TSTP Solution File: LCL868^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL868^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:23:33 EDT 2024
% Result : Theorem 0.23s 0.43s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LCL868^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.13/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37 % Computer : n003.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 02:32:23 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TH0_THM_EQU_NAR problem
% 0.16/0.37 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/sandbox2/benchmark/theBenchmark.p
% 0.16/0.39 % (15955)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.39 % (15953)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)
% 0.16/0.39 % (15956)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)
% 0.16/0.39 % (15952)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.39 % (15957)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)
% 0.16/0.39 % (15958)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.39 % (15955)Instruction limit reached!
% 0.16/0.39 % (15955)------------------------------
% 0.16/0.39 % (15955)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (15955)Termination reason: Unknown
% 0.16/0.39 % (15955)Termination phase: shuffling
% 0.16/0.39
% 0.16/0.39 % (15955)Memory used [KB]: 1023
% 0.16/0.39 % (15955)Time elapsed: 0.003 s
% 0.16/0.39 % (15955)Instructions burned: 2 (million)
% 0.16/0.39 % (15955)------------------------------
% 0.16/0.39 % (15955)------------------------------
% 0.16/0.39 % (15953)Instruction limit reached!
% 0.16/0.39 % (15953)------------------------------
% 0.16/0.39 % (15953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (15953)Termination reason: Unknown
% 0.16/0.39 % (15953)Termination phase: Preprocessing 3
% 0.16/0.39
% 0.16/0.39 % (15953)Memory used [KB]: 1023
% 0.16/0.39 % (15953)Time elapsed: 0.005 s
% 0.16/0.39 % (15953)Instructions burned: 5 (million)
% 0.16/0.39 % (15953)------------------------------
% 0.16/0.39 % (15953)------------------------------
% 0.16/0.40 % (15956)Instruction limit reached!
% 0.16/0.40 % (15956)------------------------------
% 0.16/0.40 % (15956)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (15956)Termination reason: Unknown
% 0.16/0.40 % (15956)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (15956)Memory used [KB]: 1023
% 0.16/0.40 % (15956)Time elapsed: 0.004 s
% 0.16/0.40 % (15956)Instructions burned: 2 (million)
% 0.16/0.40 % (15956)------------------------------
% 0.16/0.40 % (15956)------------------------------
% 0.16/0.40 % (15959)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)
% 0.16/0.40 % (15959)Instruction limit reached!
% 0.16/0.40 % (15959)------------------------------
% 0.16/0.40 % (15959)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (15959)Termination reason: Unknown
% 0.16/0.40 % (15959)Termination phase: Property scanning
% 0.16/0.40
% 0.16/0.40 % (15959)Memory used [KB]: 1023
% 0.16/0.40 % (15959)Time elapsed: 0.004 s
% 0.16/0.40 % (15959)Instructions burned: 4 (million)
% 0.16/0.40 % (15959)------------------------------
% 0.16/0.40 % (15959)------------------------------
% 0.16/0.40 % (15954)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)
% 0.16/0.40 % (15958)Instruction limit reached!
% 0.16/0.40 % (15958)------------------------------
% 0.16/0.40 % (15958)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (15958)Termination reason: Unknown
% 0.16/0.40 % (15958)Termination phase: Saturation
% 0.16/0.40
% 0.16/0.40 % (15958)Memory used [KB]: 5756
% 0.16/0.40 % (15958)Time elapsed: 0.013 s
% 0.16/0.40 % (15958)Instructions burned: 18 (million)
% 0.16/0.40 % (15958)------------------------------
% 0.16/0.40 % (15958)------------------------------
% 0.16/0.41 % (15960)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)
% 0.16/0.41 % (15962)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)
% 0.16/0.41 % (15962)Instruction limit reached!
% 0.16/0.41 % (15962)------------------------------
% 0.16/0.41 % (15962)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (15962)Termination reason: Unknown
% 0.16/0.41 % (15962)Termination phase: shuffling
% 0.16/0.41
% 0.16/0.41 % (15962)Memory used [KB]: 1023
% 0.16/0.41 % (15962)Time elapsed: 0.003 s
% 0.16/0.41 % (15962)Instructions burned: 3 (million)
% 0.16/0.41 % (15962)------------------------------
% 0.16/0.41 % (15962)------------------------------
% 0.16/0.41 % (15961)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)
% 0.16/0.41 % (15963)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)
% 0.16/0.42 % (15964)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.42 % (15954)Instruction limit reached!
