TSTP Solution File: GEG013^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GEG013^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n014.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 May 20 19:57:08 EDT 2024
% Result : Theorem 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEG013^1 : TPTP v8.2.0. Released v4.1.0.
% 0.11/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 18 21:56:22 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % (7947)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)
% 0.14/0.39 % (7949)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.39 % (7944)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)
% 0.14/0.39 % (7946)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (7948)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)
% 0.14/0.39 % (7945)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)
% 0.14/0.39 % (7943)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.39 % (7950)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)
% 0.14/0.39 % (7946)Instruction limit reached!
% 0.14/0.39 % (7946)------------------------------
% 0.14/0.39 % (7946)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7946)Termination reason: Unknown
% 0.14/0.39 % (7946)Termination phase: shuffling
% 0.14/0.39 % (7947)Instruction limit reached!
% 0.14/0.39 % (7947)------------------------------
% 0.14/0.39 % (7947)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7947)Termination reason: Unknown
% 0.14/0.39 % (7947)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (7947)Memory used [KB]: 1023
% 0.14/0.39 % (7947)Time elapsed: 0.003 s
% 0.14/0.39 % (7947)Instructions burned: 3 (million)
% 0.14/0.39 % (7947)------------------------------
% 0.14/0.39 % (7947)------------------------------
% 0.14/0.39
% 0.14/0.39 % (7946)Memory used [KB]: 1023
% 0.14/0.39 % (7946)Time elapsed: 0.003 s
% 0.14/0.39 % (7946)Instructions burned: 3 (million)
% 0.14/0.39 % (7946)------------------------------
% 0.14/0.39 % (7946)------------------------------
% 0.14/0.39 % (7944)Instruction limit reached!
% 0.14/0.39 % (7944)------------------------------
% 0.14/0.39 % (7944)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7944)Termination reason: Unknown
% 0.14/0.39 % (7944)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (7944)Memory used [KB]: 1151
% 0.14/0.39 % (7944)Time elapsed: 0.004 s
% 0.14/0.39 % (7944)Instructions burned: 5 (million)
% 0.14/0.39 % (7944)------------------------------
% 0.14/0.39 % (7944)------------------------------
% 0.14/0.39 % (7950)Instruction limit reached!
% 0.14/0.39 % (7950)------------------------------
% 0.14/0.39 % (7950)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7950)Termination reason: Unknown
% 0.14/0.39 % (7950)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (7950)Memory used [KB]: 1023
% 0.14/0.39 % (7950)Time elapsed: 0.003 s
% 0.14/0.39 % (7950)Instructions burned: 3 (million)
% 0.14/0.39 % (7950)------------------------------
% 0.14/0.39 % (7950)------------------------------
% 0.14/0.39 % (7948)Refutation not found, incomplete strategy
% 0.14/0.39 % (7948)------------------------------
% 0.14/0.39 % (7948)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (7948)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (7948)Memory used [KB]: 5628
% 0.14/0.39 % (7948)Time elapsed: 0.008 s
% 0.14/0.39 % (7948)Instructions burned: 11 (million)
% 0.14/0.39 % (7948)------------------------------
% 0.14/0.39 % (7948)------------------------------
% 0.14/0.40 % (7949)Instruction limit reached!
% 0.14/0.40 % (7949)------------------------------
% 0.14/0.40 % (7949)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (7949)Termination reason: Unknown
% 0.14/0.40 % (7949)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (7949)Memory used [KB]: 5628
% 0.14/0.40 % (7949)Time elapsed: 0.011 s
% 0.14/0.40 % (7949)Instructions burned: 18 (million)
% 0.14/0.40 % (7949)------------------------------
% 0.14/0.40 % (7949)------------------------------
% 0.14/0.40 % (7945)Instruction limit reached!
