TSTP Solution File: LCL865^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL865^1 : 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/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 : Tue May 21 00:23:32 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL865^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 02:23:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.14/0.38 % (15598)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (15600)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 % (15599)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 % (15602)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 % (15602)Instruction limit reached!
% 0.14/0.39 % (15602)------------------------------
% 0.14/0.39 % (15602)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (15602)Termination reason: Unknown
% 0.14/0.39 % (15602)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (15602)Memory used [KB]: 1023
% 0.14/0.39 % (15602)Time elapsed: 0.003 s
% 0.14/0.39 % (15602)Instructions burned: 2 (million)
% 0.14/0.39 % (15602)------------------------------
% 0.14/0.39 % (15602)------------------------------
% 0.14/0.39 % (15605)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 % (15603)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)
% 0.14/0.40 % (15605)Instruction limit reached!
% 0.14/0.40 % (15605)------------------------------
% 0.14/0.40 % (15605)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15605)Termination reason: Unknown
% 0.14/0.40 % (15605)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (15605)Memory used [KB]: 1023
% 0.14/0.40 % (15605)Time elapsed: 0.006 s
% 0.14/0.40 % (15605)Instructions burned: 4 (million)
% 0.14/0.40 % (15605)------------------------------
% 0.14/0.40 % (15605)------------------------------
% 0.14/0.40 % (15604)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.40 % (15599)Instruction limit reached!
% 0.14/0.40 % (15599)------------------------------
% 0.14/0.40 % (15599)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15599)Termination reason: Unknown
% 0.14/0.40 % (15599)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (15599)Memory used [KB]: 1023
% 0.14/0.40 % (15599)Time elapsed: 0.005 s
% 0.14/0.40 % (15599)Instructions burned: 4 (million)
% 0.14/0.40 % (15599)------------------------------
% 0.14/0.40 % (15599)------------------------------
% 0.14/0.40 % (15601)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.40 % (15601)Instruction limit reached!
% 0.14/0.40 % (15601)------------------------------
% 0.14/0.40 % (15601)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15601)Termination reason: Unknown
% 0.14/0.40 % (15601)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (15601)Memory used [KB]: 1023
% 0.14/0.40 % (15601)Time elapsed: 0.004 s
% 0.14/0.40 % (15601)Instructions burned: 2 (million)
% 0.14/0.40 % (15601)------------------------------
% 0.14/0.40 % (15601)------------------------------
% 0.14/0.40 % (15600)Instruction limit reached!
% 0.14/0.40 % (15600)------------------------------
% 0.14/0.40 % (15600)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (15600)Termination reason: Unknown
% 0.14/0.40 % (15600)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (15600)Memory used [KB]: 5756
% 0.14/0.40 % (15600)Time elapsed: 0.020 s
% 0.14/0.40 % (15600)Instructions burned: 28 (million)
% 0.14/0.40 % (15600)------------------------------
% 0.14/0.40 % (15600)------------------------------
% 0.14/0.41 % (15598)First to succeed.
% 0.14/0.41 % (15604)Instruction limit reached!
% 0.14/0.41 % (15604)------------------------------
% 0.14/0.41 % (15604)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (15604)Termination reason: Unknown
% 0.14/0.41 % (15604)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (15604)Memory used [KB]: 5756
% 0.14/0.41 % (15604)Time elapsed: 0.015 s
% 0.14/0.41 % (15604)Instructions burned: 18 (million)
% 0.14/0.41 % (15604)------------------------------
% 0.14/0.41 % (15604)------------------------------
% 0.14/0.41 % (15606)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)
% 0.14/0.41 % (15609)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)
% 0.14/0.41 % (15608)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 % (15598)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% 0.22/0.41 thf(type_def_5, type, mu: $tType).
% 0.22/0.41 thf(func_def_0, type, mu: $tType).
% 0.22/0.41 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.41 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.41 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.41 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.41 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.41 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.41 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.41 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.41 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.41 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.22/0.41 thf(func_def_50, type, sK2: $i > $i).
% 0.22/0.41 thf(func_def_62, type, sK14: $i > $i).
% 0.22/0.41 thf(f627,plain,(
% 0.22/0.41 $false),
% 0.22/0.41 inference(avatar_sat_refutation,[],[f257,f273,f278,f283,f295,f300,f305,f309,f343,f365,f386,f436,f459,f469,f555,f578,f613,f626])).
% 0.22/0.41 thf(f626,plain,(
% 0.22/0.41 ~spl1_1 | ~spl1_11),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f625])).
% 0.22/0.41 thf(f625,plain,(
% 0.22/0.41 $false | (~spl1_1 | ~spl1_11)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f617])).
% 0.22/0.41 thf(f617,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_1 | ~spl1_11)),
% 0.22/0.41 inference(superposition,[],[f294,f253])).
% 0.22/0.41 thf(f253,plain,(
% 0.22/0.41 ( ! [X3 : $i] : (($true = (sK0 @ X3 @ X3))) ) | ~spl1_1),
% 0.22/0.41 inference(avatar_component_clause,[],[f252])).
% 0.22/0.41 thf(f252,plain,(
% 0.22/0.41 spl1_1 <=> ! [X3] : ($true = (sK0 @ X3 @ X3))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.22/0.41 thf(f294,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK7 @ X1))) ) | ~spl1_11),
% 0.22/0.41 inference(avatar_component_clause,[],[f293])).
