TSTP Solution File: GEG011^1 by Vampire---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : GEG011^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n028.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 06:03:01 EDT 2024
% Result : Theorem 0.22s 0.52s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEG011^1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 12:01:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.36 Running higher-order theorem proving
% 0.12/0.36 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
% 0.22/0.38 % (7613)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)
% 0.22/0.38 % (7615)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (7612)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38 % (7616)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)
% 0.22/0.38 % (7614)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)
% 0.22/0.38 % (7617)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)
% 0.22/0.38 % (7618)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (7615)Instruction limit reached!
% 0.22/0.38 % (7615)------------------------------
% 0.22/0.38 % (7615)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (7615)Termination reason: Unknown
% 0.22/0.38 % (7615)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (7615)Memory used [KB]: 1023
% 0.22/0.38 % (7615)Time elapsed: 0.004 s
% 0.22/0.38 % (7615)Instructions burned: 2 (million)
% 0.22/0.38 % (7615)------------------------------
% 0.22/0.38 % (7615)------------------------------
% 0.22/0.38 % (7616)Instruction limit reached!
% 0.22/0.38 % (7616)------------------------------
% 0.22/0.38 % (7616)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (7616)Termination reason: Unknown
% 0.22/0.38 % (7616)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (7616)Memory used [KB]: 1023
% 0.22/0.38 % (7616)Time elapsed: 0.004 s
% 0.22/0.38 % (7616)Instructions burned: 3 (million)
% 0.22/0.38 % (7616)------------------------------
% 0.22/0.38 % (7616)------------------------------
% 0.22/0.38 % (7613)Instruction limit reached!
% 0.22/0.38 % (7613)------------------------------
% 0.22/0.38 % (7613)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.38 % (7613)Termination reason: Unknown
% 0.22/0.38 % (7613)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (7613)Memory used [KB]: 1151
% 0.22/0.38 % (7613)Time elapsed: 0.004 s
% 0.22/0.38 % (7613)Instructions burned: 4 (million)
% 0.22/0.38 % (7613)------------------------------
% 0.22/0.38 % (7613)------------------------------
% 0.22/0.39 % (7617)Refutation not found, incomplete strategy
% 0.22/0.39 % (7617)------------------------------
% 0.22/0.39 % (7617)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (7617)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39
% 0.22/0.39
% 0.22/0.39 % (7617)Memory used [KB]: 5628
% 0.22/0.39 % (7617)Time elapsed: 0.011 s
% 0.22/0.39 % (7617)Instructions burned: 15 (million)
% 0.22/0.39 % (7617)------------------------------
% 0.22/0.39 % (7617)------------------------------
% 0.22/0.39 % (7618)Instruction limit reached!
% 0.22/0.39 % (7618)------------------------------
% 0.22/0.39 % (7618)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (7618)Termination reason: Unknown
% 0.22/0.39 % (7618)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (7618)Memory used [KB]: 5628
% 0.22/0.39 % (7618)Time elapsed: 0.012 s
% 0.22/0.39 % (7618)Instructions burned: 18 (million)
% 0.22/0.39 % (7618)------------------------------
% 0.22/0.39 % (7618)------------------------------
% 0.22/0.39 % (7614)Instruction limit reached!
% 0.22/0.39 % (7614)------------------------------
% 0.22/0.39 % (7614)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.39 % (7614)Termination reason: Unknown
% 0.22/0.39 % (7614)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (7614)Memory used [KB]: 5756
% 0.22/0.39 % (7614)Time elapsed: 0.016 s
% 0.22/0.39 % (7614)Instructions burned: 28 (million)
% 0.22/0.39 % (7614)------------------------------
% 0.22/0.39 % (7614)------------------------------
% 0.22/0.40 % (7619)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)
% 0.22/0.40 % (7620)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)
% 0.22/0.40 % (7621)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)
% 0.22/0.40 % (7619)Instruction limit reached!
% 0.22/0.40 % (7619)------------------------------
% 0.22/0.40 % (7619)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.40 % (7619)Termination reason: Unknown
% 0.22/0.40 % (7619)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (7619)Memory used [KB]: 1023
% 0.22/0.40 % (7619)Time elapsed: 0.004 s
% 0.22/0.40 % (7619)Instructions burned: 3 (million)
% 0.22/0.40 % (7619)------------------------------
% 0.22/0.40 % (7619)------------------------------
% 0.22/0.41 % (7622)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)
% 0.22/0.41 % (7623)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)
% 0.22/0.41 % (7621)Instruction limit reached!
% 0.22/0.41 % (7621)------------------------------
% 0.22/0.41 % (7621)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (7621)Termination reason: Unknown
% 0.22/0.41 % (7621)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (7621)Memory used [KB]: 1151
% 0.22/0.41 % (7621)Time elapsed: 0.010 s
% 0.22/0.41 % (7621)Instructions burned: 15 (million)
% 0.22/0.41 % (7621)------------------------------
% 0.22/0.41 % (7621)------------------------------
% 0.22/0.41 % (7622)Instruction limit reached!
% 0.22/0.41 % (7622)------------------------------
% 0.22/0.41 % (7622)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (7622)Termination reason: Unknown
% 0.22/0.41 % (7622)Termination phase: shuffling
% 0.22/0.41
% 0.22/0.41 % (7622)Memory used [KB]: 1023
% 0.22/0.41 % (7622)Time elapsed: 0.004 s
% 0.22/0.41 % (7622)Instructions burned: 3 (million)
% 0.22/0.41 % (7622)------------------------------
% 0.22/0.41 % (7622)------------------------------
% 0.22/0.41 % (7624)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.41 % (7624)Instruction limit reached!
% 0.22/0.41 % (7624)------------------------------
% 0.22/0.41 % (7624)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.41 % (7624)Termination reason: Unknown
% 0.22/0.41 % (7624)Termination phase: Naming
% 0.22/0.41
% 0.22/0.41 % (7624)Memory used [KB]: 1151
% 0.22/0.41 % (7624)Time elapsed: 0.007 s
% 0.22/0.41 % (7624)Instructions burned: 8 (million)
% 0.22/0.41 % (7624)------------------------------
% 0.22/0.41 % (7624)------------------------------
% 0.22/0.41 % (7625)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.42 % (7620)Instruction limit reached!
% 0.22/0.42 % (7620)------------------------------
% 0.22/0.42 % (7620)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (7620)Termination reason: Unknown
% 0.22/0.42 % (7620)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (7620)Memory used [KB]: 5884
% 0.22/0.42 % (7620)Time elapsed: 0.023 s
% 0.22/0.42 % (7620)Instructions burned: 37 (million)
% 0.22/0.42 % (7620)------------------------------
% 0.22/0.42 % (7620)------------------------------
% 0.22/0.42 % (7628)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)
% 0.22/0.42 % (7630)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)
% 0.22/0.42 % (7628)Instruction limit reached!
% 0.22/0.42 % (7628)------------------------------
% 0.22/0.42 % (7628)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (7628)Termination reason: Unknown
% 0.22/0.42 % (7628)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (7628)Memory used [KB]: 1023
% 0.22/0.42 % (7628)Time elapsed: 0.004 s
% 0.22/0.42 % (7628)Instructions burned: 3 (million)
% 0.22/0.42 % (7628)------------------------------
% 0.22/0.42 % (7628)------------------------------
% 0.22/0.42 % (7625)Instruction limit reached!
% 0.22/0.42 % (7625)------------------------------
% 0.22/0.42 % (7625)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (7625)Termination reason: Unknown
% 0.22/0.42 % (7625)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (7625)Memory used [KB]: 5628
% 0.22/0.42 % (7625)Time elapsed: 0.011 s
% 0.22/0.42 % (7625)Instructions burned: 17 (million)
% 0.22/0.42 % (7625)------------------------------
% 0.22/0.42 % (7625)------------------------------
% 0.22/0.42 % (7630)Instruction limit reached!
