TSTP Solution File: LCL707^1 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 11:33:18 EDT 2024
% Result : Theorem 0.16s 0.37s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : LCL707^1 : TPTP v8.2.0. Bugfixed v5.1.0.
% 0.09/0.10 % Command : run_vampire %s %d THM
% 0.09/0.31 % Computer : n019.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Sat Jun 22 16:51:23 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.16/0.33 This is a TH0_THM_EQU_NAR problem
% 0.16/0.33 Running higher-order theorem proving
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.16/0.35 % (19197)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)
% 0.16/0.35 % (19198)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.35 % (19194)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)
% 0.16/0.35 % (19195)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.35 % (19196)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)
% 0.16/0.35 % (19193)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)
% 0.16/0.35 % (19195)Instruction limit reached!
% 0.16/0.35 % (19195)------------------------------
% 0.16/0.35 % (19195)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (19195)Termination reason: Unknown
% 0.16/0.35 % (19195)Termination phase: shuffling
% 0.16/0.35 % (19196)Instruction limit reached!
% 0.16/0.35 % (19196)------------------------------
% 0.16/0.35 % (19196)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (19196)Termination reason: Unknown
% 0.16/0.35 % (19196)Termination phase: shuffling
% 0.16/0.35
% 0.16/0.35 % (19196)Memory used [KB]: 1023
% 0.16/0.35 % (19196)Time elapsed: 0.003 s
% 0.16/0.35 % (19196)Instructions burned: 3 (million)
% 0.16/0.35 % (19196)------------------------------
% 0.16/0.35 % (19196)------------------------------
% 0.16/0.35
% 0.16/0.35 % (19195)Memory used [KB]: 1023
% 0.16/0.35 % (19195)Time elapsed: 0.003 s
% 0.16/0.35 % (19195)Instructions burned: 2 (million)
% 0.16/0.35 % (19195)------------------------------
% 0.16/0.35 % (19195)------------------------------
% 0.16/0.35 % (19193)Instruction limit reached!
% 0.16/0.35 % (19193)------------------------------
% 0.16/0.35 % (19193)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.35 % (19193)Termination reason: Unknown
% 0.16/0.35 % (19193)Termination phase: Property scanning
% 0.16/0.35
% 0.16/0.35 % (19193)Memory used [KB]: 1023
% 0.16/0.35 % (19193)Time elapsed: 0.004 s
% 0.16/0.35 % (19193)Instructions burned: 4 (million)
% 0.16/0.35 % (19193)------------------------------
% 0.16/0.35 % (19193)------------------------------
% 0.16/0.35 % (19192)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.36 % (19198)Instruction limit reached!
% 0.16/0.36 % (19198)------------------------------
% 0.16/0.36 % (19198)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (19198)Termination reason: Unknown
% 0.16/0.36 % (19198)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (19198)Memory used [KB]: 5756
% 0.16/0.36 % (19198)Time elapsed: 0.011 s
% 0.16/0.36 % (19198)Instructions burned: 19 (million)
% 0.16/0.36 % (19198)------------------------------
% 0.16/0.36 % (19198)------------------------------
% 0.16/0.36 % (19194)Instruction limit reached!
% 0.16/0.36 % (19194)------------------------------
% 0.16/0.36 % (19194)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (19194)Termination reason: Unknown
% 0.16/0.36 % (19194)Termination phase: Saturation
% 0.16/0.36
% 0.16/0.36 % (19194)Memory used [KB]: 5756
% 0.16/0.36 % (19194)Time elapsed: 0.016 s
% 0.16/0.36 % (19194)Instructions burned: 27 (million)
% 0.16/0.36 % (19194)------------------------------
% 0.16/0.36 % (19194)------------------------------
% 0.16/0.36 % (19199)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)
% 0.16/0.36 % (19200)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)
% 0.16/0.36 % (19201)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)
% 0.16/0.36 % (19192)First to succeed.
% 0.16/0.36 % (19199)Instruction limit reached!