% 0.22/0.41 thf(f293,plain,(
% 0.22/0.41 spl1_11 <=> ! [X1] : ($false = (sK0 @ sK7 @ X1))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_11])])).
% 0.22/0.41 thf(f613,plain,(
% 0.22/0.41 ~spl1_1 | ~spl1_5 | ~spl1_10),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f612])).
% 0.22/0.41 thf(f612,plain,(
% 0.22/0.41 $false | (~spl1_1 | ~spl1_5 | ~spl1_10)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f604])).
% 0.22/0.41 thf(f604,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_1 | ~spl1_5 | ~spl1_10)),
% 0.22/0.41 inference(superposition,[],[f253,f601])).
% 0.22/0.41 thf(f601,plain,(
% 0.22/0.41 ((sK0 @ sK4 @ sK4) = $false) | (~spl1_5 | ~spl1_10)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f592])).
% 0.22/0.41 thf(f592,plain,(
% 0.22/0.41 ($true = $false) | ((sK0 @ sK4 @ sK4) = $false) | (~spl1_5 | ~spl1_10)),
% 0.22/0.41 inference(superposition,[],[f582,f291])).
% 0.22/0.41 thf(f291,plain,(
% 0.22/0.41 ($true = (sK0 @ sK4 @ sK5)) | ~spl1_10),
% 0.22/0.41 inference(avatar_component_clause,[],[f289])).
% 0.22/0.41 thf(f289,plain,(
% 0.22/0.41 spl1_10 <=> ($true = (sK0 @ sK4 @ sK5))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_10])])).
% 0.22/0.41 thf(f582,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK5)) | ($false = (sK0 @ X0 @ sK4))) ) | ~spl1_5),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f579])).
% 0.22/0.41 thf(f579,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK5)) | ($false = (sK0 @ X0 @ sK4)) | ($true = $false)) ) | ~spl1_5),
% 0.22/0.41 inference(superposition,[],[f268,f250])).
% 0.22/0.41 thf(f250,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X1 @ X3)) | ($false = (sK0 @ X2 @ X3)) | ($false = (sK0 @ X2 @ X1))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f249])).
% 0.22/0.41 thf(f249,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X1 @ X3)) | (((sK0 @ X2 @ X1) & (sK0 @ X2 @ X3)) = $false)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f248])).
% 0.22/0.41 thf(f248,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK0 @ X2 @ X1) & (sK0 @ X2 @ X3)) => (sK0 @ X1 @ X3)))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f247])).
% 0.22/0.41 thf(f247,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK0 @ X2 @ X1) & (sK0 @ X2 @ Y0)) => (sK0 @ X1 @ Y0))) @ X3) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f246])).
% 0.22/0.41 thf(f246,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ X2 @ X1) & (sK0 @ X2 @ Y0)) => (sK0 @ X1 @ Y0)))))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f245])).
% 0.22/0.41 thf(f245,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ X1) & (sK0 @ Y0 @ Y1)) => (sK0 @ X1 @ Y1))))) @ X2))) )),
% 0.22/0.41 inference(pi_clausification,[],[f244])).
% 0.22/0.41 thf(f244,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ X1) & (sK0 @ Y0 @ Y1)) => (sK0 @ X1 @ Y1)))))))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f243])).
% 0.22/0.41 thf(f243,plain,(
% 0.22/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))) @ X1) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f242])).
% 0.22/0.41 thf(f242,plain,(
% 0.22/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2)))))))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f241])).
% 0.22/0.41 thf(f241,plain,(
% 0.22/0.41 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ sK0))),
% 0.22/0.41 inference(duplicate_literal_removal,[],[f152])).
% 0.22/0.41 thf(f152,plain,(
% 0.22/0.41 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ sK0)) | ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ sK0))),
% 0.22/0.41 inference(definition_unfolding,[],[f107,f103,f103])).
% 0.22/0.41 thf(f103,plain,(
% 0.22/0.41 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f69])).
% 0.22/0.41 thf(f69,plain,(
% 0.22/0.41 (meuclidean = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f68])).
% 0.22/0.41 thf(f68,plain,(
% 0.22/0.41 (meuclidean = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X1) & (X0 @ X2 @ X3)) => (X0 @ X3 @ X1)))))),
% 0.22/0.41 inference(rectify,[],[f22])).
% 0.22/0.41 thf(f22,axiom,(
% 0.22/0.41 (meuclidean = (^[X6 : $i > $i > $o] : (! [X10,X8,X9] : (((X6 @ X8 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X9 @ X10)))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',meuclidean)).
% 0.22/0.41 thf(f107,plain,(
% 0.22/0.41 ((meuclidean @ sK0) = $true) | ((meuclidean @ sK0) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f99])).
% 0.22/0.41 thf(f99,plain,(
% 0.22/0.41 (((msymmetric @ sK0) != $true) | ($true != (mserial @ sK0)) | ((meuclidean @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ($true != (mreflexive @ sK0))) & ((((msymmetric @ sK0) = $true) & ($true = (mserial @ sK0)) & ((meuclidean @ sK0) = $true)) | (((meuclidean @ sK0) = $true) & ($true = (mreflexive @ sK0))))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f97,f98])).