% 0.22/0.42 % (7630)------------------------------
% 0.22/0.42 % (7630)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.42 % (7630)Termination reason: Unknown
% 0.22/0.42 % (7630)Termination phase: shuffling
% 0.22/0.42
% 0.22/0.42 % (7630)Memory used [KB]: 1023
% 0.22/0.42 % (7630)Time elapsed: 0.004 s
% 0.22/0.42 % (7630)Instructions burned: 3 (million)
% 0.22/0.42 % (7630)------------------------------
% 0.22/0.42 % (7630)------------------------------
% 0.22/0.43 % (7634)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)
% 0.22/0.43 % (7637)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)
% 0.22/0.43 % (7634)Instruction limit reached!
% 0.22/0.43 % (7634)------------------------------
% 0.22/0.43 % (7634)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.43 % (7634)Termination reason: Unknown
% 0.22/0.43 % (7634)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (7634)Memory used [KB]: 1151
% 0.22/0.43 % (7634)Time elapsed: 0.006 s
% 0.22/0.43 % (7634)Instructions burned: 7 (million)
% 0.22/0.43 % (7634)------------------------------
% 0.22/0.43 % (7634)------------------------------
% 0.22/0.44 % (7637)Instruction limit reached!
% 0.22/0.44 % (7637)------------------------------
% 0.22/0.44 % (7637)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (7637)Termination reason: Unknown
% 0.22/0.44 % (7637)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (7637)Memory used [KB]: 1151
% 0.22/0.44 % (7637)Time elapsed: 0.004 s
% 0.22/0.44 % (7637)Instructions burned: 3 (million)
% 0.22/0.44 % (7637)------------------------------
% 0.22/0.44 % (7637)------------------------------
% 0.22/0.44 % (7640)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.44 % (7641)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)
% 0.22/0.44 % (7642)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.44 % (7640)Instruction limit reached!
% 0.22/0.44 % (7640)------------------------------
% 0.22/0.44 % (7640)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.44 % (7640)Termination reason: Unknown
% 0.22/0.44 % (7640)Termination phase: shuffling
% 0.22/0.44
% 0.22/0.44 % (7640)Memory used [KB]: 1151
% 0.22/0.44 % (7640)Time elapsed: 0.005 s
% 0.22/0.44 % (7640)Instructions burned: 5 (million)
% 0.22/0.44 % (7640)------------------------------
% 0.22/0.44 % (7640)------------------------------
% 0.22/0.45 % (7648)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.45 % (7641)Instruction limit reached!
% 0.22/0.45 % (7641)------------------------------
% 0.22/0.45 % (7641)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.45 % (7641)Termination reason: Unknown
% 0.22/0.45 % (7641)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (7641)Memory used [KB]: 5756
% 0.22/0.45 % (7641)Time elapsed: 0.014 s
% 0.22/0.45 % (7641)Instructions burned: 19 (million)
% 0.22/0.45 % (7641)------------------------------
% 0.22/0.45 % (7641)------------------------------
% 0.22/0.45 % (7650)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)
% 0.22/0.45 % (7648)Instruction limit reached!
% 0.22/0.45 % (7648)------------------------------
% 0.22/0.45 % (7648)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.45 % (7648)Termination reason: Unknown
% 0.22/0.45 % (7648)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (7648)Memory used [KB]: 1151
% 0.22/0.45 % (7648)Time elapsed: 0.006 s
% 0.22/0.45 % (7648)Instructions burned: 7 (million)
% 0.22/0.45 % (7648)------------------------------
% 0.22/0.45 % (7648)------------------------------
% 0.22/0.46 % (7653)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)
% 0.22/0.46 % (7650)Refutation not found, incomplete strategy
% 0.22/0.46 % (7650)------------------------------
% 0.22/0.46 % (7650)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.46 % (7650)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 % (7650)Memory used [KB]: 5628
% 0.22/0.46 % (7650)Time elapsed: 0.009 s
% 0.22/0.46 % (7650)Instructions burned: 12 (million)
% 0.22/0.46 % (7650)------------------------------
% 0.22/0.46 % (7650)------------------------------
% 0.22/0.47 % (7659)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.47 % (7653)Instruction limit reached!
% 0.22/0.47 % (7653)------------------------------
% 0.22/0.47 % (7653)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.47 % (7653)Termination reason: Unknown
% 0.22/0.47 % (7653)Termination phase: Saturation
% 0.22/0.47
% 0.22/0.47 % (7653)Memory used [KB]: 5756
% 0.22/0.47 % (7653)Time elapsed: 0.013 s
% 0.22/0.47 % (7653)Instructions burned: 21 (million)
% 0.22/0.47 % (7653)------------------------------
% 0.22/0.47 % (7653)------------------------------
% 0.22/0.47 % (7661)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)
% 0.22/0.47 % (7659)Instruction limit reached!
% 0.22/0.47 % (7659)------------------------------
% 0.22/0.47 % (7659)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.47 % (7659)Termination reason: Unknown
% 0.22/0.47 % (7659)Termination phase: Property scanning
% 0.22/0.47
% 0.22/0.47 % (7659)Memory used [KB]: 1151
% 0.22/0.47 % (7659)Time elapsed: 0.005 s
% 0.22/0.47 % (7659)Instructions burned: 5 (million)
% 0.22/0.47 % (7659)------------------------------
% 0.22/0.47 % (7659)------------------------------
% 0.22/0.47 % (7661)Instruction limit reached!
% 0.22/0.47 % (7661)------------------------------
% 0.22/0.47 % (7661)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.47 % (7661)Termination reason: Unknown
% 0.22/0.47 % (7661)Termination phase: SInE selection
% 0.22/0.47
% 0.22/0.47 % (7661)Memory used [KB]: 1151
% 0.22/0.47 % (7661)Time elapsed: 0.006 s
% 0.22/0.47 % (7661)Instructions burned: 7 (million)
% 0.22/0.47 % (7661)------------------------------
% 0.22/0.47 % (7661)------------------------------
% 0.22/0.48 % (7664)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.48 % (7670)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.22/0.48 % (7672)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.22/0.49 % (7675)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2999ds/879Mi)
% 0.22/0.49 % (7612)Instruction limit reached!
% 0.22/0.49 % (7612)------------------------------
% 0.22/0.49 % (7612)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.49 % (7612)Termination reason: Unknown
% 0.22/0.49 % (7612)Termination phase: Saturation
% 0.22/0.49
% 0.22/0.49 % (7612)Memory used [KB]: 7164
% 0.22/0.49 % (7612)Time elapsed: 0.111 s
% 0.22/0.49 % (7612)Instructions burned: 184 (million)
% 0.22/0.49 % (7612)------------------------------
% 0.22/0.49 % (7612)------------------------------
% 0.22/0.49 % (7672)Refutation not found, incomplete strategy
% 0.22/0.49 % (7672)------------------------------
% 0.22/0.49 % (7672)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.49 % (7672)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.49
% 0.22/0.49
% 0.22/0.49 % (7672)Memory used [KB]: 5756
% 0.22/0.49 % (7672)Time elapsed: 0.009 s
% 0.22/0.49 % (7672)Instructions burned: 16 (million)
% 0.22/0.49 % (7672)------------------------------
% 0.22/0.49 % (7672)------------------------------
% 0.22/0.50 % (7683)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.50 % (7683)Instruction limit reached!
% 0.22/0.50 % (7683)------------------------------
% 0.22/0.50 % (7683)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.50 % (7683)Termination reason: Unknown
% 0.22/0.50 % (7683)Termination phase: shuffling
% 0.22/0.50
% 0.22/0.50 % (7683)Memory used [KB]: 1151
% 0.22/0.50 % (7683)Time elapsed: 0.003 s
% 0.22/0.50 % (7683)Instructions burned: 4 (million)
% 0.22/0.50 % (7683)------------------------------
% 0.22/0.50 % (7683)------------------------------
% 0.22/0.51 % (7682)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.22/0.51 % (7664)First to succeed.
% 0.22/0.51 % (7689)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.22/0.51 % (7682)Instruction limit reached!
% 0.22/0.51 % (7682)------------------------------
% 0.22/0.51 % (7682)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.51 % (7682)Termination reason: Unknown
% 0.22/0.51 % (7682)Termination phase: Saturation
% 0.22/0.51
% 0.22/0.51 % (7682)Memory used [KB]: 5628
% 0.22/0.51 % (7682)Time elapsed: 0.011 s
% 0.22/0.51 % (7682)Instructions burned: 17 (million)
% 0.22/0.51 % (7682)------------------------------
% 0.22/0.51 % (7682)------------------------------
% 0.22/0.52 % (7664)Refutation found. Thanks to Tanya!