% 0.16/0.36 % (19199)------------------------------
% 0.16/0.36 % (19199)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.36 % (19199)Termination reason: Unknown
% 0.16/0.36 % (19199)Termination phase: shuffling
% 0.16/0.36
% 0.16/0.36 % (19199)Memory used [KB]: 1023
% 0.16/0.36 % (19199)Time elapsed: 0.003 s
% 0.16/0.36 % (19199)Instructions burned: 3 (million)
% 0.16/0.36 % (19199)------------------------------
% 0.16/0.36 % (19199)------------------------------
% 0.16/0.37 % (19197)Also succeeded, but the first one will report.
% 0.16/0.37 % (19192)Refutation found. Thanks to Tanya!
% 0.16/0.37 % SZS status Theorem for theBenchmark
% 0.16/0.37 % SZS output start Proof for theBenchmark
% 0.16/0.37 thf(type_def_5, type, mu: $tType).
% 0.16/0.37 thf(func_def_0, type, mu: $tType).
% 0.16/0.37 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.16/0.37 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_15, type, mtrue: $i > $o).
% 0.16/0.37 thf(func_def_16, type, mfalse: $i > $o).
% 0.16/0.37 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.37 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.16/0.37 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.16/0.37 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.16/0.37 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.37 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.37 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.16/0.37 thf(func_def_51, type, sK3: $i > $o).
% 0.16/0.37 thf(func_def_52, type, sK4: $i > $o).
% 0.16/0.37 thf(f294,plain,(
% 0.16/0.37 $false),
% 0.16/0.37 inference(avatar_sat_refutation,[],[f233,f254,f280,f287,f293])).
% 0.16/0.37 thf(f293,plain,(
% 0.16/0.37 ~spl1_1 | spl1_3),
% 0.16/0.37 inference(avatar_contradiction_clause,[],[f292])).
% 0.16/0.37 thf(f292,plain,(
% 0.16/0.37 $false | (~spl1_1 | spl1_3)),
% 0.16/0.37 inference(subsumption_resolution,[],[f290,f226])).
% 0.16/0.37 thf(f226,plain,(
% 0.16/0.37 ($true != (sK3 @ sK5)) | spl1_3),
% 0.16/0.37 inference(avatar_component_clause,[],[f225])).
% 0.16/0.37 thf(f225,plain,(
% 0.16/0.37 spl1_3 <=> ($true = (sK3 @ sK5))),
% 0.16/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.16/0.37 thf(f290,plain,(
% 0.16/0.37 ($true = (sK3 @ sK5)) | ~spl1_1),
% 0.16/0.37 inference(superposition,[],[f181,f220])).
% 0.16/0.37 thf(f220,plain,(
% 0.16/0.37 (sK6 = sK5) | ~spl1_1),
% 0.16/0.37 inference(avatar_component_clause,[],[f218])).
% 0.16/0.37 thf(f218,plain,(
% 0.16/0.37 spl1_1 <=> (sK6 = sK5)),
% 0.16/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.16/0.37 thf(f181,plain,(
% 0.16/0.37 ($true = (sK3 @ sK6))),
% 0.16/0.37 inference(not_proxy_clausification,[],[f174])).
% 0.16/0.37 thf(f174,plain,(
% 0.16/0.37 ($false = (~ (sK3 @ sK6)))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.16/0.37 thf(f172,plain,(
% 0.16/0.37 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK6 @ Y0)))))) | (~ (sK3 @ sK6))))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f171])).
% 0.16/0.37 thf(f171,plain,(
% 0.16/0.37 ($false = ((sK4 @ sK6) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK6 @ Y0)))))) | (~ (sK3 @ sK6)))))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f169])).
% 0.16/0.37 thf(f169,plain,(
% 0.16/0.37 ($false = (((sK4 @ sK6) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK6 @ Y0)))))) | (~ (sK3 @ sK6)))) | (~ (sK0 @ sK2 @ sK6))))),
% 0.16/0.37 inference(beta_eta_normalization,[],[f168])).
% 0.16/0.37 thf(f168,plain,(
% 0.16/0.37 ($false = ((^[Y0 : $i]: (((sK4 @ Y0) | ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))) @ sK6))),
% 0.16/0.37 inference(sigma_clausification,[],[f151])).
% 0.16/0.37 thf(f151,plain,(
% 0.16/0.37 ((!! @ $i @ (^[Y0 : $i]: (((sK4 @ Y0) | ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f150])).