% 0.22/0.41 thf(f98,plain,(
% 0.22/0.41 ? [X0 : $i > $i > $o] : ((($true != (msymmetric @ X0)) | ($true != (mserial @ X0)) | ((meuclidean @ X0) != $true) | ((meuclidean @ X0) != $true) | ($true != (mreflexive @ X0))) & ((($true = (msymmetric @ X0)) & ($true = (mserial @ X0)) & ((meuclidean @ X0) = $true)) | (((meuclidean @ X0) = $true) & ($true = (mreflexive @ X0))))) => ((((msymmetric @ sK0) != $true) | ($true != (mserial @ sK0)) | ((meuclidean @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ($true != (mreflexive @ sK0))) & ((((msymmetric @ sK0) = $true) & ($true = (mserial @ sK0)) & ((meuclidean @ sK0) = $true)) | (((meuclidean @ sK0) = $true) & ($true = (mreflexive @ sK0)))))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f97,plain,(
% 0.22/0.41 ? [X0 : $i > $i > $o] : ((($true != (msymmetric @ X0)) | ($true != (mserial @ X0)) | ((meuclidean @ X0) != $true) | ((meuclidean @ X0) != $true) | ($true != (mreflexive @ X0))) & ((($true = (msymmetric @ X0)) & ($true = (mserial @ X0)) & ((meuclidean @ X0) = $true)) | (((meuclidean @ X0) = $true) & ($true = (mreflexive @ X0)))))),
% 0.22/0.41 inference(flattening,[],[f96])).
% 0.22/0.41 thf(f96,plain,(
% 0.22/0.41 ? [X0 : $i > $i > $o] : (((($true != (msymmetric @ X0)) | ($true != (mserial @ X0)) | ((meuclidean @ X0) != $true)) | (((meuclidean @ X0) != $true) | ($true != (mreflexive @ X0)))) & ((($true = (msymmetric @ X0)) & ($true = (mserial @ X0)) & ((meuclidean @ X0) = $true)) | (((meuclidean @ X0) = $true) & ($true = (mreflexive @ X0)))))),
% 0.22/0.41 inference(nnf_transformation,[],[f95])).
% 0.22/0.41 thf(f95,plain,(
% 0.22/0.41 ? [X0 : $i > $i > $o] : ((((meuclidean @ X0) = $true) & ($true = (mreflexive @ X0))) <~> (($true = (msymmetric @ X0)) & ($true = (mserial @ X0)) & ((meuclidean @ X0) = $true)))),
% 0.22/0.41 inference(ennf_transformation,[],[f61])).
% 0.22/0.41 thf(f61,plain,(
% 0.22/0.41 ~! [X0 : $i > $i > $o] : ((((meuclidean @ X0) = $true) & ($true = (mreflexive @ X0))) <=> (($true = (msymmetric @ X0)) & ($true = (mserial @ X0)) & ((meuclidean @ X0) = $true)))),
% 0.22/0.41 inference(fool_elimination,[],[f60])).
% 0.22/0.41 thf(f60,plain,(
% 0.22/0.41 ~! [X0 : $i > $i > $o] : (((meuclidean @ X0) & (mreflexive @ X0)) <=> ((mserial @ X0) & (msymmetric @ X0) & (meuclidean @ X0)))),
% 0.22/0.41 inference(rectify,[],[f33])).
% 0.22/0.41 thf(f33,negated_conjecture,(
% 0.22/0.41 ~! [X6 : $i > $i > $o] : (((meuclidean @ X6) & (mreflexive @ X6)) <=> ((mserial @ X6) & (msymmetric @ X6) & (meuclidean @ X6)))),
% 0.22/0.41 inference(negated_conjecture,[],[f32])).
% 0.22/0.41 thf(f32,conjecture,(
% 0.22/0.41 ! [X6 : $i > $i > $o] : (((meuclidean @ X6) & (mreflexive @ X6)) <=> ((mserial @ X6) & (msymmetric @ X6) & (meuclidean @ X6)))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.22/0.41 thf(f268,plain,(
% 0.22/0.41 ($false = (sK0 @ sK5 @ sK4)) | ~spl1_5),
% 0.22/0.41 inference(avatar_component_clause,[],[f266])).
% 0.22/0.41 thf(f266,plain,(
% 0.22/0.41 spl1_5 <=> ($false = (sK0 @ sK5 @ sK4))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.22/0.41 thf(f578,plain,(
% 0.22/0.41 ~spl1_1 | ~spl1_3),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f577])).
% 0.22/0.41 thf(f577,plain,(
% 0.22/0.41 $false | (~spl1_1 | ~spl1_3)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f568])).
% 0.22/0.41 thf(f568,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 0.22/0.41 inference(superposition,[],[f253,f260])).
% 0.22/0.41 thf(f260,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK13 @ X1))) ) | ~spl1_3),
% 0.22/0.41 inference(avatar_component_clause,[],[f259])).
% 0.22/0.41 thf(f259,plain,(
% 0.22/0.41 spl1_3 <=> ! [X1] : ($false = (sK0 @ sK13 @ X1))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.22/0.41 thf(f555,plain,(
% 0.22/0.41 ~spl1_4 | ~spl1_7 | ~spl1_8),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f554])).
% 0.22/0.41 thf(f554,plain,(
% 0.22/0.41 $false | (~spl1_4 | ~spl1_7 | ~spl1_8)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f545])).
% 0.22/0.41 thf(f545,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_4 | ~spl1_7 | ~spl1_8)),
% 0.22/0.41 inference(superposition,[],[f277,f541])).