% 0.16/0.42 % (15954)------------------------------
% 0.16/0.42 % (15954)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (15954)Termination reason: Unknown
% 0.16/0.42 % (15954)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (15954)Memory used [KB]: 5756
% 0.16/0.42 % (15954)Time elapsed: 0.019 s
% 0.16/0.42 % (15954)Instructions burned: 28 (million)
% 0.16/0.42 % (15954)------------------------------
% 0.16/0.42 % (15954)------------------------------
% 0.16/0.42 % (15961)Instruction limit reached!
% 0.16/0.42 % (15961)------------------------------
% 0.16/0.42 % (15961)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (15961)Termination reason: Unknown
% 0.16/0.42 % (15961)Termination phase: Saturation
% 0.16/0.42
% 0.16/0.42 % (15961)Memory used [KB]: 5756
% 0.16/0.42 % (15961)Time elapsed: 0.033 s
% 0.16/0.42 % (15961)Instructions burned: 15 (million)
% 0.16/0.42 % (15961)------------------------------
% 0.16/0.42 % (15961)------------------------------
% 0.16/0.42 % (15964)Instruction limit reached!
% 0.16/0.42 % (15964)------------------------------
% 0.16/0.42 % (15964)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (15964)Termination reason: Unknown
% 0.16/0.42 % (15964)Termination phase: Function definition elimination
% 0.16/0.42
% 0.16/0.42 % (15964)Memory used [KB]: 1023
% 0.16/0.42 % (15964)Time elapsed: 0.006 s
% 0.16/0.42 % (15964)Instructions burned: 8 (million)
% 0.16/0.42 % (15964)------------------------------
% 0.16/0.42 % (15964)------------------------------
% 0.16/0.42 % (15965)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.42 % (15960)First to succeed.
% 0.23/0.43 % (15960)Refutation found. Thanks to Tanya!
% 0.23/0.43 % SZS status Theorem for theBenchmark
% 0.23/0.43 % SZS output start Proof for theBenchmark
% 0.23/0.43 thf(type_def_5, type, mu: $tType).
% 0.23/0.43 thf(func_def_0, type, mu: $tType).
% 0.23/0.43 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.23/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_15, type, mtrue: $i > $o).
% 0.23/0.43 thf(func_def_16, type, mfalse: $i > $o).
% 0.23/0.43 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.23/0.43 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_49, type, ph1: !>[X0: $tType]:(X0)).
% 0.23/0.43 thf(func_def_50, type, sK2: $i > $i > $o).
% 0.23/0.43 thf(f355,plain,(
% 0.23/0.43 $false),
% 0.23/0.43 inference(avatar_sat_refutation,[],[f178,f183,f192,f197,f200,f201,f210,f211,f212,f271,f279,f354])).
% 0.23/0.43 thf(f354,plain,(
% 0.23/0.43 ~spl0_3 | ~spl0_4 | ~spl0_7),
% 0.23/0.43 inference(avatar_contradiction_clause,[],[f353])).
% 0.23/0.43 thf(f353,plain,(
% 0.23/0.43 $false | (~spl0_3 | ~spl0_4 | ~spl0_7)),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f352])).
% 0.23/0.43 thf(f352,plain,(
% 0.23/0.43 ($false = $true) | (~spl0_3 | ~spl0_4 | ~spl0_7)),
% 0.23/0.43 inference(forward_demodulation,[],[f342,f209])).
% 0.23/0.43 thf(f209,plain,(
% 0.23/0.43 ($false = (sK2 @ sK8 @ sK3)) | ~spl0_7),
% 0.23/0.43 inference(avatar_component_clause,[],[f207])).
% 0.23/0.43 thf(f207,plain,(
% 0.23/0.43 spl0_7 <=> ($false = (sK2 @ sK8 @ sK3))),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.23/0.43 thf(f342,plain,(
% 0.23/0.43 ((sK2 @ sK8 @ sK3) = $true) | (~spl0_3 | ~spl0_4)),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f340])).
% 0.23/0.43 thf(f340,plain,(
% 0.23/0.43 ((sK2 @ sK8 @ sK3) = $true) | ($false = $true) | (~spl0_3 | ~spl0_4)),
% 0.23/0.43 inference(superposition,[],[f182,f317])).
% 0.23/0.43 thf(f317,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (sK2 @ sK6 @ X0)) | ((sK2 @ sK8 @ X0) = $true)) ) | ~spl0_3),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f315])).