% 0.14/0.40 % (7945)------------------------------
% 0.14/0.40 % (7945)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (7945)Termination reason: Unknown
% 0.14/0.40 % (7945)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (7945)Memory used [KB]: 5756
% 0.14/0.40 % (7945)Time elapsed: 0.017 s
% 0.14/0.40 % (7945)Instructions burned: 27 (million)
% 0.14/0.40 % (7945)------------------------------
% 0.14/0.40 % (7945)------------------------------
% 0.14/0.40 % (7951)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)
% 0.14/0.40 % (7952)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)
% 0.14/0.40 % (7954)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)
% 0.14/0.40 % (7953)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)
% 0.14/0.41 % (7953)Instruction limit reached!
% 0.14/0.41 % (7953)------------------------------
% 0.14/0.41 % (7953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (7953)Termination reason: Unknown
% 0.14/0.41 % (7953)Termination phase: shuffling
% 0.14/0.41
% 0.14/0.41 % (7953)Memory used [KB]: 1023
% 0.14/0.41 % (7953)Time elapsed: 0.004 s
% 0.14/0.41 % (7953)Instructions burned: 4 (million)
% 0.14/0.41 % (7953)------------------------------
% 0.14/0.41 % (7953)------------------------------
% 0.14/0.41 % (7955)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.41 % (7956)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.41 % (7952)Instruction limit reached!
% 0.14/0.41 % (7952)------------------------------
% 0.14/0.41 % (7952)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (7952)Termination reason: Unknown
% 0.14/0.41 % (7952)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (7952)Memory used [KB]: 1151
% 0.14/0.41 % (7952)Time elapsed: 0.009 s
% 0.14/0.41 % (7952)Instructions burned: 15 (million)
% 0.14/0.41 % (7952)------------------------------
% 0.14/0.41 % (7952)------------------------------
% 0.14/0.41 % (7955)Instruction limit reached!
% 0.14/0.41 % (7955)------------------------------
% 0.14/0.41 % (7955)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (7955)Termination reason: Unknown
% 0.14/0.41 % (7955)Termination phase: SInE selection
% 0.14/0.41
% 0.14/0.41 % (7955)Memory used [KB]: 1151
% 0.14/0.41 % (7955)Time elapsed: 0.006 s
% 0.14/0.41 % (7955)Instructions burned: 8 (million)
% 0.14/0.41 % (7955)------------------------------
% 0.14/0.41 % (7955)------------------------------
% 0.14/0.41 % (7943)First to succeed.
% 0.14/0.42 % (7956)Instruction limit reached!
% 0.14/0.42 % (7956)------------------------------
% 0.14/0.42 % (7956)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (7957)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)
% 0.14/0.42 % (7956)Termination reason: Unknown
% 0.14/0.42 % (7956)Termination phase: Saturation
% 0.14/0.42
% 0.14/0.42 % (7956)Memory used [KB]: 5628
% 0.14/0.42 % (7956)Time elapsed: 0.010 s
% 0.14/0.42 % (7956)Instructions burned: 16 (million)
% 0.14/0.42 % (7956)------------------------------
% 0.14/0.42 % (7956)------------------------------
% 0.14/0.42 % (7957)Instruction limit reached!
% 0.14/0.42 % (7957)------------------------------
% 0.14/0.42 % (7957)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (7957)Termination reason: Unknown
% 0.14/0.42 % (7957)Termination phase: shuffling
% 0.14/0.42
% 0.14/0.42 % (7957)Memory used [KB]: 1151
% 0.14/0.42 % (7957)Time elapsed: 0.004 s
% 0.14/0.42 % (7957)Instructions burned: 4 (million)
% 0.14/0.42 % (7957)------------------------------
% 0.14/0.42 % (7957)------------------------------
% 0.14/0.42 % (7943)Refutation found. Thanks to Tanya!
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% 0.14/0.42 thf(type_def_5, type, mu: $tType).
% 0.14/0.42 thf(type_def_7, type, reg: $tType).
% 0.14/0.42 thf(func_def_0, type, mu: $tType).
% 0.14/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_33, type, reg: $tType).
% 0.14/0.42 thf(func_def_34, type, c: reg > reg > $o).
% 0.14/0.42 thf(func_def_35, type, dc: reg > reg > $o).
% 0.14/0.42 thf(func_def_36, type, p: reg > reg > $o).
% 0.14/0.42 thf(func_def_37, type, eq: reg > reg > $o).