% 0.22/0.41 thf(f541,plain,(
% 0.22/0.41 ($false = (sK0 @ sK11 @ sK12)) | (~spl1_4 | ~spl1_8)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f532])).
% 0.22/0.41 thf(f532,plain,(
% 0.22/0.41 ($false = (sK0 @ sK11 @ sK12)) | ($true = $false) | (~spl1_4 | ~spl1_8)),
% 0.22/0.41 inference(superposition,[],[f473,f282])).
% 0.22/0.41 thf(f282,plain,(
% 0.22/0.41 ((sK0 @ sK11 @ sK10) = $true) | ~spl1_8),
% 0.22/0.41 inference(avatar_component_clause,[],[f280])).
% 0.22/0.41 thf(f280,plain,(
% 0.22/0.41 spl1_8 <=> ((sK0 @ sK11 @ sK10) = $true)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 0.22/0.41 thf(f473,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK10)) | ((sK0 @ X0 @ sK12) = $false)) ) | ~spl1_4),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f471])).
% 0.22/0.41 thf(f471,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true = $false) | ((sK0 @ X0 @ sK12) = $false) | ($false = (sK0 @ X0 @ sK10))) ) | ~spl1_4),
% 0.22/0.41 inference(superposition,[],[f250,f264])).
% 0.22/0.41 thf(f264,plain,(
% 0.22/0.41 ($false = (sK0 @ sK10 @ sK12)) | ~spl1_4),
% 0.22/0.41 inference(avatar_component_clause,[],[f262])).
% 0.22/0.41 thf(f262,plain,(
% 0.22/0.41 spl1_4 <=> ($false = (sK0 @ sK10 @ sK12))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.22/0.41 thf(f277,plain,(
% 0.22/0.41 ($true = (sK0 @ sK11 @ sK12)) | ~spl1_7),
% 0.22/0.41 inference(avatar_component_clause,[],[f275])).
% 0.22/0.41 thf(f275,plain,(
% 0.22/0.41 spl1_7 <=> ($true = (sK0 @ sK11 @ sK12))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.22/0.41 thf(f469,plain,(
% 0.22/0.41 ~spl1_3 | ~spl1_14),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f468])).
% 0.22/0.41 thf(f468,plain,(
% 0.22/0.41 $false | (~spl1_3 | ~spl1_14)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f461])).
% 0.22/0.41 thf(f461,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_3 | ~spl1_14)),
% 0.22/0.41 inference(superposition,[],[f260,f308])).
% 0.22/0.41 thf(f308,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = (sK0 @ X1 @ (sK2 @ X1)))) ) | ~spl1_14),
% 0.22/0.41 inference(avatar_component_clause,[],[f307])).
% 0.22/0.41 thf(f307,plain,(
% 0.22/0.41 spl1_14 <=> ! [X1] : ($true = (sK0 @ X1 @ (sK2 @ X1)))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_14])])).
% 0.22/0.41 thf(f459,plain,(
% 0.22/0.41 ~spl1_1 | ~spl1_6),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f458])).
% 0.22/0.41 thf(f458,plain,(
% 0.22/0.41 $false | (~spl1_1 | ~spl1_6)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f450])).
% 0.22/0.41 thf(f450,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_1 | ~spl1_6)),
% 0.22/0.41 inference(superposition,[],[f253,f272])).
% 0.22/0.41 thf(f272,plain,(
% 0.22/0.41 ($false = (sK0 @ sK3 @ sK3)) | ~spl1_6),
% 0.22/0.41 inference(avatar_component_clause,[],[f270])).
% 0.22/0.41 thf(f270,plain,(
% 0.22/0.41 spl1_6 <=> ($false = (sK0 @ sK3 @ sK3))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.22/0.41 thf(f436,plain,(
% 0.22/0.41 ~spl1_9 | ~spl1_12 | ~spl1_13),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f435])).
% 0.22/0.41 thf(f435,plain,(
% 0.22/0.41 $false | (~spl1_9 | ~spl1_12 | ~spl1_13)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f426])).
% 0.22/0.41 thf(f426,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_9 | ~spl1_12 | ~spl1_13)),
% 0.22/0.41 inference(superposition,[],[f424,f304])).
% 0.22/0.41 thf(f304,plain,(
% 0.22/0.41 ($true = (sK0 @ sK8 @ sK6)) | ~spl1_13),
% 0.22/0.41 inference(avatar_component_clause,[],[f302])).
% 0.22/0.41 thf(f302,plain,(
% 0.22/0.41 spl1_13 <=> ($true = (sK0 @ sK8 @ sK6))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_13])])).
% 0.22/0.41 thf(f424,plain,(
% 0.22/0.41 ($false = (sK0 @ sK8 @ sK6)) | (~spl1_9 | ~spl1_12)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f417])).
% 0.22/0.41 thf(f417,plain,(
% 0.22/0.41 ($false = (sK0 @ sK8 @ sK6)) | ($true = $false) | (~spl1_9 | ~spl1_12)),
% 0.22/0.41 inference(superposition,[],[f299,f396])).
% 0.22/0.41 thf(f396,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK9)) | ((sK0 @ X0 @ sK6) = $false)) ) | ~spl1_9),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f389])).
% 0.22/0.41 thf(f389,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK9)) | ($true = $false) | ((sK0 @ X0 @ sK6) = $false)) ) | ~spl1_9),
% 0.22/0.41 inference(superposition,[],[f287,f250])).