% 0.22/0.52 % SZS status Theorem for theBenchmark
% 0.22/0.52 % SZS output start Proof for theBenchmark
% 0.22/0.52 thf(type_def_5, type, mu: $tType).
% 0.22/0.52 thf(type_def_7, type, reg: $tType).
% 0.22/0.52 thf(func_def_0, type, mu: $tType).
% 0.22/0.52 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.52 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.52 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.52 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.52 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.52 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.52 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.52 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.52 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.52 thf(func_def_33, type, reg: $tType).
% 0.22/0.52 thf(func_def_34, type, c: reg > reg > $o).
% 0.22/0.52 thf(func_def_35, type, dc: reg > reg > $o).
% 0.22/0.52 thf(func_def_36, type, p: reg > reg > $o).
% 0.22/0.52 thf(func_def_37, type, eq: reg > reg > $o).
% 0.22/0.52 thf(func_def_38, type, o: reg > reg > $o).
% 0.22/0.52 thf(func_def_39, type, po: reg > reg > $o).
% 0.22/0.52 thf(func_def_40, type, ec: reg > reg > $o).
% 0.22/0.52 thf(func_def_41, type, pp: reg > reg > $o).
% 0.22/0.52 thf(func_def_42, type, tpp: reg > reg > $o).
% 0.22/0.52 thf(func_def_43, type, ntpp: reg > reg > $o).
% 0.22/0.52 thf(func_def_44, type, catalunya: reg).
% 0.22/0.52 thf(func_def_45, type, france: reg).
% 0.22/0.52 thf(func_def_46, type, spain: reg).
% 0.22/0.52 thf(func_def_47, type, paris: reg).
% 0.22/0.52 thf(func_def_48, type, a: $i > $i > $o).
% 0.22/0.52 thf(func_def_49, type, fool: $i > $i > $o).
% 0.22/0.52 thf(func_def_66, type, sK1: reg > reg).
% 0.22/0.52 thf(func_def_67, type, sK2: reg > reg).
% 0.22/0.52 thf(func_def_68, type, sK3: reg > reg).
% 0.22/0.52 thf(func_def_69, type, sK4: reg).
% 0.22/0.52 thf(func_def_72, type, sK7: reg).
% 0.22/0.52 thf(func_def_73, type, sK8: reg > reg).
% 0.22/0.52 thf(func_def_74, type, sK9: reg > reg).
% 0.22/0.52 thf(func_def_75, type, sK10: reg > reg).
% 0.22/0.52 thf(func_def_76, type, sK11: reg).
% 0.22/0.52 thf(func_def_77, type, sK12: reg > reg).
% 0.22/0.52 thf(func_def_78, type, sK13: reg > reg).
% 0.22/0.52 thf(func_def_79, type, sK14: reg > reg).
% 0.22/0.52 thf(func_def_80, type, sK15: reg).
% 0.22/0.52 thf(func_def_81, type, sK16: reg).
% 0.22/0.52 thf(func_def_82, type, sK17: reg).
% 0.22/0.52 thf(func_def_83, type, sK18: $i > ($i > $o) > $i).
% 0.22/0.52 thf(func_def_84, type, sK19: reg > reg).
% 0.22/0.52 thf(func_def_85, type, sK20: reg > reg).
% 0.22/0.52 thf(func_def_86, type, sK21: $i > ($i > $o) > $i).
% 0.22/0.52 thf(func_def_87, type, sK22: reg).
% 0.22/0.52 thf(func_def_88, type, sK23: reg > reg).
% 0.22/0.52 thf(func_def_89, type, sK24: reg > reg).
% 0.22/0.52 thf(func_def_90, type, sK25: reg > reg).
% 0.22/0.52 thf(func_def_91, type, sK26: reg > reg).
% 0.22/0.52 thf(func_def_92, type, sK27: reg > reg).
% 0.22/0.52 thf(func_def_93, type, sK28: reg).
% 0.22/0.52 thf(func_def_94, type, sK29: $i > ($i > $o) > $i).
% 0.22/0.52 thf(func_def_95, type, ph30: !>[X0: $tType]:(X0)).
% 0.22/0.52 thf(f1023,plain,(
% 0.22/0.52 $false),
% 0.22/0.52 inference(avatar_sat_refutation,[],[f581,f662,f667,f672,f673,f687,f871,f884,f973,f976,f1022])).
% 0.22/0.52 thf(f1022,plain,(
% 0.22/0.52 ~spl0_23 | ~spl0_25 | ~spl0_29),
% 0.22/0.52 inference(avatar_contradiction_clause,[],[f1021])).
% 0.22/0.52 thf(f1021,plain,(
% 0.22/0.52 $false | (~spl0_23 | ~spl0_25 | ~spl0_29)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f1020])).
% 0.22/0.52 thf(f1020,plain,(
% 0.22/0.52 ($true = $false) | (~spl0_23 | ~spl0_25 | ~spl0_29)),
% 0.22/0.52 inference(backward_demodulation,[],[f666,f1017])).
% 0.22/0.52 thf(f1017,plain,(
% 0.22/0.52 ((c @ sK16 @ paris) = $false) | (~spl0_23 | ~spl0_29)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f1013])).
% 0.22/0.52 thf(f1013,plain,(
% 0.22/0.52 ($true = $false) | ((c @ sK16 @ paris) = $false) | (~spl0_23 | ~spl0_29)),
% 0.22/0.52 inference(superposition,[],[f686,f991])).
% 0.22/0.52 thf(f991,plain,(
% 0.22/0.52 ($false = (c @ sK16 @ france)) | ~spl0_23),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f983])).
% 0.22/0.52 thf(f983,plain,(
% 0.22/0.52 ($true = $false) | ($false = (c @ sK16 @ france)) | ~spl0_23),
% 0.22/0.52 inference(superposition,[],[f339,f657])).
% 0.22/0.52 thf(f657,plain,(
% 0.22/0.52 ($false = (c @ sK16 @ sK7)) | ~spl0_23),
% 0.22/0.52 inference(avatar_component_clause,[],[f655])).
% 0.22/0.52 thf(f655,plain,(
% 0.22/0.52 spl0_23 <=> ($false = (c @ sK16 @ sK7))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_23])])).
% 0.22/0.52 thf(f339,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = (c @ X1 @ sK7)) | ($false = (c @ X1 @ france))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f338])).
% 0.22/0.52 thf(f338,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = ((c @ X1 @ france) => (c @ X1 @ sK7)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f337])).
% 0.22/0.52 thf(f337,plain,(
% 0.22/0.52 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ sK7))) @ X1) = $true)) )),
% 0.22/0.52 inference(pi_clausification,[],[f336])).
% 0.22/0.52 thf(f336,plain,(
% 0.22/0.52 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ sK7)))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f295])).
% 0.22/0.52 thf(f295,plain,(
% 0.22/0.52 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france)))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f294])).
% 0.22/0.52 thf(f294,plain,(
% 0.22/0.52 ($true = ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK7)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ sK7)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france))))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f292])).
% 0.22/0.52 thf(f292,plain,(
% 0.22/0.52 ($true = (((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK7)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ sK7)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france))))))) & ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK7)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ sK7)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain)))))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f290])).
% 0.22/0.52 thf(f290,plain,(
% 0.22/0.52 ($false = ((((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK7)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ sK7)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france))))))) & ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK7)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ sK7)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain)))))))) => (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))))))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f289])).
% 0.22/0.52 thf(f289,plain,(
% 0.22/0.52 ($false = ((^[Y0 : reg]: ((((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ Y0)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))) & ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ Y0)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) => (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))) @ sK7))),
% 0.22/0.52 inference(sigma_clausification,[],[f286])).
% 0.22/0.52 thf(f286,plain,(
% 0.22/0.52 ($false = (!! @ reg @ (^[Y0 : reg]: ((((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ Y0)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))) & ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ Y0)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) => (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f285])).