% 0.23/0.43 thf(f315,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (sK2 @ sK6 @ X0)) | ($false = $true) | ((sK2 @ sK8 @ X0) = $true)) ) | ~spl0_3),
% 0.23/0.43 inference(superposition,[],[f222,f304])).
% 0.23/0.43 thf(f304,plain,(
% 0.23/0.43 ((sK2 @ sK6 @ sK8) = $true) | ~spl0_3),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f297])).
% 0.23/0.43 thf(f297,plain,(
% 0.23/0.43 ($false = $true) | ((sK2 @ sK6 @ sK8) = $true) | ~spl0_3),
% 0.23/0.43 inference(superposition,[],[f284,f224])).
% 0.23/0.43 thf(f224,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ X1 @ X1) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f223])).
% 0.23/0.43 thf(f223,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (sK2 @ Y0 @ Y0)) @ X1))) )),
% 0.23/0.43 inference(pi_clausification,[],[f213])).
% 0.23/0.43 thf(f213,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0))) = $true)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f143])).
% 0.23/0.43 thf(f143,plain,(
% 0.23/0.43 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0)))) = $true)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f141])).
% 0.23/0.43 thf(f141,plain,(
% 0.23/0.43 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0)))))))) & (!! @ $i @ (^[Y0 : $i]: (sK2 @ Y0 @ Y0)))) => (((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f140])).
% 0.23/0.43 thf(f140,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) => (((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))) @ sK2))),
% 0.23/0.43 inference(sigma_clausification,[],[f139])).
% 0.23/0.43 thf(f139,plain,(
% 0.23/0.43 ($false = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) => (((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1)))))))))))))),
% 0.23/0.43 inference(not_proxy_clausification,[],[f138])).
% 0.23/0.43 thf(f138,plain,(
% 0.23/0.43 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) => (((!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (Y0 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f137])).
% 0.23/0.43 thf(f137,plain,(
% 0.23/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2)))) @ Y0)) => ((((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y4 @ Y2)) => (Y1 @ Y3 @ Y2))))))))) @ Y0)) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y3 @ Y2) & (Y1 @ Y4 @ Y3)) => (Y1 @ Y4 @ Y2))))))))) @ Y0)))))) = $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f97,f113,f115,f109,f113,f125])).
% 0.23/0.43 thf(f125,plain,(
% 0.23/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f81])).
% 0.23/0.43 thf(f81,plain,(
% 0.23/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.23/0.43 inference(fool_elimination,[],[f80])).
% 0.23/0.43 thf(f80,plain,(
% 0.23/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))) = mtransitive)),
% 0.23/0.43 inference(rectify,[],[f21])).
% 0.23/0.43 thf(f21,axiom,(
% 0.23/0.43 ((^[X6 : $i > $i > $o] : (! [X8,X9,X10] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.23/0.43 thf(f109,plain,(
% 0.23/0.43 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f52])).
% 0.23/0.43 thf(f52,plain,(
% 0.23/0.43 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.23/0.43 inference(fool_elimination,[],[f51])).
% 0.23/0.43 thf(f51,plain,(
% 0.23/0.43 ((^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))) = mserial)),
% 0.23/0.43 inference(rectify,[],[f20])).
% 0.23/0.43 thf(f20,axiom,(
% 0.23/0.43 ((^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))) = mserial)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial)).
% 0.23/0.43 thf(f115,plain,(
% 0.23/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.23/0.43 inference(cnf_transformation,[],[f79])).
% 0.23/0.43 thf(f79,plain,(
% 0.23/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.23/0.43 inference(fool_elimination,[],[f78])).
% 0.23/0.43 thf(f78,plain,(
% 0.23/0.43 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.23/0.43 inference(rectify,[],[f18])).
% 0.23/0.43 thf(f18,axiom,(
% 0.23/0.43 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.23/0.43 thf(f113,plain,(
% 0.23/0.43 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f50])).
% 0.23/0.43 thf(f50,plain,(
% 0.23/0.43 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.23/0.43 inference(fool_elimination,[],[f49])).
% 0.23/0.43 thf(f49,plain,(
% 0.23/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X2 @ X3)))) = meuclidean)),
% 0.23/0.43 inference(rectify,[],[f22])).
