80 ~(mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (big_f @ X0)))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_f @ X0)) @ (mbox_s4 @ p))))))) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (big_f @ X11))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (big_f @ X11))))) @ (mbox_s4 @ p)))))))),
% 3.01/0.80 inference(negated_conjecture,[],[f37])).
% 3.01/0.80 thf(f37,conjecture,(
% 3.01/0.80 (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (big_f @ X0)))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_f @ X0)) @ (mbox_s4 @ p))))))) @ (mand @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (big_f @ X11))))))) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X11 : mu] : (mbox_s4 @ (big_f @ X11))))) @ (mbox_s4 @ p)))))))),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel22)).
% 3.01/0.80 thf(f7088,plain,(
% 3.01/0.80 ~spl0_2 | ~spl0_5),
% 3.01/0.80 inference(avatar_contradiction_clause,[],[f7087])).
% 3.01/0.80 thf(f7087,plain,(
% 3.01/0.80 $false | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(trivial_inequality_removal,[],[f7086])).
% 3.01/0.80 thf(f7086,plain,(
% 3.01/0.80 ($false = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(forward_demodulation,[],[f7085,f2269])).
% 3.01/0.80 thf(f2269,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0))))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2268])).
% 3.01/0.80 thf(f2268,plain,(
% 3.01/0.80 ($false = ($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0)))))) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f2252,f2267])).
% 3.01/0.80 thf(f2267,plain,(
% 3.01/0.80 ($true = (exists_in_world @ sK7 @ sK6)) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f2252])).
% 3.01/0.80 thf(f2252,plain,(
% 3.01/0.80 ($false = ((exists_in_world @ sK7 @ sK6) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0)))))) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f2251])).
% 3.01/0.80 thf(f2251,plain,(
% 3.01/0.80 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (big_f @ Y0 @ Y1)))))) @ sK7)) | ~spl0_2),
% 3.01/0.80 inference(sigma_clausification,[],[f2057])).
% 3.01/0.80 thf(f7085,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0)))) = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(boolean_simplification,[],[f7084])).
% 3.01/0.80 thf(f7084,plain,(
% 3.01/0.80 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(boolean_simplification,[],[f7083])).
% 3.01/0.80 thf(f7083,plain,(
% 3.01/0.80 (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(forward_demodulation,[],[f7046,f166])).
% 3.01/0.80 thf(f7046,plain,(
% 3.01/0.80 (((~ (rel_s4 @ sK6 @ sK6)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0))))) = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(boolean_simplification,[],[f7045])).
% 3.01/0.80 thf(f7045,plain,(
% 3.01/0.80 (((~ (rel_s4 @ sK6 @ sK6)) | ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(boolean_simplification,[],[f7037])).
% 3.01/0.80 thf(f7037,plain,(
% 3.01/0.80 (((~ (rel_s4 @ sK6 @ sK6)) | ((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ sK7 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_5)),
% 3.01/0.80 inference(superposition,[],[f7013,f1431])).
% 3.01/0.80 thf(f1431,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_5),
% 3.01/0.80 inference(avatar_component_clause,[],[f1430])).
% 3.01/0.80 thf(f1430,plain,(
% 3.01/0.80 spl0_5 <=> ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (p @ Y0)))) = $true)),
% 3.01/0.80 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 3.01/0.80 thf(f7013,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK6 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (big_f @ sK7 @ Y0)))))) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f7011])).
% 3.01/0.80 thf(f7011,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))) @ X1) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(pi_clausification,[],[f3515])).
% 3.01/0.80 thf(f3515,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1)))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3514])).
% 3.01/0.80 thf(f3514,plain,(
% 3.01/0.80 (($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(forward_demodulation,[],[f3511,f2267])).
% 3.01/0.80 thf(f3511,plain,(
% 3.01/0.80 (((exists_in_world @ sK7 @ sK6) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3510])).
% 3.01/0.80 thf(f3510,plain,(
% 3.01/0.80 (((exists_in_world @ sK7 @ sK6) => (~ (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3509])).