% 0.22/0.52 thf(f285,plain,(
% 0.22/0.52 (((~ (a @ sK5 @ sK6)) | (!! @ reg @ (^[Y0 : reg]: ((((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ Y0)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))) & ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y0)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ Y0)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) => (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ Y0)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))))) = $false)),
% 0.22/0.52 inference(beta_eta_normalization,[],[f284])).
% 0.22/0.52 thf(f284,plain,(
% 0.22/0.52 ($false = ((^[Y0 : $i]: ((~ (a @ sK5 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: ((((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y1)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ Y1)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))) & ((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y1)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ Y1)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) => (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))))))) @ sK6))),
% 0.22/0.52 inference(sigma_clausification,[],[f283])).
% 0.22/0.52 thf(f283,plain,(
% 0.22/0.52 ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK5 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: ((((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y1)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ Y1)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))) & ((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y1)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ Y1)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) => (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ Y1)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))))))) = $false)),
% 0.22/0.52 inference(beta_eta_normalization,[],[f282])).
% 0.22/0.52 thf(f282,plain,(
% 0.22/0.52 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: ((((~ (?? @ reg @ (^[Y3 : reg]: (((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ france)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ france)) & ((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y2)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ Y2)))))) & ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ france) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))) & ((~ (?? @ reg @ (^[Y3 : reg]: (((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ spain)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ spain)) & ((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y2)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ Y2)))))) & ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ spain) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))) => (((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ paris) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))))) & ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ catalunya) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))))))))))))) @ sK5))),
% 0.22/0.52 inference(sigma_clausification,[],[f281])).
% 0.22/0.52 thf(f281,plain,(
% 0.22/0.52 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: ((((~ (?? @ reg @ (^[Y3 : reg]: (((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ france)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ france)) & ((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y2)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ Y2)))))) & ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ france) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))) & ((~ (?? @ reg @ (^[Y3 : reg]: (((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ spain)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ spain)) & ((~ (?? @ reg @ (^[Y4 : reg]: ((!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y2)))) & (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y4) => (c @ Y5 @ Y3)))))))) & (c @ Y3 @ Y2)))))) & ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ spain) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))) => (((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ paris) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))))) & ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ catalunya) => (c @ Y3 @ Y2)))) & (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya))))))))))))))))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f215])).
% 0.22/0.52 thf(f215,plain,(
% 0.22/0.52 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: ((((^[Y2 : reg]: ((^[Y3 : reg]: ((~ (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: ((~ ((^[Y7 : reg]: ((^[Y8 : reg]: (?? @ reg @ (^[Y9 : reg]: (((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y8) & ((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y7))))))) @ Y5 @ Y6)) & (c @ Y5 @ Y6))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: ((~ ((^[Y7 : reg]: ((^[Y8 : reg]: (?? @ reg @ (^[Y9 : reg]: (((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y8) & ((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y7))))))) @ Y5 @ Y6)) & (c @ Y5 @ Y6))))) @ Y4 @ Y3))))) & ((^[Y4 : reg]: ((^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4)))))) @ Y2 @ Y3))))) @ france @ Y1) & ((^[Y2 : reg]: ((^[Y3 : reg]: ((~ (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: ((~ ((^[Y7 : reg]: ((^[Y8 : reg]: (?? @ reg @ (^[Y9 : reg]: (((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y8) & ((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y7))))))) @ Y5 @ Y6)) & (c @ Y5 @ Y6))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: ((~ ((^[Y7 : reg]: ((^[Y8 : reg]: (?? @ reg @ (^[Y9 : reg]: (((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y8) & ((^[Y10 : reg]: ((^[Y11 : reg]: (!! @ reg @ (^[Y12 : reg]: ((c @ Y12 @ Y10) => (c @ Y12 @ Y11))))))) @ Y9 @ Y7))))))) @ Y5 @ Y6)) & (c @ Y5 @ Y6))))) @ Y4 @ Y3))))) & ((^[Y4 : reg]: ((^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4)))))) @ Y2 @ Y3))))) @ spain @ Y1)) => (((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ paris @ Y1) & ((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ catalunya @ Y1)))))))))),
% 0.22/0.52 inference(definition_unfolding,[],[f169,f172,f196,f212,f212,f210,f210])).
% 0.22/0.52 thf(f210,plain,(
% 0.22/0.52 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)))))))),
% 0.22/0.52 inference(definition_unfolding,[],[f164,f148,f148])).
% 0.22/0.52 thf(f148,plain,(
% 0.22/0.52 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f61])).
% 0.22/0.52 thf(f61,plain,(
% 0.22/0.52 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 0.22/0.52 inference(fool_elimination,[],[f60])).
% 0.22/0.52 thf(f60,plain,(
% 0.22/0.52 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 0.22/0.52 inference(rectify,[],[f35])).
% 0.22/0.52 thf(f35,axiom,(
% 0.22/0.52 (p = (^[X0 : reg, X1 : reg] : (! [X11 : reg] : ((c @ X11 @ X0) => (c @ X11 @ X1)))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',p)).
% 0.22/0.52 thf(f164,plain,(
% 0.22/0.52 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f113])).
% 0.22/0.52 thf(f113,plain,(
% 0.22/0.52 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))),
% 0.22/0.52 inference(fool_elimination,[],[f112])).
% 0.22/0.52 thf(f112,plain,(
% 0.22/0.52 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 0.22/0.52 inference(rectify,[],[f40])).
% 0.22/0.52 thf(f40,axiom,(
% 0.22/0.52 (pp = (^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pp)).
% 0.22/0.52 thf(f212,plain,(
% 0.22/0.52 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1))))) & ((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1))))))),
% 0.22/0.52 inference(definition_unfolding,[],[f195,f209,f209,f210])).
% 0.22/0.52 thf(f209,plain,(
% 0.22/0.52 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2))))))) @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
% 0.22/0.52 inference(definition_unfolding,[],[f163,f207])).
% 0.22/0.52 thf(f207,plain,(
% 0.22/0.52 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y0))))))))),
% 0.22/0.52 inference(definition_unfolding,[],[f187,f148,f148])).
% 0.22/0.52 thf(f187,plain,(
% 0.22/0.52 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f105])).
% 0.22/0.52 thf(f105,plain,(
% 0.22/0.52 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))),
% 0.22/0.52 inference(fool_elimination,[],[f104])).
% 0.22/0.52 thf(f104,plain,(
% 0.22/0.52 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X0) & (p @ X2 @ X1)))))),
% 0.22/0.52 inference(rectify,[],[f37])).
% 0.22/0.52 thf(f37,axiom,(
% 0.22/0.52 (o = (^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((p @ X11 @ X0) & (p @ X11 @ X1)))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',o)).
% 0.22/0.52 thf(f163,plain,(
% 0.22/0.52 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f119])).
% 0.22/0.52 thf(f119,plain,(
% 0.22/0.52 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
% 0.22/0.52 inference(fool_elimination,[],[f118])).
% 0.22/0.52 thf(f118,plain,(
% 0.22/0.52 (ec = (^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))))),
% 0.22/0.52 inference(rectify,[],[f39])).
% 0.22/0.52 thf(f39,axiom,(
% 0.22/0.52 (ec = (^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ec)).
% 0.22/0.52 thf(f195,plain,(
% 0.22/0.52 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))) & (pp @ Y0 @ Y1))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f55])).
% 0.22/0.52 thf(f55,plain,(
% 0.22/0.52 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))) & (pp @ Y0 @ Y1))))))),
% 0.22/0.52 inference(fool_elimination,[],[f54])).
% 0.22/0.52 thf(f54,plain,(
% 0.22/0.52 ((^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ~? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)))) = ntpp)),
% 0.22/0.52 inference(rectify,[],[f42])).
% 0.22/0.52 thf(f42,axiom,(
% 0.22/0.52 ((^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ~? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)))) = ntpp)),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ntpp)).
% 0.22/0.52 thf(f196,plain,(
% 0.22/0.52 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f53])).
% 0.22/0.52 thf(f53,plain,(
% 0.22/0.52 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.22/0.52 inference(fool_elimination,[],[f52])).
% 0.22/0.52 thf(f52,plain,(
% 0.22/0.52 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.22/0.52 inference(rectify,[],[f16])).