% 0.23/0.43 thf(f22,axiom,(
% 0.23/0.43 ((^[X6 : $i > $i > $o] : (! [X8,X9,X10] : (((X6 @ X8 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X9 @ X10)))) = meuclidean)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean)).
% 0.23/0.43 thf(f97,plain,(
% 0.23/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((meuclidean @ Y0) & (mreflexive @ Y0)) => (((mserial @ Y0) & (meuclidean @ Y0)) & (mtransitive @ Y0)))))) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f42])).
% 0.23/0.43 thf(f42,plain,(
% 0.23/0.43 ((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((meuclidean @ Y0) & (mreflexive @ Y0)) => (((mserial @ Y0) & (meuclidean @ Y0)) & (mtransitive @ Y0)))))) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f41])).
% 0.23/0.43 thf(f41,plain,(
% 0.23/0.43 ~! [X0 : $i > $i > $o] : (((mreflexive @ X0) & (meuclidean @ X0)) => ((mtransitive @ X0) & (meuclidean @ X0) & (mserial @ X0)))),
% 0.23/0.43 inference(rectify,[],[f33])).
% 0.23/0.43 thf(f33,negated_conjecture,(
% 0.23/0.43 ~! [X6 : $i > $i > $o] : (((mreflexive @ X6) & (meuclidean @ X6)) => ((mtransitive @ X6) & (meuclidean @ X6) & (mserial @ X6)))),
% 0.23/0.43 inference(negated_conjecture,[],[f32])).
% 0.23/0.43 thf(f32,conjecture,(
% 0.23/0.43 ! [X6 : $i > $i > $o] : (((mreflexive @ X6) & (meuclidean @ X6)) => ((mtransitive @ X6) & (meuclidean @ X6) & (mserial @ X6)))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.23/0.43 thf(f284,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (sK2 @ sK8 @ X0)) | ((sK2 @ sK6 @ X0) = $true)) ) | ~spl0_3),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f281])).
% 0.23/0.43 thf(f281,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ($false = (sK2 @ sK8 @ X0)) | ((sK2 @ sK6 @ X0) = $true)) ) | ~spl0_3),
% 0.23/0.43 inference(superposition,[],[f177,f222])).
% 0.23/0.43 thf(f177,plain,(
% 0.23/0.43 ((sK2 @ sK8 @ sK6) = $true) | ~spl0_3),
% 0.23/0.43 inference(avatar_component_clause,[],[f175])).
% 0.23/0.43 thf(f175,plain,(
% 0.23/0.43 spl0_3 <=> ((sK2 @ sK8 @ sK6) = $true)),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.23/0.43 thf(f222,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (sK2 @ X3 @ X2)) | ((sK2 @ X3 @ X1) = $false) | ((sK2 @ X2 @ X1) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f221])).
% 0.23/0.43 thf(f221,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK2 @ X2 @ X1) = $true) | (((sK2 @ X3 @ X2) & (sK2 @ X3 @ X1)) = $false)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f220])).
% 0.23/0.43 thf(f220,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK2 @ X3 @ X2) & (sK2 @ X3 @ X1)) => (sK2 @ X2 @ X1)) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f219])).
% 0.23/0.43 thf(f219,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK2 @ Y0 @ X2) & (sK2 @ Y0 @ X1)) => (sK2 @ X2 @ X1))) @ X3) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f218])).
% 0.23/0.43 thf(f218,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ X2) & (sK2 @ Y0 @ X1)) => (sK2 @ X2 @ X1)))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f217])).
% 0.23/0.43 thf(f217,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ X1)) => (sK2 @ Y0 @ X1))))) @ X2) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f216])).
% 0.23/0.43 thf(f216,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ X1)) => (sK2 @ Y0 @ X1)))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f215])).
% 0.23/0.43 thf(f215,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f214])).
% 0.23/0.43 thf(f214,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0)))))))) = $true)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f143])).
% 0.23/0.43 thf(f182,plain,(
% 0.23/0.43 ((sK2 @ sK6 @ sK3) = $true) | ~spl0_4),
% 0.23/0.43 inference(avatar_component_clause,[],[f180])).
% 0.23/0.43 thf(f180,plain,(
% 0.23/0.43 spl0_4 <=> ((sK2 @ sK6 @ sK3) = $true)),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.23/0.43 thf(f279,plain,(
% 0.23/0.43 ~spl0_1),
% 0.23/0.43 inference(avatar_contradiction_clause,[],[f278])).