% 0.22/0.41 thf(f287,plain,(
% 0.22/0.41 ($false = (sK0 @ sK6 @ sK9)) | ~spl1_9),
% 0.22/0.41 inference(avatar_component_clause,[],[f285])).
% 0.22/0.41 thf(f285,plain,(
% 0.22/0.41 spl1_9 <=> ($false = (sK0 @ sK6 @ sK9))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_9])])).
% 0.22/0.41 thf(f299,plain,(
% 0.22/0.41 ($true = (sK0 @ sK8 @ sK9)) | ~spl1_12),
% 0.22/0.41 inference(avatar_component_clause,[],[f297])).
% 0.22/0.41 thf(f297,plain,(
% 0.22/0.41 spl1_12 <=> ($true = (sK0 @ sK8 @ sK9))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_12])])).
% 0.22/0.41 thf(f386,plain,(
% 0.22/0.41 ~spl1_11 | ~spl1_14),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f385])).
% 0.22/0.41 thf(f385,plain,(
% 0.22/0.41 $false | (~spl1_11 | ~spl1_14)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f375])).
% 0.22/0.41 thf(f375,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_11 | ~spl1_14)),
% 0.22/0.41 inference(superposition,[],[f294,f308])).
% 0.22/0.41 thf(f365,plain,(
% 0.22/0.41 ~spl1_2 | ~spl1_5 | ~spl1_10),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f364])).
% 0.22/0.41 thf(f364,plain,(
% 0.22/0.41 $false | (~spl1_2 | ~spl1_5 | ~spl1_10)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f356])).
% 0.22/0.41 thf(f356,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_2 | ~spl1_5 | ~spl1_10)),
% 0.22/0.41 inference(superposition,[],[f350,f291])).
% 0.22/0.41 thf(f350,plain,(
% 0.22/0.41 ($false = (sK0 @ sK4 @ sK5)) | (~spl1_2 | ~spl1_5)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f346])).
% 0.22/0.41 thf(f346,plain,(
% 0.22/0.41 ($true = $false) | ($false = (sK0 @ sK4 @ sK5)) | (~spl1_2 | ~spl1_5)),
% 0.22/0.41 inference(superposition,[],[f268,f256])).
% 0.22/0.41 thf(f256,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (sK0 @ X2 @ X1)) | ($false = (sK0 @ X1 @ X2))) ) | ~spl1_2),
% 0.22/0.41 inference(avatar_component_clause,[],[f255])).
% 0.22/0.41 thf(f255,plain,(
% 0.22/0.41 spl1_2 <=> ! [X2,X1] : (($false = (sK0 @ X1 @ X2)) | ($true = (sK0 @ X2 @ X1)))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.22/0.41 thf(f343,plain,(
% 0.22/0.41 ~spl1_2 | ~spl1_6 | ~spl1_14),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f342])).
% 0.22/0.41 thf(f342,plain,(
% 0.22/0.41 $false | (~spl1_2 | ~spl1_6 | ~spl1_14)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f336])).
% 0.22/0.41 thf(f336,plain,(
% 0.22/0.41 ($true = $false) | (~spl1_2 | ~spl1_6 | ~spl1_14)),
% 0.22/0.41 inference(superposition,[],[f308,f329])).
% 0.22/0.41 thf(f329,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ sK3 @ X0))) ) | (~spl1_2 | ~spl1_6)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f324])).
% 0.22/0.41 thf(f324,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ sK3 @ X0)) | ($true = $false)) ) | (~spl1_2 | ~spl1_6)),
% 0.22/0.41 inference(superposition,[],[f322,f256])).
% 0.22/0.41 thf(f322,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK3))) ) | ~spl1_6),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f321])).
% 0.22/0.41 thf(f321,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK3)) | ($true = $false)) ) | ~spl1_6),
% 0.22/0.41 inference(duplicate_literal_removal,[],[f315])).
% 0.22/0.41 thf(f315,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($false = (sK0 @ X0 @ sK3)) | ($true = $false) | ($false = (sK0 @ X0 @ sK3))) ) | ~spl1_6),
% 0.22/0.41 inference(superposition,[],[f272,f250])).
% 0.22/0.41 thf(f309,plain,(
% 0.22/0.41 spl1_1 | spl1_14),
% 0.22/0.41 inference(avatar_split_clause,[],[f159,f307,f252])).
% 0.22/0.41 thf(f159,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (sK0 @ X1 @ (sK2 @ X1))) | ((sK0 @ X2 @ X2) = $true)) )),
% 0.22/0.41 inference(sigma_clausification,[],[f158])).
% 0.22/0.41 thf(f158,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (?? @ $i @ (sK0 @ X1))) | ((sK0 @ X2 @ X2) = $true)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f157])).
% 0.22/0.41 thf(f157,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (?? @ $i @ (sK0 @ X1))) | ($true = ((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ X2))) )),
% 0.22/0.41 inference(pi_clausification,[],[f156])).
% 0.22/0.41 thf(f156,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true) | ($true = (?? @ $i @ (sK0 @ X1)))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f155])).
% 0.22/0.41 thf(f155,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f154])).
% 0.22/0.41 thf(f154,plain,(
% 0.22/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true)),
% 0.22/0.41 inference(beta_eta_normalization,[],[f151])).
% 0.22/0.41 thf(f151,plain,(
% 0.22/0.41 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) = $true) | ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0))),
% 0.22/0.41 inference(definition_unfolding,[],[f108,f132,f131])).