% 0.22/0.52 thf(f16,axiom,(
% 0.22/0.52 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.22/0.52 thf(f172,plain,(
% 0.22/0.52 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.52 inference(cnf_transformation,[],[f85])).
% 0.22/0.52 thf(f85,plain,(
% 0.22/0.52 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.52 inference(fool_elimination,[],[f84])).
% 0.22/0.52 thf(f84,plain,(
% 0.22/0.52 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.22/0.52 inference(rectify,[],[f28])).
% 0.22/0.52 thf(f28,axiom,(
% 0.22/0.52 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.52 thf(f169,plain,(
% 0.22/0.52 ($true != (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((ntpp @ france @ Y1) & (ntpp @ spain @ Y1)) => ((pp @ paris @ Y1) & (pp @ catalunya @ Y1)))))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f146])).
% 0.22/0.52 thf(f146,plain,(
% 0.22/0.52 ($true != (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((ntpp @ france @ Y1) & (ntpp @ spain @ Y1)) => ((pp @ paris @ Y1) & (pp @ catalunya @ Y1)))))))))),
% 0.22/0.52 inference(flattening,[],[f99])).
% 0.22/0.52 thf(f99,plain,(
% 0.22/0.52 ~($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((ntpp @ france @ Y1) & (ntpp @ spain @ Y1)) => ((pp @ paris @ Y1) & (pp @ catalunya @ Y1)))))))))),
% 0.22/0.52 inference(fool_elimination,[],[f98])).
% 0.22/0.52 thf(f98,plain,(
% 0.22/0.52 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : (((ntpp @ spain @ X1) & (ntpp @ france @ X1)) => ((pp @ catalunya @ X1) & (pp @ paris @ X1)))))))),
% 0.22/0.52 inference(rectify,[],[f50])).
% 0.22/0.52 thf(f50,negated_conjecture,(
% 0.22/0.52 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X11 : reg] : (((ntpp @ spain @ X11) & (ntpp @ france @ X11)) => ((pp @ catalunya @ X11) & (pp @ paris @ X11)))))))),
% 0.22/0.52 inference(negated_conjecture,[],[f49])).
% 0.22/0.52 thf(f49,conjecture,(
% 0.22/0.52 (mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X11 : reg] : (((ntpp @ spain @ X11) & (ntpp @ france @ X11)) => ((pp @ catalunya @ X11) & (pp @ paris @ X11)))))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.22/0.52 thf(f686,plain,(
% 0.22/0.52 ( ! [X3 : reg] : (($true = (c @ X3 @ france)) | ($false = (c @ X3 @ paris))) ) | ~spl0_29),
% 0.22/0.52 inference(avatar_component_clause,[],[f685])).
% 0.22/0.52 thf(f685,plain,(
% 0.22/0.52 spl0_29 <=> ! [X3 : reg] : (($true = (c @ X3 @ france)) | ($false = (c @ X3 @ paris)))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_29])])).
% 0.22/0.52 thf(f666,plain,(
% 0.22/0.52 ((c @ sK16 @ paris) = $true) | ~spl0_25),
% 0.22/0.52 inference(avatar_component_clause,[],[f664])).
% 0.22/0.52 thf(f664,plain,(
% 0.22/0.52 spl0_25 <=> ((c @ sK16 @ paris) = $true)),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_25])])).
% 0.22/0.52 thf(f976,plain,(
% 0.22/0.52 ~spl0_1),
% 0.22/0.52 inference(avatar_contradiction_clause,[],[f975])).
% 0.22/0.52 thf(f975,plain,(
% 0.22/0.52 $false | ~spl0_1),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f974])).
% 0.22/0.52 thf(f974,plain,(
% 0.22/0.52 ($true = $false) | ~spl0_1),
% 0.22/0.52 inference(backward_demodulation,[],[f288,f567])).
% 0.22/0.52 thf(f567,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X1 @ X2))) ) | ~spl0_1),
% 0.22/0.52 inference(avatar_component_clause,[],[f566])).
% 0.22/0.52 thf(f566,plain,(
% 0.22/0.52 spl0_1 <=> ! [X2,X1] : ($false = (a @ X1 @ X2))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.22/0.52 thf(f288,plain,(
% 0.22/0.52 ($true = (a @ sK5 @ sK6))),
% 0.22/0.52 inference(not_proxy_clausification,[],[f287])).
% 0.22/0.52 thf(f287,plain,(
% 0.22/0.52 ($false = (~ (a @ sK5 @ sK6)))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f285])).
% 0.22/0.52 thf(f973,plain,(
% 0.22/0.52 ~spl0_4 | ~spl0_24 | ~spl0_26),
% 0.22/0.52 inference(avatar_contradiction_clause,[],[f972])).
% 0.22/0.52 thf(f972,plain,(
% 0.22/0.52 $false | (~spl0_4 | ~spl0_24 | ~spl0_26)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f971])).
% 0.22/0.52 thf(f971,plain,(
% 0.22/0.52 ($true = $false) | (~spl0_4 | ~spl0_24 | ~spl0_26)),
% 0.22/0.52 inference(backward_demodulation,[],[f671,f970])).
% 0.22/0.52 thf(f970,plain,(
% 0.22/0.52 ($false = (c @ sK17 @ catalunya)) | (~spl0_4 | ~spl0_24)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f962])).
% 0.22/0.52 thf(f962,plain,(
% 0.22/0.52 ($true = $false) | ($false = (c @ sK17 @ catalunya)) | (~spl0_4 | ~spl0_24)),
% 0.22/0.52 inference(superposition,[],[f960,f580])).
% 0.22/0.52 thf(f580,plain,(
% 0.22/0.52 ( ! [X3 : reg] : (($true = (c @ X3 @ spain)) | ((c @ X3 @ catalunya) = $false)) ) | ~spl0_4),
% 0.22/0.52 inference(avatar_component_clause,[],[f579])).
% 0.22/0.52 thf(f579,plain,(
% 0.22/0.52 spl0_4 <=> ! [X3 : reg] : (((c @ X3 @ catalunya) = $false) | ($true = (c @ X3 @ spain)))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.22/0.52 thf(f960,plain,(
% 0.22/0.52 ($false = (c @ sK17 @ spain)) | ~spl0_24),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f957])).
% 0.22/0.52 thf(f957,plain,(
% 0.22/0.52 ($true = $false) | ($false = (c @ sK17 @ spain)) | ~spl0_24),
% 0.22/0.52 inference(superposition,[],[f390,f661])).
% 0.22/0.52 thf(f661,plain,(
% 0.22/0.52 ((c @ sK17 @ sK7) = $false) | ~spl0_24),
% 0.22/0.52 inference(avatar_component_clause,[],[f659])).
% 0.22/0.52 thf(f659,plain,(
% 0.22/0.52 spl0_24 <=> ((c @ sK17 @ sK7) = $false)),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_24])])).
% 0.22/0.52 thf(f390,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = (c @ X1 @ sK7)) | ((c @ X1 @ spain) = $false)) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f389])).
% 0.22/0.52 thf(f389,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = ((c @ X1 @ spain) => (c @ X1 @ sK7)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f388])).
% 0.22/0.52 thf(f388,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ sK7))) @ X1))) )),
% 0.22/0.52 inference(pi_clausification,[],[f387])).
% 0.22/0.52 thf(f387,plain,(
% 0.22/0.52 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ sK7)))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f345])).
% 0.22/0.52 thf(f345,plain,(
% 0.22/0.52 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain)))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f293])).
% 0.22/0.52 thf(f293,plain,(
% 0.22/0.52 ($true = ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ sK7)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ sK7)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain))))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f292])).
% 0.22/0.52 thf(f671,plain,(
% 0.22/0.52 ($true = (c @ sK17 @ catalunya)) | ~spl0_26),
% 0.22/0.52 inference(avatar_component_clause,[],[f669])).
% 0.22/0.52 thf(f669,plain,(
% 0.22/0.52 spl0_26 <=> ($true = (c @ sK17 @ catalunya))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_26])])).
% 0.22/0.52 thf(f884,plain,(
% 0.22/0.52 ~spl0_22 | ~spl0_29),
% 0.22/0.52 inference(avatar_contradiction_clause,[],[f883])).