% 0.23/0.43 thf(f278,plain,(
% 0.23/0.43 $false | ~spl0_1),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f274])).
% 0.23/0.43 thf(f274,plain,(
% 0.23/0.43 ($false = $true) | ~spl0_1),
% 0.23/0.43 inference(superposition,[],[f224,f169])).
% 0.23/0.43 thf(f169,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK7 @ X1))) ) | ~spl0_1),
% 0.23/0.43 inference(avatar_component_clause,[],[f168])).
% 0.23/0.43 thf(f168,plain,(
% 0.23/0.43 spl0_1 <=> ! [X1] : ($false = (sK2 @ sK7 @ X1))),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.23/0.43 thf(f271,plain,(
% 0.23/0.43 ~spl0_2 | ~spl0_5 | ~spl0_6),
% 0.23/0.43 inference(avatar_contradiction_clause,[],[f270])).
% 0.23/0.43 thf(f270,plain,(
% 0.23/0.43 $false | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f269])).
% 0.23/0.43 thf(f269,plain,(
% 0.23/0.43 ($false = $true) | (~spl0_2 | ~spl0_5 | ~spl0_6)),
% 0.23/0.43 inference(forward_demodulation,[],[f263,f173])).
% 0.23/0.43 thf(f173,plain,(
% 0.23/0.43 ($false = (sK2 @ sK5 @ sK4)) | ~spl0_2),
% 0.23/0.43 inference(avatar_component_clause,[],[f171])).
% 0.23/0.43 thf(f171,plain,(
% 0.23/0.43 spl0_2 <=> ($false = (sK2 @ sK5 @ sK4))),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.23/0.43 thf(f263,plain,(
% 0.23/0.43 ($true = (sK2 @ sK5 @ sK4)) | (~spl0_5 | ~spl0_6)),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f251])).
% 0.23/0.43 thf(f251,plain,(
% 0.23/0.43 ($true = (sK2 @ sK5 @ sK4)) | ($false = $true) | (~spl0_5 | ~spl0_6)),
% 0.23/0.43 inference(superposition,[],[f246,f191])).
% 0.23/0.43 thf(f191,plain,(
% 0.23/0.43 ((sK2 @ sK9 @ sK4) = $true) | ~spl0_5),
% 0.23/0.43 inference(avatar_component_clause,[],[f189])).
% 0.23/0.43 thf(f189,plain,(
% 0.23/0.43 spl0_5 <=> ((sK2 @ sK9 @ sK4) = $true)),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.23/0.43 thf(f246,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (sK2 @ sK9 @ X0)) | ((sK2 @ sK5 @ X0) = $true)) ) | ~spl0_6),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f243])).
% 0.23/0.43 thf(f243,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ($false = (sK2 @ sK9 @ X0)) | ((sK2 @ sK5 @ X0) = $true)) ) | ~spl0_6),
% 0.23/0.43 inference(superposition,[],[f196,f222])).
% 0.23/0.43 thf(f196,plain,(
% 0.23/0.43 ((sK2 @ sK9 @ sK5) = $true) | ~spl0_6),
% 0.23/0.43 inference(avatar_component_clause,[],[f194])).
% 0.23/0.43 thf(f194,plain,(
% 0.23/0.43 spl0_6 <=> ((sK2 @ sK9 @ sK5) = $true)),
% 0.23/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.23/0.43 thf(f212,plain,(
% 0.23/0.43 spl0_1 | spl0_7 | spl0_2),
% 0.23/0.43 inference(avatar_split_clause,[],[f202,f171,f207,f168])).
% 0.23/0.43 thf(f202,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK7 @ X1)) | ($false = (sK2 @ sK5 @ sK4)) | ($false = (sK2 @ sK8 @ sK3))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f161])).
% 0.23/0.43 thf(f161,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) => (sK2 @ sK5 @ sK4)) = $false) | ($false = (sK2 @ sK8 @ sK3)) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f160])).
% 0.23/0.43 thf(f160,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (((sK2 @ sK6 @ sK3) & (sK2 @ sK8 @ sK6)) => (sK2 @ sK8 @ sK3))) | ($false = (sK2 @ sK7 @ X1)) | ((((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) => (sK2 @ sK5 @ sK4)) = $false)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f159])).
% 0.23/0.43 thf(f159,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK7 @ X1)) | ($false = ((^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4))) @ sK9)) | ($false = (((sK2 @ sK6 @ sK3) & (sK2 @ sK8 @ sK6)) => (sK2 @ sK8 @ sK3)))) )),
% 0.23/0.43 inference(sigma_clausification,[],[f158])).