% 3.01/0.80 thf(f3509,plain,(
% 3.01/0.80 (((exists_in_world @ sK7 @ sK6) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))) | $false))) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f2835,f3500])).
% 3.01/0.80 thf(f3500,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f3499])).
% 3.01/0.80 thf(f3499,plain,(
% 3.01/0.80 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f3455,f3495])).
% 3.01/0.80 thf(f3495,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1)))))))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f3455])).
% 3.01/0.80 thf(f3455,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f2863])).
% 3.01/0.80 thf(f2863,plain,(
% 3.01/0.80 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2858])).
% 3.01/0.80 thf(f2858,plain,(
% 3.01/0.80 (($true => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ sK7 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f2835,f2267])).
% 3.01/0.80 thf(f2835,plain,(
% 3.01/0.80 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK6) => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ X1 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f2833])).
% 3.01/0.80 thf(f2833,plain,(
% 3.01/0.80 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))) @ X1) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(pi_clausification,[],[f2097])).
% 3.01/0.80 thf(f2097,plain,(
% 3.01/0.80 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2096])).
% 3.01/0.80 thf(f2096,plain,(
% 3.01/0.80 (($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2082])).
% 3.01/0.80 thf(f2082,plain,(
% 3.01/0.80 (((~ $true) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_f @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f405,f2077])).
% 3.01/0.80 thf(f2077,plain,(
% 3.01/0.80 ((rel_s4 @ sK4 @ sK6) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f2065])).
% 3.01/0.80 thf(f2065,plain,(
% 3.01/0.80 (($true => (rel_s4 @ sK4 @ sK6)) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f1948,f2061])).
% 3.01/0.80 thf(f1948,plain,(
% 3.01/0.80 ( ! [X0 : $i] : ((((rel_s4 @ sK5 @ X0) => (rel_s4 @ sK4 @ X0)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f1940])).
% 3.01/0.80 thf(f1940,plain,(
% 3.01/0.80 ( ! [X0 : $i] : (((($true & (rel_s4 @ sK5 @ X0)) => (rel_s4 @ sK4 @ X0)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f195,f1915])).
% 3.01/0.80 thf(f1872,plain,(
% 3.01/0.80 ~spl0_1),
% 3.01/0.80 inference(avatar_contradiction_clause,[],[f1871])).
% 3.01/0.80 thf(f1871,plain,(
% 3.01/0.80 $false | ~spl0_1),
% 3.01/0.80 inference(trivial_inequality_removal,[],[f1870])).
% 3.01/0.80 thf(f1870,plain,(
% 3.01/0.80 ($false = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1869])).
% 3.01/0.80 thf(f1869,plain,(
% 3.01/0.80 ((~ $true) = $true) | ~spl0_1),
% 3.01/0.80 inference(backward_demodulation,[],[f1726,f1862])).
% 3.01/0.80 thf(f1862,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0)))) = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1860])).
% 3.01/0.80 thf(f1860,plain,(
% 3.01/0.80 (($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(superposition,[],[f1849,f1747])).
% 3.01/0.80 thf(f1747,plain,(
% 3.01/0.80 ((exists_in_world @ (sK2 @ sK3) @ sK10) = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1735])).
% 3.01/0.80 thf(f1735,plain,(
% 3.01/0.80 (($true => (exists_in_world @ (sK2 @ sK3) @ sK10)) = $true) | ~spl0_1),
% 3.01/0.80 inference(superposition,[],[f250,f1708])).
% 3.01/0.80 thf(f1708,plain,(
% 3.01/0.80 ((rel_s4 @ sK4 @ sK10) = $true) | ~spl0_1),
% 3.01/0.80 inference(not_proxy_clausification,[],[f1705])).
% 3.01/0.80 thf(f1705,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK4 @ sK10))) | ~spl0_1),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f1696])).
% 3.01/0.80 thf(f1696,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK4 @ sK10)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (p @ Y0))))))) | ~spl0_1),
% 3.01/0.80 inference(beta_eta_normalization,[],[f1695])).