% 0.14/0.42 thf(func_def_38, type, o: reg > reg > $o).
% 0.14/0.42 thf(func_def_39, type, po: reg > reg > $o).
% 0.14/0.42 thf(func_def_40, type, ec: reg > reg > $o).
% 0.14/0.42 thf(func_def_41, type, pp: reg > reg > $o).
% 0.14/0.42 thf(func_def_42, type, tpp: reg > reg > $o).
% 0.14/0.42 thf(func_def_43, type, ntpp: reg > reg > $o).
% 0.14/0.42 thf(func_def_44, type, catalunya: reg).
% 0.14/0.42 thf(func_def_45, type, france: reg).
% 0.14/0.42 thf(func_def_46, type, spain: reg).
% 0.14/0.42 thf(func_def_47, type, paris: reg).
% 0.14/0.42 thf(func_def_48, type, a: $i > $i > $o).
% 0.14/0.42 thf(func_def_49, type, fool: $i > $i > $o).
% 0.14/0.42 thf(func_def_66, type, sK1: $i > ($i > $o) > $i).
% 0.14/0.42 thf(func_def_67, type, sK2: reg).
% 0.14/0.42 thf(func_def_68, type, sK3: reg).
% 0.14/0.42 thf(func_def_69, type, sK4: reg > reg).
% 0.14/0.42 thf(func_def_70, type, sK5: reg > reg).
% 0.14/0.42 thf(func_def_71, type, sK6: reg > reg).
% 0.14/0.42 thf(func_def_72, type, sK7: reg > reg).
% 0.14/0.42 thf(func_def_73, type, sK8: $i > ($i > $o) > $i).
% 0.14/0.42 thf(func_def_74, type, sK9: reg > reg).
% 0.14/0.42 thf(func_def_75, type, sK10: reg > reg).
% 0.14/0.42 thf(func_def_76, type, sK11: reg > reg).
% 0.14/0.42 thf(func_def_77, type, sK12: $i > ($i > $o) > $i).
% 0.14/0.42 thf(func_def_78, type, sK13: reg).
% 0.14/0.42 thf(func_def_79, type, sK14: reg > reg).
% 0.14/0.42 thf(func_def_80, type, sK15: reg > reg).
% 0.14/0.42 thf(func_def_81, type, sK16: reg > reg).
% 0.14/0.42 thf(f581,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(avatar_sat_refutation,[],[f437,f574,f580])).
% 0.14/0.42 thf(f580,plain,(
% 0.14/0.42 ~spl0_1),
% 0.14/0.42 inference(avatar_contradiction_clause,[],[f579])).
% 0.14/0.42 thf(f579,plain,(
% 0.14/0.42 $false | ~spl0_1),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f576])).
% 0.14/0.42 thf(f576,plain,(
% 0.14/0.42 ($false = $true) | ~spl0_1),
% 0.14/0.42 inference(superposition,[],[f416,f432])).
% 0.14/0.42 thf(f432,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X1 @ X2))) ) | ~spl0_1),
% 0.14/0.42 inference(avatar_component_clause,[],[f431])).
% 0.14/0.42 thf(f431,plain,(
% 0.14/0.42 spl0_1 <=> ! [X2,X1] : ($false = (a @ X1 @ X2))),
% 0.14/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.42 thf(f416,plain,(
% 0.14/0.42 ((a @ sK17 @ sK18) = $true)),
% 0.14/0.42 inference(not_proxy_clausification,[],[f415])).
% 0.14/0.42 thf(f415,plain,(
% 0.14/0.42 ($false = (~ (a @ sK17 @ sK18)))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f413])).
% 0.14/0.42 thf(f413,plain,(
% 0.14/0.42 ($false = ((~ (a @ sK17 @ sK18)) | (?? @ reg @ (^[Y0 : reg]: (?? @ reg @ (^[Y1 : reg]: (~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))))))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f412])).
% 0.14/0.42 thf(f412,plain,(
% 0.14/0.42 ($false = ((^[Y0 : $i]: ((~ (a @ sK17 @ Y0)) | (?? @ reg @ (^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (~ ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y1) => (c @ Y3 @ Y2)))))))))))) @ sK18))),
% 0.14/0.42 inference(sigma_clausification,[],[f411])).