% 0.23/0.43 thf(f158,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4))))) | ($false = (((sK2 @ sK6 @ sK3) & (sK2 @ sK8 @ sK6)) => (sK2 @ sK8 @ sK3))) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f157])).
% 0.23/0.43 thf(f157,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((sK2 @ sK6 @ sK3) & (sK2 @ Y0 @ sK6)) => (sK2 @ Y0 @ sK3))) @ sK8) = $false) | ($false = (sK2 @ sK7 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4)))))) )),
% 0.23/0.43 inference(sigma_clausification,[],[f156])).
% 0.23/0.43 thf(f156,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK6 @ sK3) & (sK2 @ Y0 @ sK6)) => (sK2 @ Y0 @ sK3))))) | ($false = (sK2 @ sK7 @ X1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4)))))) )),
% 0.23/0.43 inference(pi_clausification,[],[f155])).
% 0.23/0.43 thf(f155,plain,(
% 0.23/0.43 ((?? @ $i @ (sK2 @ sK7)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK6 @ sK3) & (sK2 @ Y0 @ sK6)) => (sK2 @ Y0 @ sK3)))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f154])).
% 0.23/0.43 thf(f154,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0))) @ sK7)) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK6 @ sK3) & (sK2 @ Y0 @ sK6)) => (sK2 @ Y0 @ sK3))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4)))))),
% 0.23/0.43 inference(sigma_clausification,[],[f153])).
% 0.23/0.43 thf(f153,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK6 @ sK3) & (sK2 @ Y0 @ sK6)) => (sK2 @ Y0 @ sK3)))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f152])).
% 0.23/0.43 thf(f152,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ sK3))))) @ sK6)) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4)))))),
% 0.23/0.43 inference(sigma_clausification,[],[f151])).
% 0.23/0.43 thf(f151,plain,(
% 0.23/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ sK3))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ Y0 @ sK5) & (sK2 @ Y0 @ sK4)) => (sK2 @ sK5 @ sK4))))) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f150])).
% 0.23/0.43 thf(f150,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ sK4)) => (sK2 @ Y0 @ sK4))))) @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ sK3)))))))),
% 0.23/0.43 inference(sigma_clausification,[],[f149])).
% 0.23/0.43 thf(f149,plain,(
% 0.23/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ sK4)) => (sK2 @ Y0 @ sK4))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ sK3))))))) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f148])).
% 0.23/0.43 thf(f148,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0))))))) @ sK4)) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ sK3)))))))),
% 0.23/0.43 inference(sigma_clausification,[],[f147])).
% 0.23/0.43 thf(f147,plain,(
% 0.23/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0))))))))) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y1 @ Y0)) => (sK2 @ Y1 @ sK3)))))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f146])).
% 0.23/0.43 thf(f146,plain,(
% 0.23/0.43 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))) @ sK3)) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0)))))))))),
% 0.23/0.43 inference(sigma_clausification,[],[f145])).
% 0.23/0.43 thf(f145,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0)))))))))),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f144])).
% 0.23/0.43 thf(f144,plain,(
% 0.23/0.43 ($false = ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0)))))))))) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0)))))))) = $false)),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f142])).
% 0.23/0.43 thf(f142,plain,(
% 0.23/0.43 ($false = (((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK2 @ Y0)))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y2 @ Y1) & (sK2 @ Y2 @ Y0)) => (sK2 @ Y1 @ Y0))))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y2 @ Y1)) => (sK2 @ Y2 @ Y0))))))))))),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f141])).
% 0.23/0.43 thf(f211,plain,(
% 0.23/0.43 spl0_5 | spl0_1 | spl0_7),
% 0.23/0.43 inference(avatar_split_clause,[],[f204,f207,f168,f189])).
% 0.23/0.43 thf(f204,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ sK9 @ sK4) = $true) | ($false = (sK2 @ sK8 @ sK3)) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f203])).
% 0.23/0.43 thf(f203,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK8 @ sK3)) | (((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) = $true) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f161])).
% 0.23/0.43 thf(f210,plain,(
% 0.23/0.43 spl0_6 | spl0_7 | spl0_1),
% 0.23/0.43 inference(avatar_split_clause,[],[f205,f168,f207,f194])).