% 3.01/0.80 thf(f1695,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK10)) | ~spl0_1),
% 3.01/0.80 inference(sigma_clausification,[],[f1688])).
% 3.01/0.80 thf(f1688,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) | ~spl0_1),
% 3.01/0.80 inference(not_proxy_clausification,[],[f239])).
% 3.01/0.80 thf(f239,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(avatar_component_clause,[],[f238])).
% 3.01/0.80 thf(f238,plain,(
% 3.01/0.80 spl0_1 <=> ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true)),
% 3.01/0.80 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 3.01/0.80 thf(f250,plain,(
% 3.01/0.80 ( ! [X0 : $i] : ((((rel_s4 @ sK4 @ X0) => (exists_in_world @ (sK2 @ sK3) @ X0)) = $true)) )),
% 3.01/0.80 inference(boolean_simplification,[],[f247])).
% 3.01/0.80 thf(f247,plain,(
% 3.01/0.80 ( ! [X0 : $i] : (((($true & (rel_s4 @ sK4 @ X0)) => (exists_in_world @ (sK2 @ sK3) @ X0)) = $true)) )),
% 3.01/0.80 inference(superposition,[],[f176,f234])).
% 3.01/0.80 thf(f234,plain,(
% 3.01/0.80 ((exists_in_world @ (sK2 @ sK3) @ sK4) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f229])).
% 3.01/0.80 thf(f229,plain,(
% 3.01/0.80 (($true => (exists_in_world @ (sK2 @ sK3) @ sK4)) = $true)),
% 3.01/0.80 inference(superposition,[],[f184,f220])).
% 3.01/0.80 thf(f220,plain,(
% 3.01/0.80 ((rel_s4 @ sK3 @ sK4) = $true)),
% 3.01/0.80 inference(not_proxy_clausification,[],[f213])).
% 3.01/0.80 thf(f184,plain,(
% 3.01/0.80 ( ! [X0 : $i,X1 : $i] : ((((rel_s4 @ X0 @ X1) => (exists_in_world @ (sK2 @ X0) @ X1)) = $true)) )),
% 3.01/0.80 inference(boolean_simplification,[],[f180])).
% 3.01/0.80 thf(f180,plain,(
% 3.01/0.80 ( ! [X0 : $i,X1 : $i] : (((($true & (rel_s4 @ X0 @ X1)) => (exists_in_world @ (sK2 @ X0) @ X1)) = $true)) )),
% 3.01/0.80 inference(superposition,[],[f176,f170])).
% 3.01/0.80 thf(f176,plain,(
% 3.01/0.80 ( ! [X2 : mu,X3 : $i,X1 : $i] : (((((exists_in_world @ X2 @ X3) & (rel_s4 @ X3 @ X1)) => (exists_in_world @ X2 @ X1)) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f175])).
% 3.01/0.80 thf(f175,plain,(
% 3.01/0.80 ( ! [X2 : mu,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((exists_in_world @ X2 @ Y0) & (rel_s4 @ Y0 @ X1)) => (exists_in_world @ X2 @ X1))) @ X3) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f174])).
% 3.01/0.80 thf(f174,plain,(
% 3.01/0.80 ( ! [X2 : mu,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((exists_in_world @ X2 @ Y0) & (rel_s4 @ Y0 @ X1)) => (exists_in_world @ X2 @ X1)))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f173])).
% 3.01/0.80 thf(f173,plain,(
% 3.01/0.80 ( ! [X2 : mu,X1 : $i] : ((((^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (((exists_in_world @ Y0 @ Y1) & (rel_s4 @ Y1 @ X1)) => (exists_in_world @ Y0 @ X1))))) @ X2) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f172])).
% 3.01/0.80 thf(f172,plain,(
% 3.01/0.80 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: (!! @ $i @ (^[Y1 : $i]: (((exists_in_world @ Y0 @ Y1) & (rel_s4 @ Y1 @ X1)) => (exists_in_world @ Y0 @ X1)))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f171])).