% 0.22/0.41 thf(f131,plain,(
% 0.22/0.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.22/0.41 inference(cnf_transformation,[],[f88])).
% 0.22/0.41 thf(f88,plain,(
% 0.22/0.41 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.22/0.41 inference(fool_elimination,[],[f87])).
% 0.22/0.41 thf(f87,plain,(
% 0.22/0.41 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.22/0.41 inference(rectify,[],[f18])).
% 0.22/0.41 thf(f18,axiom,(
% 0.22/0.41 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.22/0.41 thf(f132,plain,(
% 0.22/0.41 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f42])).
% 0.22/0.41 thf(f42,plain,(
% 0.22/0.41 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.22/0.41 inference(fool_elimination,[],[f41])).
% 0.22/0.41 thf(f41,plain,(
% 0.22/0.41 (mserial = (^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))))),
% 0.22/0.41 inference(rectify,[],[f20])).
% 0.22/0.41 thf(f20,axiom,(
% 0.22/0.41 (mserial = (^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mserial)).
% 0.22/0.41 thf(f108,plain,(
% 0.22/0.41 ($true = (mserial @ sK0)) | ($true = (mreflexive @ sK0))),
% 0.22/0.41 inference(cnf_transformation,[],[f99])).
% 0.22/0.41 thf(f305,plain,(
% 0.22/0.41 spl1_13 | spl1_6 | spl1_10 | spl1_11),
% 0.22/0.41 inference(avatar_split_clause,[],[f182,f293,f289,f270,f302])).
% 0.22/0.41 thf(f182,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK7 @ X1)) | ($false = (sK0 @ sK3 @ sK3)) | ($true = (sK0 @ sK8 @ sK6)) | ($true = (sK0 @ sK4 @ sK5))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f180])).
% 0.22/0.41 thf(f180,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = (sK0 @ sK4 @ sK5)) | (((sK0 @ sK8 @ sK6) & (sK0 @ sK8 @ sK9)) = $true) | ($false = (sK0 @ sK7 @ X1)) | ($false = (sK0 @ sK3 @ sK3))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f178])).
% 0.22/0.41 thf(f178,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = (sK0 @ sK4 @ sK5)) | ($false = (sK0 @ sK7 @ X1)) | ($false = (sK0 @ sK3 @ sK3)) | ((((sK0 @ sK8 @ sK6) & (sK0 @ sK8 @ sK9)) => (sK0 @ sK6 @ sK9)) = $false)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f177])).
% 0.22/0.41 thf(f177,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK3 @ sK3)) | ($false = ((^[Y0 : $i]: (((sK0 @ sK8 @ sK6) & (sK0 @ sK8 @ Y0)) => (sK0 @ sK6 @ Y0))) @ sK9)) | ($false = (sK0 @ sK7 @ X1)) | ($true = (sK0 @ sK4 @ sK5))) )),
% 0.22/0.41 inference(sigma_clausification,[],[f176])).
% 0.22/0.41 thf(f176,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK8 @ sK6) & (sK0 @ sK8 @ Y0)) => (sK0 @ sK6 @ Y0))))) | ($true = (sK0 @ sK4 @ sK5)) | ($false = (sK0 @ sK7 @ X1)) | ($false = (sK0 @ sK3 @ sK3))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f175])).
% 0.22/0.41 thf(f175,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK7 @ X1)) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK6) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK6 @ Y1))))) @ sK8)) | ($false = (sK0 @ sK3 @ sK3)) | ($true = (sK0 @ sK4 @ sK5))) )),
% 0.22/0.41 inference(sigma_clausification,[],[f174])).
% 0.22/0.41 thf(f174,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK7 @ X1)) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK6) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK6 @ Y1))))))) | ($true = (sK0 @ sK4 @ sK5))) )),
% 0.22/0.41 inference(pi_clausification,[],[f173])).
% 0.22/0.41 thf(f173,plain,(
% 0.22/0.41 ($false = (?? @ $i @ (sK0 @ sK7))) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK6) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK6 @ Y1))))))) | ($true = (sK0 @ sK4 @ sK5))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f172])).
% 0.22/0.41 thf(f172,plain,(
% 0.22/0.41 ($false = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ sK7)) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK6) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK6 @ Y1))))))) | ($true = (sK0 @ sK4 @ sK5))),
% 0.22/0.41 inference(sigma_clausification,[],[f171])).
% 0.22/0.41 thf(f171,plain,(
% 0.22/0.41 ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($true = (sK0 @ sK4 @ sK5)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK6) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK6 @ Y1)))))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f170])).
% 0.22/0.41 thf(f170,plain,(
% 0.22/0.41 ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))) @ sK6) = $false) | ($true = (sK0 @ sK4 @ sK5))),
% 0.22/0.41 inference(sigma_clausification,[],[f169])).
% 0.22/0.41 thf(f169,plain,(
% 0.22/0.41 ($true = (sK0 @ sK4 @ sK5)) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f167])).
% 0.22/0.41 thf(f167,plain,(
% 0.22/0.41 ($false = (sK0 @ sK3 @ sK3)) | ($false = ((sK0 @ sK4 @ sK5) => (sK0 @ sK5 @ sK4))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2)))))))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f166])).
% 0.22/0.41 thf(f166,plain,(
% 0.22/0.41 ($false = ((^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK0 @ Y0 @ sK4))) @ sK5)) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(sigma_clausification,[],[f165])).