% 0.22/0.52 thf(f883,plain,(
% 0.22/0.52 $false | (~spl0_22 | ~spl0_29)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f882])).
% 0.22/0.52 thf(f882,plain,(
% 0.22/0.52 ($true = $false) | (~spl0_22 | ~spl0_29)),
% 0.22/0.52 inference(backward_demodulation,[],[f344,f881])).
% 0.22/0.52 thf(f881,plain,(
% 0.22/0.52 ((c @ sK11 @ sK7) = $false) | (~spl0_22 | ~spl0_29)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f877])).
% 0.22/0.52 thf(f877,plain,(
% 0.22/0.52 ((c @ sK11 @ sK7) = $false) | ($true = $false) | (~spl0_22 | ~spl0_29)),
% 0.22/0.52 inference(superposition,[],[f839,f653])).
% 0.22/0.52 thf(f653,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = (c @ X1 @ paris)) | ((c @ X1 @ sK7) = $false)) ) | ~spl0_22),
% 0.22/0.52 inference(avatar_component_clause,[],[f652])).
% 0.22/0.52 thf(f652,plain,(
% 0.22/0.52 spl0_22 <=> ! [X1 : reg] : (((c @ X1 @ sK7) = $false) | ($true = (c @ X1 @ paris)))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])).
% 0.22/0.52 thf(f839,plain,(
% 0.22/0.52 ($false = (c @ sK11 @ paris)) | ~spl0_29),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f837])).
% 0.22/0.52 thf(f837,plain,(
% 0.22/0.52 ($false = (c @ sK11 @ paris)) | ($true = $false) | ~spl0_29),
% 0.22/0.52 inference(superposition,[],[f343,f686])).
% 0.22/0.52 thf(f343,plain,(
% 0.22/0.52 ((c @ sK11 @ france) = $false)),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f342])).
% 0.22/0.52 thf(f342,plain,(
% 0.22/0.52 ($false = ((c @ sK11 @ sK7) => (c @ sK11 @ france)))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f341])).
% 0.22/0.52 thf(f341,plain,(
% 0.22/0.52 ($false = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france))) @ sK11))),
% 0.22/0.52 inference(sigma_clausification,[],[f340])).
% 0.22/0.52 thf(f340,plain,(
% 0.22/0.52 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france)))))),
% 0.22/0.52 inference(not_proxy_clausification,[],[f335])).
% 0.22/0.52 thf(f335,plain,(
% 0.22/0.52 ($true = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ france))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f295])).
% 0.22/0.52 thf(f344,plain,(
% 0.22/0.52 ((c @ sK11 @ sK7) = $true)),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f342])).
% 0.22/0.52 thf(f871,plain,(
% 0.22/0.52 ~spl0_4 | ~spl0_21),
% 0.22/0.52 inference(avatar_contradiction_clause,[],[f870])).
% 0.22/0.52 thf(f870,plain,(
% 0.22/0.52 $false | (~spl0_4 | ~spl0_21)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f869])).
% 0.22/0.52 thf(f869,plain,(
% 0.22/0.52 ($true = $false) | (~spl0_4 | ~spl0_21)),
% 0.22/0.52 inference(backward_demodulation,[],[f395,f868])).
% 0.22/0.52 thf(f868,plain,(
% 0.22/0.52 ($false = (c @ sK15 @ sK7)) | (~spl0_4 | ~spl0_21)),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f861])).
% 0.22/0.52 thf(f861,plain,(
% 0.22/0.52 ($false = (c @ sK15 @ sK7)) | ($true = $false) | (~spl0_4 | ~spl0_21)),
% 0.22/0.52 inference(superposition,[],[f650,f814])).
% 0.22/0.52 thf(f814,plain,(
% 0.22/0.52 ($false = (c @ sK15 @ catalunya)) | ~spl0_4),
% 0.22/0.52 inference(trivial_inequality_removal,[],[f811])).
% 0.22/0.52 thf(f811,plain,(
% 0.22/0.52 ($false = (c @ sK15 @ catalunya)) | ($true = $false) | ~spl0_4),
% 0.22/0.52 inference(superposition,[],[f580,f394])).
% 0.22/0.52 thf(f394,plain,(
% 0.22/0.52 ($false = (c @ sK15 @ spain))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f393])).
% 0.22/0.52 thf(f393,plain,(
% 0.22/0.52 (((c @ sK15 @ sK7) => (c @ sK15 @ spain)) = $false)),
% 0.22/0.52 inference(beta_eta_normalization,[],[f392])).
% 0.22/0.52 thf(f392,plain,(
% 0.22/0.52 ($false = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain))) @ sK15))),
% 0.22/0.52 inference(sigma_clausification,[],[f391])).
% 0.22/0.52 thf(f391,plain,(
% 0.22/0.52 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain)))))),
% 0.22/0.52 inference(not_proxy_clausification,[],[f386])).
% 0.22/0.52 thf(f386,plain,(
% 0.22/0.52 ($true = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ spain))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f345])).
% 0.22/0.52 thf(f650,plain,(
% 0.22/0.52 ( ! [X2 : reg] : (($true = (c @ X2 @ catalunya)) | ($false = (c @ X2 @ sK7))) ) | ~spl0_21),
% 0.22/0.52 inference(avatar_component_clause,[],[f649])).
% 0.22/0.52 thf(f649,plain,(
% 0.22/0.52 spl0_21 <=> ! [X2 : reg] : (($false = (c @ X2 @ sK7)) | ($true = (c @ X2 @ catalunya)))),
% 0.22/0.52 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])).
% 0.22/0.52 thf(f395,plain,(
% 0.22/0.52 ($true = (c @ sK15 @ sK7))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f393])).
% 0.22/0.52 thf(f687,plain,(
% 0.22/0.52 spl0_29 | spl0_1),
% 0.22/0.52 inference(avatar_split_clause,[],[f274,f566,f685])).
% 0.22/0.52 thf(f274,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (c @ X3 @ france)) | ($false = (a @ X1 @ X2)) | ($false = (c @ X3 @ paris))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f273])).
% 0.22/0.52 thf(f273,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((c @ X3 @ paris) => (c @ X3 @ france))) | ($false = (a @ X1 @ X2))) )),
% 0.22/0.52 inference(not_proxy_clausification,[],[f272])).
% 0.22/0.52 thf(f272,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (~ (a @ X1 @ X2))) | ($true = ((c @ X3 @ paris) => (c @ X3 @ france)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f271])).
% 0.22/0.52 thf(f271,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = (~ (a @ X1 @ X2))) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X3))) )),
% 0.22/0.52 inference(pi_clausification,[],[f270])).
% 0.22/0.52 thf(f270,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) | ($true = (~ (a @ X1 @ X2)))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f226])).
% 0.22/0.52 thf(f226,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))))) | ($true = (~ (a @ X1 @ X2)))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f225])).
% 0.22/0.52 thf(f225,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))))) | ($true = (~ (a @ X1 @ X2)))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f224])).
% 0.22/0.52 thf(f224,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (a @ X1 @ X2)) | ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))))))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f223])).
% 0.22/0.52 thf(f223,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))))))) @ X2))) )),
% 0.22/0.52 inference(pi_clausification,[],[f222])).
% 0.22/0.52 thf(f222,plain,(
% 0.22/0.52 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris)))))))))))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f221])).
% 0.22/0.52 thf(f221,plain,(
% 0.22/0.52 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))))))))) @ X1) = $true)) )),
% 0.22/0.52 inference(pi_clausification,[],[f220])).
% 0.22/0.52 thf(f220,plain,(
% 0.22/0.52 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris)))))))))))))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f217])).
% 0.22/0.52 thf(f217,plain,(
% 0.22/0.52 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2))))) & ((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2))))) @ paris @ france)))))),
% 0.22/0.52 inference(definition_unfolding,[],[f185,f172,f196,f212])).
% 0.22/0.52 thf(f185,plain,(
% 0.22/0.52 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))))),
% 0.22/0.52 inference(cnf_transformation,[],[f115])).
% 0.22/0.52 thf(f115,plain,(
% 0.22/0.52 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))))),
% 0.22/0.52 inference(fool_elimination,[],[f114])).