% 0.23/0.43 thf(f205,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK8 @ sK3)) | ($false = (sK2 @ sK7 @ X1)) | ((sK2 @ sK9 @ sK5) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f203])).
% 0.23/0.43 thf(f201,plain,(
% 0.23/0.43 spl0_1 | spl0_5 | spl0_3),
% 0.23/0.43 inference(avatar_split_clause,[],[f198,f175,f189,f168])).
% 0.23/0.43 thf(f198,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ sK8 @ sK6) = $true) | ((sK2 @ sK9 @ sK4) = $true) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f184])).
% 0.23/0.43 thf(f184,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK7 @ X1)) | ((sK2 @ sK8 @ sK6) = $true) | (((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f164])).
% 0.23/0.43 thf(f164,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((sK2 @ sK6 @ sK3) & (sK2 @ sK8 @ sK6)) = $true) | (((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) = $true) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f162])).
% 0.23/0.43 thf(f162,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK7 @ X1)) | ((((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) => (sK2 @ sK5 @ sK4)) = $false) | (((sK2 @ sK6 @ sK3) & (sK2 @ sK8 @ sK6)) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f160])).
% 0.23/0.43 thf(f200,plain,(
% 0.23/0.43 spl0_1 | spl0_3 | spl0_6),
% 0.23/0.43 inference(avatar_split_clause,[],[f199,f194,f175,f168])).
% 0.23/0.43 thf(f199,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($false = (sK2 @ sK7 @ X1)) | ((sK2 @ sK8 @ sK6) = $true) | ((sK2 @ sK9 @ sK5) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f184])).
% 0.23/0.43 thf(f197,plain,(
% 0.23/0.43 spl0_4 | spl0_6 | spl0_1),
% 0.23/0.43 inference(avatar_split_clause,[],[f187,f168,f194,f180])).
% 0.23/0.43 thf(f187,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ sK6 @ sK3) = $true) | ($false = (sK2 @ sK7 @ X1)) | ((sK2 @ sK9 @ sK5) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f185])).
% 0.23/0.43 thf(f185,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((sK2 @ sK9 @ sK5) & (sK2 @ sK9 @ sK4)) = $true) | ($false = (sK2 @ sK7 @ X1)) | ((sK2 @ sK6 @ sK3) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f164])).
% 0.23/0.43 thf(f192,plain,(
% 0.23/0.43 spl0_5 | spl0_1 | spl0_4),
% 0.23/0.43 inference(avatar_split_clause,[],[f186,f180,f168,f189])).
% 0.23/0.43 thf(f186,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ sK9 @ sK4) = $true) | ((sK2 @ sK6 @ sK3) = $true) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f185])).
% 0.23/0.43 thf(f183,plain,(
% 0.23/0.43 spl0_2 | spl0_1 | spl0_4),
% 0.23/0.43 inference(avatar_split_clause,[],[f166,f180,f168,f171])).
% 0.23/0.43 thf(f166,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ sK6 @ sK3) = $true) | ($false = (sK2 @ sK5 @ sK4)) | ($false = (sK2 @ sK7 @ X1))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f163])).
% 0.23/0.43 thf(f163,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((sK2 @ sK6 @ sK3) & (sK2 @ sK8 @ sK6)) = $true) | ($false = (sK2 @ sK7 @ X1)) | ($false = (sK2 @ sK5 @ sK4))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f162])).
% 0.23/0.43 thf(f178,plain,(
% 0.23/0.43 spl0_1 | spl0_2 | spl0_3),
% 0.23/0.43 inference(avatar_split_clause,[],[f165,f175,f171,f168])).
% 0.23/0.43 thf(f165,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((sK2 @ sK8 @ sK6) = $true) | ($false = (sK2 @ sK7 @ X1)) | ($false = (sK2 @ sK5 @ sK4))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f163])).
% 0.23/0.43 % SZS output end Proof for theBenchmark
% 0.23/0.43 % (15960)------------------------------
% 0.23/0.43 % (15960)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (15960)Termination reason: Refutation
% 0.23/0.43
% 0.23/0.43 % (15960)Memory used [KB]: 5756
% 0.23/0.43 % (15960)Time elapsed: 0.024 s
% 0.23/0.43 % (15960)Instructions burned: 28 (million)
% 0.23/0.43 % (15960)------------------------------
% 0.23/0.43 % (15960)------------------------------
% 0.23/0.43 % (15951)Success in time 0.06 s
% 0.23/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------