% 3.01/0.80 thf(f171,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y1 @ Y2) & (rel_s4 @ Y2 @ Y0)) => (exists_in_world @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f125])).
% 3.01/0.80 thf(f125,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y1 @ Y2) & (rel_s4 @ Y2 @ Y0)) => (exists_in_world @ Y1 @ Y0)))))))) = $true)),
% 3.01/0.80 inference(cnf_transformation,[],[f90])).
% 3.01/0.80 thf(f90,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ $i @ (^[Y2 : $i]: (((exists_in_world @ Y1 @ Y2) & (rel_s4 @ Y2 @ Y0)) => (exists_in_world @ Y1 @ Y0)))))))) = $true)),
% 3.01/0.80 inference(fool_elimination,[],[f89])).
% 3.01/0.80 thf(f89,plain,(
% 3.01/0.80 ! [X0,X1 : mu,X2] : (((rel_s4 @ X0 @ X2) & (exists_in_world @ X1 @ X0)) => (exists_in_world @ X1 @ X2))),
% 3.01/0.80 inference(rectify,[],[f36])).
% 3.01/0.80 thf(f36,axiom,(
% 3.01/0.80 ! [X6,X0 : mu,X2] : (((rel_s4 @ X6 @ X2) & (exists_in_world @ X0 @ X6)) => (exists_in_world @ X0 @ X2))),
% 3.01/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cumulative_ax)).
% 3.01/0.80 thf(f1849,plain,(
% 3.01/0.80 ( ! [X1 : mu] : ((((exists_in_world @ X1 @ sK10) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ X1 @ Y0))))) = $true)) ) | ~spl0_1),
% 3.01/0.80 inference(beta_eta_normalization,[],[f1846])).
% 3.01/0.80 thf(f1846,plain,(
% 3.01/0.80 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK10) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK10 @ Y1)) | (big_f @ Y0 @ Y1)))))) @ X1) = $true)) ) | ~spl0_1),
% 3.01/0.80 inference(pi_clausification,[],[f1787])).
% 3.01/0.80 thf(f1787,plain,(
% 3.01/0.80 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK10) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK10 @ Y1)) | (big_f @ Y0 @ Y1))))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1786])).
% 3.01/0.80 thf(f1786,plain,(
% 3.01/0.80 (($false | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK10) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK10 @ Y1)) | (big_f @ Y0 @ Y1)))))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1785])).
% 3.01/0.80 thf(f1785,plain,(
% 3.01/0.80 (((~ $true) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK10) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK10 @ Y1)) | (big_f @ Y0 @ Y1)))))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(superposition,[],[f1769,f166])).
% 3.01/0.80 thf(f1769,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK10 @ X1)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ X1 @ Y1)) | (big_f @ Y0 @ Y1)))))))) = $true)) ) | ~spl0_1),
% 3.01/0.80 inference(beta_eta_normalization,[],[f1768])).
% 3.01/0.80 thf(f1768,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))) @ X1) = $true)) ) | ~spl0_1),
% 3.01/0.80 inference(pi_clausification,[],[f1731])).
% 3.01/0.80 thf(f1731,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2)))))))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(not_proxy_clausification,[],[f1725])).
% 3.01/0.80 thf(f1725,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2)))))))))))) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1723])).
% 3.01/0.80 thf(f1723,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))) | $false)) | ~spl0_1),
% 3.01/0.80 inference(backward_demodulation,[],[f1707,f1719])).
% 3.01/0.80 thf(f1719,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (p @ Y0)))) = $false) | ~spl0_1),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f1707])).
% 3.01/0.80 thf(f1707,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (p @ Y0)))))) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1706])).
% 3.01/0.80 thf(f1706,plain,(
% 3.01/0.80 (($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (p @ Y0)))))) = $false) | ~spl0_1),
% 3.01/0.80 inference(backward_demodulation,[],[f1696,f1705])).
% 3.01/0.80 thf(f1726,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1721])).