% 0.22/0.52 thf(f114,plain,(
% 0.22/0.52 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))),
% 0.22/0.52 inference(rectify,[],[f48])).
% 0.22/0.52 thf(f48,axiom,(
% 0.22/0.52 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 0.22/0.52 thf(f673,plain,(
% 0.22/0.52 spl0_26 | spl0_21 | spl0_25 | spl0_22),
% 0.22/0.52 inference(avatar_split_clause,[],[f414,f652,f664,f649,f669])).
% 0.22/0.52 thf(f414,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($false = (c @ X2 @ sK7)) | ((c @ X1 @ sK7) = $false) | ((c @ sK16 @ paris) = $true) | ($true = (c @ sK17 @ catalunya)) | ($true = (c @ X2 @ catalunya)) | ($true = (c @ X1 @ paris))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f413])).
% 0.22/0.52 thf(f413,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($true = (c @ X2 @ catalunya)) | ($true = (c @ sK17 @ catalunya)) | ($false = (c @ X2 @ sK7)) | ($true = ((c @ X1 @ sK7) => (c @ X1 @ paris))) | ((c @ sK16 @ paris) = $true)) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f412])).
% 0.22/0.52 thf(f412,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (((c @ sK16 @ paris) = $true) | ($true = ((c @ X2 @ sK7) => (c @ X2 @ catalunya))) | ($true = ((c @ X1 @ sK7) => (c @ X1 @ paris))) | ($true = (c @ sK17 @ catalunya))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f411])).
% 0.22/0.52 thf(f411,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($true = ((c @ X1 @ sK7) => (c @ X1 @ paris))) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))) @ X2)) | ((c @ sK16 @ paris) = $true) | ($true = (c @ sK17 @ catalunya))) )),
% 0.22/0.52 inference(pi_clausification,[],[f410])).
% 0.22/0.52 thf(f410,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (((c @ sK16 @ paris) = $true) | ($true = (c @ sK17 @ catalunya)) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))) | ($true = ((c @ X1 @ sK7) => (c @ X1 @ paris)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f409])).
% 0.22/0.52 thf(f409,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))) | ($true = (c @ sK17 @ catalunya)) | ((c @ sK16 @ paris) = $true) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))) @ X1))) )),
% 0.22/0.52 inference(pi_clausification,[],[f408])).
% 0.22/0.52 thf(f408,plain,(
% 0.22/0.52 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))) | ((c @ sK16 @ paris) = $true) | ($true = (c @ sK17 @ catalunya)) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))),
% 0.22/0.52 inference(not_proxy_clausification,[],[f407])).
% 0.22/0.52 thf(f407,plain,(
% 0.22/0.52 ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))) | ((c @ sK16 @ paris) = $true) | ($true = (c @ sK17 @ catalunya))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f405])).
% 0.22/0.52 thf(f405,plain,(
% 0.22/0.52 ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($true = (c @ sK17 @ catalunya)) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))),
% 0.22/0.52 inference(not_proxy_clausification,[],[f404])).
% 0.22/0.52 thf(f404,plain,(
% 0.22/0.52 ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) | ($true = (c @ sK17 @ catalunya)) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7)))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f402])).
% 0.22/0.52 thf(f402,plain,(
% 0.22/0.52 (((c @ sK17 @ catalunya) => (c @ sK17 @ sK7)) = $false) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7)))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f401])).
% 0.22/0.52 thf(f401,plain,(
% 0.22/0.52 ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) | ($false = ((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7))) @ sK17))),
% 0.22/0.52 inference(sigma_clausification,[],[f400])).
% 0.22/0.52 thf(f400,plain,(
% 0.22/0.52 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7))))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f399])).
% 0.22/0.52 thf(f399,plain,(
% 0.22/0.52 ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = ((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ sK7))) @ sK16)) | ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7)))))),
% 0.22/0.52 inference(sigma_clausification,[],[f398])).
% 0.22/0.52 thf(f398,plain,(
% 0.22/0.52 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ sK7))))) | ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f397])).
% 0.22/0.52 thf(f397,plain,(
% 0.22/0.52 ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))) | ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ sK7))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f396])).
% 0.22/0.52 thf(f396,plain,(
% 0.22/0.52 ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))))) | ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f291])).
% 0.22/0.52 thf(f291,plain,(
% 0.22/0.52 ($false = (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ sK7)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f290])).
% 0.22/0.52 thf(f672,plain,(
% 0.22/0.52 spl0_23 | spl0_21 | spl0_26 | spl0_22),
% 0.22/0.52 inference(avatar_split_clause,[],[f421,f652,f669,f649,f655])).
% 0.22/0.52 thf(f421,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($true = (c @ sK17 @ catalunya)) | ((c @ X1 @ sK7) = $false) | ($true = (c @ X2 @ catalunya)) | ($false = (c @ sK16 @ sK7)) | ($true = (c @ X1 @ paris)) | ($false = (c @ X2 @ sK7))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f420])).
% 0.22/0.52 thf(f420,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($false = (c @ sK16 @ sK7)) | ((c @ X1 @ sK7) = $false) | ($true = (c @ X1 @ paris)) | ($true = (c @ sK17 @ catalunya)) | ($true = ((c @ X2 @ sK7) => (c @ X2 @ catalunya)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f419])).
% 0.22/0.52 thf(f419,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))) @ X2)) | ($true = (c @ sK17 @ catalunya)) | ((c @ X1 @ sK7) = $false) | ($true = (c @ X1 @ paris)) | ($false = (c @ sK16 @ sK7))) )),
% 0.22/0.52 inference(pi_clausification,[],[f418])).
% 0.22/0.52 thf(f418,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))) | ($true = (c @ sK17 @ catalunya)) | ((c @ X1 @ sK7) = $false) | ($false = (c @ sK16 @ sK7)) | ($true = (c @ X1 @ paris))) )),
% 0.22/0.52 inference(not_proxy_clausification,[],[f417])).
% 0.22/0.52 thf(f417,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($true = (c @ X1 @ paris)) | ($false = (c @ sK16 @ sK7)) | ((c @ X1 @ sK7) = $false) | ($true = (c @ sK17 @ catalunya))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f416])).
% 0.22/0.52 thf(f416,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = ((c @ X1 @ sK7) => (c @ X1 @ paris))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = (c @ sK16 @ sK7)) | ($true = (c @ sK17 @ catalunya))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f415])).
% 0.22/0.52 thf(f415,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($false = (c @ sK16 @ sK7)) | ($true = (c @ sK17 @ catalunya)) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))) @ X1)) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))) )),
% 0.22/0.52 inference(pi_clausification,[],[f406])).
% 0.22/0.52 thf(f406,plain,(
% 0.22/0.52 ($true = (c @ sK17 @ catalunya)) | ($false = (c @ sK16 @ sK7)) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f405])).
% 0.22/0.52 thf(f667,plain,(
% 0.22/0.52 spl0_24 | spl0_25 | spl0_22 | spl0_21),
% 0.22/0.52 inference(avatar_split_clause,[],[f431,f649,f652,f664,f659])).
% 0.22/0.52 thf(f431,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (((c @ sK17 @ sK7) = $false) | ($true = (c @ X1 @ paris)) | ($false = (c @ X2 @ sK7)) | ((c @ X1 @ sK7) = $false) | ((c @ sK16 @ paris) = $true) | ($true = (c @ X2 @ catalunya))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f430])).
% 0.22/0.52 thf(f430,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (((c @ sK16 @ paris) = $true) | ((c @ sK17 @ sK7) = $false) | ((c @ X1 @ sK7) = $false) | ($true = (c @ X1 @ paris)) | ($true = ((c @ X2 @ sK7) => (c @ X2 @ catalunya)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f429])).
% 0.22/0.52 thf(f429,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($true = (c @ X1 @ paris)) | ((c @ sK17 @ sK7) = $false) | ((c @ sK16 @ paris) = $true) | ((c @ X1 @ sK7) = $false) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))) @ X2))) )),
% 0.22/0.52 inference(pi_clausification,[],[f428])).
% 0.22/0.52 thf(f428,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (((c @ X1 @ sK7) = $false) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))) | ($true = (c @ X1 @ paris)) | ((c @ sK17 @ sK7) = $false) | ((c @ sK16 @ paris) = $true)) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f426])).