% 0.14/0.42 thf(f411,plain,(
% 0.14/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK17 @ Y0)) | (?? @ reg @ (^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (~ ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y1) => (c @ Y3 @ Y2))))))))))))))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f410])).
% 0.14/0.42 thf(f410,plain,(
% 0.14/0.42 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (?? @ reg @ (^[Y2 : reg]: (?? @ reg @ (^[Y3 : reg]: (~ ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3)))))))))))))) @ sK17))),
% 0.14/0.42 inference(sigma_clausification,[],[f409])).
% 0.14/0.42 thf(f409,plain,(
% 0.14/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (?? @ reg @ (^[Y2 : reg]: (?? @ reg @ (^[Y3 : reg]: (~ ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))))))))))))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f218])).
% 0.14/0.42 thf(f218,plain,(
% 0.14/0.42 (((^[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]: (?? @ reg @ (^[Y2 : reg]: (~ ((^[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))))) @ Y2 @ Y1))))))))) != $true)),
% 0.14/0.42 inference(definition_unfolding,[],[f194,f173,f193,f206])).
% 0.14/0.42 thf(f206,plain,(
% 0.14/0.42 (eq = (^[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))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f170,f158,f158])).
% 0.14/0.42 thf(f158,plain,(
% 0.14/0.42 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f119])).
% 0.14/0.42 thf(f119,plain,(
% 0.14/0.42 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f118])).
% 0.14/0.42 thf(f118,plain,(
% 0.14/0.42 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))),
% 0.14/0.42 inference(rectify,[],[f35])).
% 0.14/0.42 thf(f35,axiom,(
% 0.14/0.42 (p = (^[X0 : reg, X1 : reg] : (! [X11 : reg] : ((c @ X11 @ X0) => (c @ X11 @ X1)))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',p)).
% 0.14/0.42 thf(f170,plain,(
% 0.14/0.42 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (p @ Y1 @ Y0))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f137])).
% 0.14/0.42 thf(f137,plain,(
% 0.14/0.42 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (p @ Y1 @ Y0))))))),
% 0.14/0.42 inference(fool_elimination,[],[f136])).
% 0.14/0.42 thf(f136,plain,(
% 0.14/0.42 (eq = (^[X0 : reg, X1 : reg] : ((p @ X1 @ X0) & (p @ X0 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f36])).
% 0.14/0.42 thf(f36,axiom,(
% 0.14/0.42 (eq = (^[X0 : reg, X1 : reg] : ((p @ X1 @ X0) & (p @ X0 @ X1))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eq)).
% 0.14/0.42 thf(f193,plain,(
% 0.14/0.42 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f66])).
% 0.14/0.42 thf(f66,plain,(
% 0.14/0.42 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f65])).
% 0.14/0.42 thf(f65,plain,(
% 0.14/0.42 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.14/0.42 inference(rectify,[],[f16])).
% 0.14/0.42 thf(f16,axiom,(
% 0.14/0.42 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.14/0.42 thf(f173,plain,(
% 0.14/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.42 inference(cnf_transformation,[],[f129])).
% 0.14/0.42 thf(f129,plain,(
% 0.14/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.42 inference(fool_elimination,[],[f128])).
% 0.14/0.42 thf(f128,plain,(
% 0.14/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f28])).
% 0.14/0.42 thf(f28,axiom,(
% 0.14/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.42 thf(f194,plain,(
% 0.14/0.42 ($true != (mvalid @ (mbox @ a @ (^[Y0 : $i]: (?? @ reg @ (^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (~ (eq @ Y2 @ Y1))))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f146])).
% 0.14/0.42 thf(f146,plain,(
% 0.14/0.42 ($true != (mvalid @ (mbox @ a @ (^[Y0 : $i]: (?? @ reg @ (^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (~ (eq @ Y2 @ Y1))))))))))),
% 0.14/0.42 inference(flattening,[],[f89])).
% 0.14/0.42 thf(f89,plain,(
% 0.14/0.42 ~($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (?? @ reg @ (^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (~ (eq @ Y2 @ Y1))))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f88])).