% 3.01/0.80 thf(f1721,plain,(
% 3.01/0.80 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0))))) | $false) = $true) | ~spl0_1),
% 3.01/0.80 inference(backward_demodulation,[],[f1713,f1719])).
% 3.01/0.80 thf(f1713,plain,(
% 3.01/0.80 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(boolean_simplification,[],[f1711])).
% 3.01/0.80 thf(f1711,plain,(
% 3.01/0.80 (($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK10 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_1),
% 3.01/0.80 inference(superposition,[],[f1030,f1705])).
% 3.01/0.80 thf(f1030,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (big_f @ (sK2 @ sK3) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0)))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f1028])).
% 3.01/0.80 thf(f1028,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f1007])).
% 3.01/0.80 thf(f1007,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) = $true)),
% 3.01/0.80 inference(not_proxy_clausification,[],[f991])).
% 3.01/0.80 thf(f991,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))),
% 3.01/0.80 inference(boolean_simplification,[],[f990])).
% 3.01/0.80 thf(f990,plain,(
% 3.01/0.80 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 3.01/0.80 inference(backward_demodulation,[],[f965,f986])).
% 3.01/0.80 thf(f986,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))))))) = $false)),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f965])).
% 3.01/0.80 thf(f965,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 3.01/0.80 inference(not_proxy_clausification,[],[f572])).
% 3.01/0.80 thf(f572,plain,(
% 3.01/0.80 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))) = $true)),
% 3.01/0.80 inference(boolean_simplification,[],[f569])).
% 3.01/0.80 thf(f569,plain,(
% 3.01/0.80 (($true => (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK3) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) = $true)),
% 3.01/0.80 inference(superposition,[],[f545,f234])).
% 3.01/0.80 thf(f1435,plain,(
% 3.01/0.80 spl0_5 | spl0_6 | ~spl0_2),
% 3.01/0.80 inference(avatar_split_clause,[],[f1426,f241,f1433,f1430])).
% 3.01/0.80 thf(f1426,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (p @ Y0)))) = $true) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f949])).
% 3.01/0.80 thf(f949,plain,(
% 3.01/0.80 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (p @ Y0))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f948])).
% 3.01/0.80 thf(f948,plain,(
% 3.01/0.80 (($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f938])).
% 3.01/0.80 thf(f938,plain,(
% 3.01/0.80 (((~ $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK6 @ Y0)) | (p @ Y0)))))) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f918,f374])).
% 3.01/0.80 thf(f374,plain,(
% 3.01/0.80 ((rel_s4 @ sK4 @ sK6) = $true) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f363])).
% 3.01/0.80 thf(f363,plain,(
% 3.01/0.80 (($true => (rel_s4 @ sK4 @ sK6)) = $true) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f286,f360])).
% 3.01/0.80 thf(f360,plain,(
% 3.01/0.80 ((rel_s4 @ sK5 @ sK6) = $true) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f359])).
% 3.01/0.80 thf(f359,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK5 @ sK6))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f358])).
% 3.01/0.80 thf(f358,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK5 @ sK6)) | $false)) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f344,f356])).
% 3.01/0.80 thf(f356,plain,(
% 3.01/0.80 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (big_f @ Y0 @ Y1)))))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f344])).
% 3.01/0.80 thf(f344,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK5 @ sK6)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK6) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK6 @ Y1)) | (big_f @ Y0 @ Y1))))))))) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f343])).
% 3.01/0.80 thf(f343,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))) @ sK6)) | ~spl0_2),
% 3.01/0.80 inference(sigma_clausification,[],[f330])).
% 3.01/0.80 thf(f330,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f329])).
% 3.01/0.80 thf(f329,plain,(
% 3.01/0.80 ($false = ($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2)))))))))))) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f271,f328])).
% 3.01/0.80 thf(f328,plain,(
% 3.01/0.80 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f271])).
% 3.01/0.80 thf(f271,plain,(
% 3.01/0.80 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2)))))))))))) | ~spl0_2),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f263])).