% 0.22/0.41 thf(f165,plain,(
% 0.22/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK4 @ Y0) => (sK0 @ Y0 @ sK4))))) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f164])).
% 0.22/0.41 thf(f164,plain,(
% 0.22/0.41 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))) @ sK4)) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(sigma_clausification,[],[f163])).
% 0.22/0.41 thf(f163,plain,(
% 0.22/0.41 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($false = (sK0 @ sK3 @ sK3))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f162])).
% 0.22/0.41 thf(f162,plain,(
% 0.22/0.41 ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))))) | ($false = ((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2)))))))))),
% 0.22/0.41 inference(sigma_clausification,[],[f161])).
% 0.22/0.41 thf(f161,plain,(
% 0.22/0.41 ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) != $true) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0)))))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f160])).
% 0.22/0.41 thf(f160,plain,(
% 0.22/0.41 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) != $true) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ sK0)) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ sK0)) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0))),
% 0.22/0.41 inference(duplicate_literal_removal,[],[f147])).
% 0.22/0.41 thf(f147,plain,(
% 0.22/0.41 ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ sK0)) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) != $true) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0)) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ sK0)) | ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ sK0))),
% 0.22/0.41 inference(definition_unfolding,[],[f112,f120,f132,f103,f103,f131])).
% 0.22/0.41 thf(f120,plain,(
% 0.22/0.41 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.41 inference(cnf_transformation,[],[f53])).
% 0.22/0.41 thf(f53,plain,(
% 0.22/0.41 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f52])).
% 0.22/0.41 thf(f52,plain,(
% 0.22/0.41 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))) = msymmetric)),
% 0.22/0.41 inference(rectify,[],[f19])).
% 0.22/0.41 thf(f19,axiom,(
% 0.22/0.41 ((^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.22/0.41 thf(f112,plain,(
% 0.22/0.41 ((msymmetric @ sK0) != $true) | ($true != (mserial @ sK0)) | ((meuclidean @ sK0) != $true) | ((meuclidean @ sK0) != $true) | ($true != (mreflexive @ sK0))),
% 0.22/0.41 inference(cnf_transformation,[],[f99])).
% 0.22/0.41 thf(f300,plain,(
% 0.22/0.41 spl1_12 | spl1_10 | spl1_11 | spl1_6),
% 0.22/0.41 inference(avatar_split_clause,[],[f181,f270,f293,f289,f297])).
% 0.22/0.41 thf(f181,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK7 @ X1)) | ($true = (sK0 @ sK8 @ sK9)) | ($true = (sK0 @ sK4 @ sK5)) | ($false = (sK0 @ sK3 @ sK3))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f180])).
% 0.22/0.41 thf(f295,plain,(
% 0.22/0.41 spl1_9 | spl1_10 | spl1_6 | spl1_11),
% 0.22/0.41 inference(avatar_split_clause,[],[f179,f293,f270,f289,f285])).
% 0.22/0.41 thf(f179,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK7 @ X1)) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (sK0 @ sK6 @ sK9)) | ($true = (sK0 @ sK4 @ sK5))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f178])).
% 0.22/0.41 thf(f283,plain,(
% 0.22/0.41 spl1_5 | spl1_3 | spl1_8 | spl1_6),
% 0.22/0.41 inference(avatar_split_clause,[],[f195,f270,f280,f259,f266])).
% 0.22/0.41 thf(f195,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK13 @ X1)) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (sK0 @ sK5 @ sK4)) | ((sK0 @ sK11 @ sK10) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f193])).
% 0.22/0.41 thf(f193,plain,(
% 0.22/0.41 ( ! [X1 : $i] : ((((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ sK12)) = $true) | ($false = (sK0 @ sK13 @ X1)) | ($false = (sK0 @ sK5 @ sK4)) | ($false = (sK0 @ sK3 @ sK3))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f191])).
% 0.22/0.41 thf(f191,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK13 @ X1)) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ sK12)) => (sK0 @ sK10 @ sK12))) | ($false = (sK0 @ sK5 @ sK4))) )),
% 0.22/0.41 inference(pi_clausification,[],[f190])).
% 0.22/0.41 thf(f190,plain,(
% 0.22/0.41 ($false = (sK0 @ sK5 @ sK4)) | ($false = (?? @ $i @ (sK0 @ sK13))) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ sK12)) => (sK0 @ sK10 @ sK12)))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f189])).
% 0.22/0.41 thf(f189,plain,(
% 0.22/0.41 ($false = (sK0 @ sK3 @ sK3)) | ($false = (sK0 @ sK5 @ sK4)) | ($false = (((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ sK12)) => (sK0 @ sK10 @ sK12))) | ($false = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ sK13))),
% 0.22/0.41 inference(sigma_clausification,[],[f188])).
% 0.22/0.41 thf(f188,plain,(
% 0.22/0.41 ($false = (sK0 @ sK5 @ sK4)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($false = (sK0 @ sK3 @ sK3)) | ($false = (((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ sK12)) => (sK0 @ sK10 @ sK12)))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f187])).
% 0.22/0.41 thf(f187,plain,(
% 0.22/0.41 ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($false = (sK0 @ sK5 @ sK4)) | ($false = (sK0 @ sK3 @ sK3)) | ($false = ((^[Y0 : $i]: (((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ Y0)) => (sK0 @ sK10 @ Y0))) @ sK12))),
% 0.22/0.41 inference(sigma_clausification,[],[f186])).