% 0.22/0.52 thf(f426,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ((c @ X1 @ sK7) = $false) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))) | ((c @ sK17 @ sK7) = $false) | ($true = (c @ X1 @ paris))) )),
% 0.22/0.52 inference(not_proxy_clausification,[],[f425])).
% 0.22/0.52 thf(f425,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ((c @ sK17 @ sK7) = $false) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($true = (c @ X1 @ paris)) | ((c @ X1 @ sK7) = $false)) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f424])).
% 0.22/0.52 thf(f424,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($true = ((c @ X1 @ sK7) => (c @ X1 @ paris))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ((c @ sK17 @ sK7) = $false) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f423])).
% 0.22/0.52 thf(f423,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya)))))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))) @ X1)) | ((c @ sK17 @ sK7) = $false)) )),
% 0.22/0.52 inference(pi_clausification,[],[f422])).
% 0.22/0.52 thf(f422,plain,(
% 0.22/0.52 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris))))) | ((c @ sK17 @ sK7) = $false) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))),
% 0.22/0.52 inference(not_proxy_clausification,[],[f403])).
% 0.22/0.52 thf(f403,plain,(
% 0.22/0.52 ((c @ sK17 @ sK7) = $false) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ paris)))))) | ($false = ((c @ sK16 @ paris) => (c @ sK16 @ sK7))) | ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))))),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f402])).
% 0.22/0.52 thf(f662,plain,(
% 0.22/0.52 spl0_21 | spl0_22 | spl0_23 | spl0_24),
% 0.22/0.52 inference(avatar_split_clause,[],[f434,f659,f655,f652,f649])).
% 0.22/0.52 thf(f434,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (((c @ X1 @ sK7) = $false) | ($false = (c @ X2 @ sK7)) | ($false = (c @ sK16 @ sK7)) | ($true = (c @ X1 @ paris)) | ((c @ sK17 @ sK7) = $false) | ($true = (c @ X2 @ catalunya))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f433])).
% 0.22/0.52 thf(f433,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (((c @ sK17 @ sK7) = $false) | ($false = (c @ sK16 @ sK7)) | ((c @ X1 @ sK7) = $false) | ($true = ((c @ X2 @ sK7) => (c @ X2 @ catalunya))) | ($true = (c @ X1 @ paris))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f432])).
% 0.22/0.52 thf(f432,plain,(
% 0.22/0.52 ( ! [X2 : reg,X1 : reg] : (($true = (c @ X1 @ paris)) | ($true = ((^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))) @ X2)) | ($false = (c @ sK16 @ sK7)) | ((c @ sK17 @ sK7) = $false) | ((c @ X1 @ sK7) = $false)) )),
% 0.22/0.52 inference(pi_clausification,[],[f427])).
% 0.22/0.52 thf(f427,plain,(
% 0.22/0.52 ( ! [X1 : reg] : (((c @ sK17 @ sK7) = $false) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK7) => (c @ Y0 @ catalunya))))) | ($false = (c @ sK16 @ sK7)) | ($true = (c @ X1 @ paris)) | ((c @ X1 @ sK7) = $false)) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f426])).
% 0.22/0.52 thf(f581,plain,(
% 0.22/0.52 spl0_4 | spl0_1),
% 0.22/0.52 inference(avatar_split_clause,[],[f542,f566,f579])).
% 0.22/0.52 thf(f542,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (((c @ X3 @ catalunya) = $false) | ($true = (c @ X3 @ spain)) | ($false = (a @ X1 @ X2))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f541])).
% 0.22/0.52 thf(f541,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($false = (a @ X1 @ X2)) | ($true = ((c @ X3 @ catalunya) => (c @ X3 @ spain)))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f540])).
% 0.22/0.52 thf(f540,plain,(
% 0.22/0.52 ( ! [X2 : $i,X3 : reg,X1 : $i] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X3)) | ($false = (a @ X1 @ X2))) )),
% 0.22/0.52 inference(pi_clausification,[],[f539])).
% 0.22/0.52 thf(f539,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X1 @ X2)) | ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f498])).
% 0.22/0.52 thf(f498,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))))) | ($false = (a @ X1 @ X2))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f497])).
% 0.22/0.52 thf(f497,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))))) | ($false = (a @ X1 @ X2))) )),
% 0.22/0.52 inference(not_proxy_clausification,[],[f496])).
% 0.22/0.52 thf(f496,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = (~ (a @ X1 @ X2))) | ($true = ((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))))))) )),
% 0.22/0.52 inference(binary_proxy_clausification,[],[f495])).
% 0.22/0.52 thf(f495,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (a @ X1 @ X2)) | ((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya))))) & ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))))))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f494])).
% 0.22/0.52 thf(f494,plain,(
% 0.22/0.52 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ catalunya))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya))))))))) @ X2))) )),
% 0.22/0.52 inference(pi_clausification,[],[f493])).
% 0.22/0.52 thf(f493,plain,(
% 0.22/0.52 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ catalunya))))) & ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))))))))) )),
% 0.22/0.52 inference(beta_eta_normalization,[],[f492])).
% 0.22/0.52 thf(f492,plain,(
% 0.22/0.52 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ catalunya))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya))))))))))) @ X1))) )),
% 0.22/0.52 inference(pi_clausification,[],[f491])).
% 0.22/0.52 thf(f491,plain,(
% 0.22/0.52 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ catalunya))))) & ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))))))))))),
% 0.22/0.52 inference(beta_eta_normalization,[],[f216])).
% 0.22/0.52 thf(f216,plain,(
% 0.22/0.52 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y1)))) & ((^[Y3 : reg]: ((^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2))))) @ catalunya @ spain)))))),
% 0.22/0.52 inference(definition_unfolding,[],[f184,f172,f196,f211])).
% 0.22/0.52 thf(f211,plain,(
% 0.22/0.52 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y0)))) & ((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1))))))),
% 0.22/0.52 inference(definition_unfolding,[],[f152,f209,f209,f210])).
% 0.22/0.52 thf(f152,plain,(
% 0.22/0.52 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0)))) & (pp @ Y0 @ Y1))))))),
% 0.22/0.52 inference(cnf_transformation,[],[f63])).
% 0.22/0.52 thf(f63,plain,(
% 0.22/0.52 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0)))) & (pp @ Y0 @ Y1))))))),
% 0.22/0.52 inference(fool_elimination,[],[f62])).
% 0.22/0.52 thf(f62,plain,(
% 0.22/0.52 (tpp = (^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ? [X2 : reg] : ((ec @ X2 @ X0) & (ec @ X2 @ X1)))))),
% 0.22/0.52 inference(rectify,[],[f41])).
% 0.22/0.52 thf(f41,axiom,(
% 0.22/0.52 (tpp = (^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ? [X11 : reg] : ((ec @ X11 @ X0) & (ec @ X11 @ X1)))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tpp)).
% 0.22/0.52 thf(f184,plain,(
% 0.22/0.52 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))),
% 0.22/0.52 inference(cnf_transformation,[],[f81])).
% 0.22/0.52 thf(f81,plain,(
% 0.22/0.52 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))),
% 0.22/0.52 inference(fool_elimination,[],[f80])).
% 0.22/0.52 thf(f80,plain,(
% 0.22/0.52 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))),
% 0.22/0.52 inference(rectify,[],[f46])).
% 0.22/0.52 thf(f46,axiom,(
% 0.22/0.52 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))),
% 0.22/0.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 0.22/0.52 % SZS output end Proof for theBenchmark
% 0.22/0.52 % (7664)------------------------------
% 0.22/0.52 % (7664)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.22/0.52 % (7664)Termination reason: Refutation
% 0.22/0.52
% 0.22/0.52 % (7664)Memory used [KB]: 6524
% 0.22/0.52 % (7664)Time elapsed: 0.042 s
% 0.22/0.52 % (7664)Instructions burned: 85 (million)
% 0.22/0.52 % (7664)------------------------------
% 0.22/0.52 % (7664)------------------------------
% 0.22/0.52 % (7611)Success in time 0.136 s
%------------------------------------------------------------------------------