% 0.14/0.42 thf(f88,plain,(
% 0.14/0.42 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (? [X1 : reg,X2 : reg] : ~(eq @ X1 @ X2)))))),
% 0.14/0.42 inference(rectify,[],[f50])).
% 0.14/0.42 thf(f50,negated_conjecture,(
% 0.14/0.42 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (? [X11 : reg,X1 : reg] : ~(eq @ X11 @ X1)))))),
% 0.14/0.42 inference(negated_conjecture,[],[f49])).
% 0.14/0.42 thf(f49,conjecture,(
% 0.14/0.42 (mvalid @ (mbox @ a @ (^[X0 : $i] : (? [X11 : reg,X1 : reg] : ~(eq @ X11 @ X1)))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.14/0.42 thf(f574,plain,(
% 0.14/0.42 ~spl0_2),
% 0.14/0.42 inference(avatar_contradiction_clause,[],[f573])).
% 0.14/0.42 thf(f573,plain,(
% 0.14/0.42 $false | ~spl0_2),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f555])).
% 0.14/0.42 thf(f555,plain,(
% 0.14/0.42 ($false = $true) | ~spl0_2),
% 0.14/0.42 inference(superposition,[],[f552,f168])).
% 0.14/0.42 thf(f168,plain,(
% 0.14/0.42 ( ! [X0 : reg] : (((c @ X0 @ X0) = $true)) )),
% 0.14/0.42 inference(cnf_transformation,[],[f75])).
% 0.14/0.42 thf(f75,plain,(
% 0.14/0.42 ! [X0 : reg] : ((c @ X0 @ X0) = $true)),
% 0.14/0.42 inference(fool_elimination,[],[f74])).
% 0.14/0.42 thf(f74,plain,(
% 0.14/0.42 ! [X0 : reg] : (c @ X0 @ X0)),
% 0.14/0.42 inference(rectify,[],[f32])).
% 0.14/0.42 thf(f32,axiom,(
% 0.14/0.42 ! [X0 : reg] : (c @ X0 @ X0)),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_reflexive)).
% 0.14/0.42 thf(f552,plain,(
% 0.14/0.42 ( ! [X0 : reg] : (($false = (c @ sK13 @ X0))) ) | ~spl0_2),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f544])).
% 0.14/0.42 thf(f544,plain,(
% 0.14/0.42 ( ! [X0 : reg] : (($false = $true) | ($false = (c @ sK13 @ X0))) ) | ~spl0_2),
% 0.14/0.42 inference(superposition,[],[f436,f429])).
% 0.14/0.42 thf(f429,plain,(
% 0.14/0.42 ( ! [X2 : reg,X3 : reg,X1 : reg] : (((c @ X3 @ X2) = $true) | ((c @ X3 @ X1) = $false)) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f428])).
% 0.14/0.42 thf(f428,plain,(
% 0.14/0.42 ( ! [X2 : reg,X3 : reg,X1 : reg] : ((((c @ X3 @ X1) => (c @ X3 @ X2)) = $true)) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f427])).
% 0.14/0.42 thf(f427,plain,(
% 0.14/0.42 ( ! [X2 : reg,X3 : reg,X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ X2))) @ X3))) )),
% 0.14/0.42 inference(pi_clausification,[],[f422])).
% 0.14/0.42 thf(f422,plain,(
% 0.14/0.42 ( ! [X2 : reg,X1 : reg] : (($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ X2)))))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f421])).
% 0.14/0.42 thf(f421,plain,(
% 0.14/0.42 ( ! [X2 : reg,X1 : reg] : (($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X2) => (c @ Y0 @ X1)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ X2))))))) )),
% 0.14/0.42 inference(not_proxy_clausification,[],[f420])).
% 0.14/0.42 thf(f420,plain,(
% 0.14/0.42 ( ! [X2 : reg,X1 : reg] : (((~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X2) => (c @ Y0 @ X1)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ X2)))))) = $false)) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f419])).