% 0.22/0.41 thf(f186,plain,(
% 0.22/0.41 ($false = (sK0 @ sK3 @ sK3)) | ($false = (sK0 @ sK5 @ sK4)) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK11 @ sK10) & (sK0 @ sK11 @ Y0)) => (sK0 @ sK10 @ Y0))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f185])).
% 0.22/0.41 thf(f185,plain,(
% 0.22/0.41 ($false = (sK0 @ sK5 @ sK4)) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK10) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK10 @ Y1))))) @ sK11)) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(sigma_clausification,[],[f184])).
% 0.22/0.41 thf(f184,plain,(
% 0.22/0.41 ($false = (sK0 @ sK5 @ sK4)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ sK10) & (sK0 @ Y0 @ Y1)) => (sK0 @ sK10 @ Y1)))))) = $false) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))))),
% 0.22/0.41 inference(beta_eta_normalization,[],[f183])).
% 0.22/0.41 thf(f183,plain,(
% 0.22/0.41 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))) @ sK10)) | ($false = (sK0 @ sK3 @ sK3)) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($false = (sK0 @ sK5 @ sK4))),
% 0.22/0.41 inference(sigma_clausification,[],[f168])).
% 0.22/0.41 thf(f168,plain,(
% 0.22/0.41 ($false = (sK0 @ sK5 @ sK4)) | ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ Y1 @ Y2)) => (sK0 @ Y0 @ Y2))))))))) | ($true != (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))))) | ($false = (sK0 @ sK3 @ sK3))),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f167])).
% 0.22/0.41 thf(f278,plain,(
% 0.22/0.41 spl1_7 | spl1_3 | spl1_6 | spl1_5),
% 0.22/0.41 inference(avatar_split_clause,[],[f194,f266,f270,f259,f275])).
% 0.22/0.41 thf(f194,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK3 @ sK3)) | ($false = (sK0 @ sK5 @ sK4)) | ($false = (sK0 @ sK13 @ X1)) | ($true = (sK0 @ sK11 @ sK12))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f193])).
% 0.22/0.41 thf(f273,plain,(
% 0.22/0.41 spl1_3 | spl1_4 | spl1_5 | spl1_6),
% 0.22/0.41 inference(avatar_split_clause,[],[f192,f270,f266,f262,f259])).
% 0.22/0.41 thf(f192,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (sK0 @ sK3 @ sK3)) | ($false = (sK0 @ sK10 @ sK12)) | ($false = (sK0 @ sK5 @ sK4)) | ($false = (sK0 @ sK13 @ X1))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f191])).
% 0.22/0.41 thf(f257,plain,(
% 0.22/0.41 spl1_1 | spl1_2),
% 0.22/0.41 inference(avatar_split_clause,[],[f240,f255,f252])).
% 0.22/0.41 thf(f240,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X3 @ X3)) | ($false = (sK0 @ X1 @ X2)) | ($true = (sK0 @ X2 @ X1))) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f239])).
% 0.22/0.41 thf(f239,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK0 @ X1 @ X2) => (sK0 @ X2 @ X1))) | ($true = (sK0 @ X3 @ X3))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f238])).
% 0.22/0.41 thf(f238,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK0 @ X1 @ X2) => (sK0 @ X2 @ X1))) | ($true = ((^[Y0 : $i]: (sK0 @ Y0 @ Y0)) @ X3))) )),
% 0.22/0.41 inference(pi_clausification,[],[f237])).
% 0.22/0.41 thf(f237,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true) | ($true = ((sK0 @ X1 @ X2) => (sK0 @ X2 @ X1)))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f236])).
% 0.22/0.41 thf(f236,plain,(
% 0.22/0.41 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true) | ($true = ((^[Y0 : $i]: ((sK0 @ X1 @ Y0) => (sK0 @ Y0 @ X1))) @ X2))) )),
% 0.22/0.41 inference(pi_clausification,[],[f235])).
% 0.22/0.41 thf(f235,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ X1 @ Y0) => (sK0 @ Y0 @ X1))))) | ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true)) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f234])).
% 0.22/0.41 thf(f234,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true) | ($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))) @ X1))) )),
% 0.22/0.41 inference(pi_clausification,[],[f233])).
% 0.22/0.41 thf(f233,plain,(
% 0.22/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: (sK0 @ Y0 @ Y0))) = $true)),
% 0.22/0.41 inference(beta_eta_normalization,[],[f149])).
% 0.22/0.41 thf(f149,plain,(
% 0.22/0.41 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ sK0)) | (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ sK0) = $true)),
% 0.22/0.41 inference(definition_unfolding,[],[f110,f120,f131])).
% 0.22/0.41 thf(f110,plain,(
% 0.22/0.41 ((msymmetric @ sK0) = $true) | ($true = (mreflexive @ sK0))),
% 0.22/0.41 inference(cnf_transformation,[],[f99])).
% 0.22/0.41 % SZS output end Proof for theBenchmark
% 0.22/0.41 % (15598)------------------------------
% 0.22/0.41 % (15598)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (15598)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (15598)Memory used [KB]: 5884
% 0.22/0.41 % (15598)Time elapsed: 0.034 s
% 0.22/0.41 % (15598)Instructions burned: 40 (million)
% 0.22/0.41 % (15598)------------------------------
% 0.22/0.41 % (15598)------------------------------
% 0.22/0.41 % (15597)Success in time 0.046 s
% 0.22/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------