% 3.01/0.80 thf(f263,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y0 @ Y2)) | (big_f @ Y1 @ Y2))))))))))))) | ~spl0_2),
% 3.01/0.80 inference(beta_eta_normalization,[],[f262])).
% 3.01/0.80 thf(f262,plain,(
% 3.01/0.80 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))) @ sK5)) | ~spl0_2),
% 3.01/0.80 inference(sigma_clausification,[],[f252])).
% 3.01/0.80 thf(f252,plain,(
% 3.01/0.80 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f242])).
% 3.01/0.80 thf(f286,plain,(
% 3.01/0.80 ( ! [X0 : $i] : ((((rel_s4 @ sK5 @ X0) => (rel_s4 @ sK4 @ X0)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f278])).
% 3.01/0.80 thf(f278,plain,(
% 3.01/0.80 ( ! [X0 : $i] : (((($true & (rel_s4 @ sK5 @ X0)) => (rel_s4 @ sK4 @ X0)) = $true)) ) | ~spl0_2),
% 3.01/0.80 inference(superposition,[],[f195,f275])).
% 3.01/0.80 thf(f275,plain,(
% 3.01/0.80 ((rel_s4 @ sK4 @ sK5) = $true) | ~spl0_2),
% 3.01/0.80 inference(not_proxy_clausification,[],[f274])).
% 3.01/0.80 thf(f274,plain,(
% 3.01/0.80 ($false = (~ (rel_s4 @ sK4 @ sK5))) | ~spl0_2),
% 3.01/0.80 inference(boolean_simplification,[],[f273])).
% 3.01/0.80 thf(f273,plain,(
% 3.01/0.80 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | $false)) | ~spl0_2),
% 3.01/0.80 inference(backward_demodulation,[],[f263,f271])).
% 3.01/0.80 thf(f918,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (big_f @ (sK2 @ sK4) @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0)))))) = $true)) )),
% 3.01/0.80 inference(beta_eta_normalization,[],[f913])).
% 3.01/0.80 thf(f913,plain,(
% 3.01/0.80 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1) = $true)) )),
% 3.01/0.80 inference(pi_clausification,[],[f886])).
% 3.01/0.80 thf(f886,plain,(
% 3.01/0.80 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_f @ (sK2 @ sK4) @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) = $true)),
% 3.01/0.80 inference(not_proxy_clausification,[],[f866])).
% 3.01/0.80 thf(f243,plain,(
% 3.01/0.80 spl0_1 | spl0_2),
% 3.01/0.80 inference(avatar_split_clause,[],[f236,f241,f238])).
% 3.01/0.80 thf(f236,plain,(
% 3.01/0.80 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) = $true)),
% 3.01/0.80 inference(binary_proxy_clausification,[],[f223])).
% 3.01/0.80 thf(f223,plain,(
% 3.01/0.80 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))) = $true)),
% 3.01/0.80 inference(not_proxy_clausification,[],[f219])).
% 3.01/0.80 thf(f219,plain,(
% 3.01/0.80 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))))))),
% 3.01/0.80 inference(boolean_simplification,[],[f218])).
% 3.01/0.80 thf(f218,plain,(
% 3.01/0.80 ($false = ($false | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y1 @ Y3)) | (big_f @ Y2 @ Y3))))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))))),
% 3.01/0.80 inference(backward_demodulation,[],[f215,f217])).
% 3.01/0.80 % SZS output end Proof for theBenchmark
% 3.01/0.80 % (12811)------------------------------
% 3.01/0.80 % (12811)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 3.01/0.80 % (12811)Termination reason: Refutation
% 3.01/0.80
% 3.01/0.80 % (12811)Memory used [KB]: 8443
% 3.01/0.80 % (12811)Time elapsed: 0.396 s
% 3.01/0.80 % (12811)Instructions burned: 1007 (million)
% 3.01/0.80 % (12811)------------------------------
% 3.01/0.80 % (12811)------------------------------
% 3.01/0.80 % (12780)Success in time 0.439 s
%------------------------------------------------------------------------------