% 0.14/0.42 thf(f419,plain,(
% 0.14/0.42 ( ! [X2 : reg,X1 : reg] : ((((^[Y0 : reg]: (~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ X1) => (c @ Y1 @ Y0))))))) @ X2) = $false)) )),
% 0.14/0.42 inference(pi_clausification,[],[f418])).
% 0.14/0.42 thf(f418,plain,(
% 0.14/0.42 ( ! [X1 : reg] : (($false = (?? @ reg @ (^[Y0 : reg]: (~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ X1) => (c @ Y1 @ Y0)))))))))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f417])).
% 0.14/0.42 thf(f417,plain,(
% 0.14/0.42 ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: (?? @ reg @ (^[Y1 : reg]: (~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))) @ X1))) )),
% 0.14/0.42 inference(pi_clausification,[],[f414])).
% 0.14/0.42 thf(f414,plain,(
% 0.14/0.42 ($false = (?? @ reg @ (^[Y0 : reg]: (?? @ reg @ (^[Y1 : reg]: (~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1)))))))))))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f413])).
% 0.14/0.42 thf(f436,plain,(
% 0.14/0.42 ($false = (c @ sK13 @ paris)) | ~spl0_2),
% 0.14/0.42 inference(avatar_component_clause,[],[f434])).
% 0.14/0.42 thf(f434,plain,(
% 0.14/0.42 spl0_2 <=> ($false = (c @ sK13 @ paris))),
% 0.14/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.42 thf(f437,plain,(
% 0.14/0.42 spl0_1 | spl0_2),
% 0.14/0.42 inference(avatar_split_clause,[],[f365,f434,f431])).
% 0.14/0.42 thf(f365,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (c @ sK13 @ paris)) | ($false = (a @ X1 @ X2))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f364])).
% 0.14/0.42 thf(f364,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X1 @ X2)) | ($false = ((c @ sK13 @ france) => (c @ sK13 @ paris)))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f363])).
% 0.14/0.42 thf(f363,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))) @ sK13)) | ($false = (a @ X1 @ X2))) )),
% 0.14/0.42 inference(sigma_clausification,[],[f362])).
% 0.14/0.42 thf(f362,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X1 @ X2)) | ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) )),
% 0.14/0.42 inference(not_proxy_clausification,[],[f361])).
% 0.14/0.42 thf(f361,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) | ($false = (a @ X1 @ X2))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f359])).
% 0.14/0.42 thf(f359,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))) | ($false = (a @ X1 @ X2))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f357])).
% 0.14/0.42 thf(f357,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X1 @ X2)) | ((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris))))))) = $true)) )),
% 0.14/0.42 inference(not_proxy_clausification,[],[f356])).
% 0.14/0.42 thf(f356,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (a @ X1 @ X2)) = $true) | ((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris))))))) = $true)) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f355])).
% 0.14/0.42 thf(f355,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (a @ X1 @ X2)) | (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))))))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f354])).
% 0.14/0.42 thf(f354,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris))))))))) @ X2))) )),
% 0.14/0.42 inference(pi_clausification,[],[f353])).
% 0.14/0.42 thf(f353,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris)))))))))))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f352])).
% 0.14/0.42 thf(f352,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris))))))))))) @ X1))) )),
% 0.14/0.42 inference(pi_clausification,[],[f351])).
% 0.14/0.42 thf(f351,plain,(
% 0.14/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france))))) & (~ (?? @ 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 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris)))))))))))) = $true)),
% 0.14/0.42 inference(beta_eta_normalization,[],[f217])).
% 0.14/0.42 thf(f217,plain,(
% 0.14/0.42 (((^[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]: (((^[Y3 : 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))))))) @ Y3 @ Y4))))) @ Y1 @ Y2) & (~ (?? @ 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))))))))) @ paris @ france)))) = $true)),
% 0.14/0.42 inference(definition_unfolding,[],[f183,f173,f193,f212])).
% 0.14/0.42 thf(f212,plain,(
% 0.14/0.42 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: ((~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)) & ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3))))) @ Y0 @ Y1) & (~ (?? @ 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))))))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f189,f210,f209,f209])).
% 0.14/0.42 thf(f209,plain,(
% 0.14/0.42 (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))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f157,f207])).
% 0.14/0.42 thf(f207,plain,(
% 0.14/0.42 (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))))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f163,f158,f158])).
% 0.14/0.42 thf(f163,plain,(
% 0.14/0.42 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f135])).
% 0.14/0.42 thf(f135,plain,(
% 0.14/0.42 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f134])).
% 0.14/0.42 thf(f134,plain,(
% 0.14/0.42 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X0) & (p @ X2 @ X1)))))),
% 0.14/0.42 inference(rectify,[],[f37])).
% 0.14/0.42 thf(f37,axiom,(
% 0.14/0.42 (o = (^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((p @ X11 @ X0) & (p @ X11 @ X1)))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',o)).
% 0.14/0.42 thf(f157,plain,(
% 0.14/0.42 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f105])).
% 0.14/0.42 thf(f105,plain,(
% 0.14/0.42 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))),
% 0.14/0.42 inference(fool_elimination,[],[f104])).
% 0.14/0.42 thf(f104,plain,(
% 0.14/0.42 ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)),
% 0.14/0.42 inference(rectify,[],[f39])).
% 0.14/0.42 thf(f39,axiom,(
% 0.14/0.42 ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ec)).
% 0.14/0.42 thf(f210,plain,(
% 0.14/0.42 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)) & ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f164,f158,f158])).
% 0.14/0.42 thf(f164,plain,(
% 0.14/0.42 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (p @ Y1 @ Y0)) & (p @ Y0 @ Y1))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f145])).
% 0.14/0.42 thf(f145,plain,(
% 0.14/0.42 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (p @ Y1 @ Y0)) & (p @ Y0 @ Y1))))))),
% 0.14/0.42 inference(fool_elimination,[],[f144])).
% 0.14/0.42 thf(f144,plain,(
% 0.14/0.42 ((^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & ~(p @ X1 @ X0))) = pp)),
% 0.14/0.42 inference(rectify,[],[f40])).
% 0.14/0.42 thf(f40,axiom,(
% 0.14/0.42 ((^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & ~(p @ X1 @ X0))) = pp)),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',pp)).
% 0.14/0.42 thf(f189,plain,(
% 0.14/0.42 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0))))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f91])).
% 0.14/0.42 thf(f91,plain,(
% 0.14/0.42 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0))))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f90])).
% 0.14/0.42 thf(f90,plain,(
% 0.14/0.42 (ntpp = (^[X0 : reg, X1 : reg] : (~? [X2 : reg] : ((ec @ X2 @ X0) & (ec @ X2 @ X1)) & (pp @ X0 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f42])).
% 0.14/0.42 thf(f42,axiom,(
% 0.14/0.42 (ntpp = (^[X0 : reg, X1 : reg] : (~? [X11 : reg] : ((ec @ X11 @ X0) & (ec @ X11 @ X1)) & (pp @ X0 @ X1))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ntpp)).
% 0.14/0.42 thf(f183,plain,(
% 0.14/0.42 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))))),
% 0.14/0.42 inference(cnf_transformation,[],[f109])).
% 0.14/0.42 thf(f109,plain,(
% 0.14/0.42 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))))),
% 0.14/0.42 inference(fool_elimination,[],[f108])).
% 0.14/0.42 thf(f108,plain,(
% 0.14/0.42 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))),
% 0.14/0.42 inference(rectify,[],[f48])).
% 0.14/0.42 thf(f48,axiom,(
% 0.14/0.42 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))),
% 0.14/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3)).
% 0.14/0.42 % SZS output end Proof for theBenchmark
% 0.14/0.42 % (7943)------------------------------
% 0.14/0.42 % (7943)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (7943)Termination reason: Refutation
% 0.14/0.42
% 0.14/0.42 % (7943)Memory used [KB]: 6140
% 0.14/0.42 % (7943)Time elapsed: 0.034 s
% 0.14/0.42 % (7943)Instructions burned: 46 (million)
% 0.14/0.42 % (7943)------------------------------
% 0.14/0.42 % (7943)------------------------------
% 0.14/0.42 % (7942)Success in time 0.055 s
% 0.14/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------