% 0.16/0.37 thf(f150,plain,(
% 0.16/0.37 ($false = ((!! @ $i @ (^[Y0 : $i]: (((sK3 @ Y0) | ((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK4 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: (((sK4 @ Y0) | ((~ (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y1) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK3 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.16/0.37 inference(beta_eta_normalization,[],[f149])).
% 0.16/0.37 thf(f149,plain,(
% 0.16/0.37 ($false = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (((sK3 @ Y1) | ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ Y1 @ Y2)))))) | (~ (Y0 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: (((Y0 @ Y1) | ((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (sK0 @ Y1 @ Y2)))))) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))))) @ sK4))),
% 0.16/0.37 inference(sigma_clausification,[],[f148])).
% 0.16/0.37 thf(f148,plain,(
% 0.16/0.37 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (((sK3 @ Y1) | ((~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (sK0 @ Y1 @ Y2)))))) | (~ (Y0 @ Y1)))) | (~ (sK0 @ sK2 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: (((Y0 @ Y1) | ((~ (!! @ $i @ (^[Y2 : $i]: ((sK3 @ Y2) | (~ (sK0 @ Y1 @ Y2)))))) | (~ (sK3 @ Y1)))) | (~ (sK0 @ sK2 @ Y1)))))))))),
% 0.16/0.37 inference(beta_eta_normalization,[],[f147])).
% 0.16/0.37 thf(f147,plain,(
% 0.16/0.37 ($false = ((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2) | ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (Y1 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: (((Y1 @ Y2) | ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))))))) @ sK3))),
% 0.16/0.37 inference(sigma_clausification,[],[f146])).
% 0.16/0.37 thf(f146,plain,(
% 0.16/0.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2) | ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (Y1 @ Y2)))) | (~ (sK0 @ sK2 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: (((Y1 @ Y2) | ((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (sK0 @ Y2 @ Y3)))))) | (~ (Y0 @ Y2)))) | (~ (sK0 @ sK2 @ Y2)))))))))) = $false)),
% 0.16/0.37 inference(beta_eta_normalization,[],[f145])).
% 0.16/0.37 thf(f145,plain,(
% 0.16/0.37 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) | ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y2 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: (((Y2 @ Y3) | ((~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))))))))) @ sK2) = $false)),
% 0.16/0.37 inference(sigma_clausification,[],[f144])).
% 0.16/0.37 thf(f144,plain,(
% 0.16/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) | ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y2 @ Y3)))) | (~ (sK0 @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: (((Y2 @ Y3) | ((~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3)))))))))))))),
% 0.16/0.37 inference(boolean_simplification,[],[f143])).
% 0.16/0.37 thf(f143,plain,(
% 0.16/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) | (~ (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y2 @ Y3)))))) | (~ (sK0 @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: (((Y2 @ Y3) | ((~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3)))) | (~ (sK0 @ Y0 @ Y3)))))))))))))),
% 0.16/0.37 inference(boolean_simplification,[],[f142])).
% 0.16/0.37 thf(f142,plain,(
% 0.16/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y3) | (~ (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y2 @ Y3)))))) | (~ (sK0 @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: (((Y2 @ Y3) | (~ (~ ((~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (sK0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3)))))) | (~ (sK0 @ Y0 @ Y3)))))))))))))),
% 0.16/0.37 inference(beta_eta_normalization,[],[f140])).
% 0.16/0.37 thf(f140,plain,(
% 0.16/0.37 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : ($i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ Y0 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ Y0)) @ Y1)) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ Y1 @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ sK0 @ Y1)) @ Y0)))))))))),
% 0.16/0.37 inference(definition_unfolding,[],[f102,f104,f98,f98,f99,f112,f132,f131,f112,f112,f132,f131,f112])).
% 0.16/0.37 thf(f131,plain,(
% 0.16/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.16/0.37 inference(definition_unfolding,[],[f114,f129,f99,f129,f129])).
% 0.16/0.37 thf(f129,plain,(
% 0.16/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f73])).
% 0.16/0.37 thf(f73,plain,(
% 0.16/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.37 inference(fool_elimination,[],[f72])).
% 0.16/0.37 thf(f72,plain,(
% 0.16/0.37 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.16/0.37 inference(rectify,[],[f3])).
% 0.16/0.37 thf(f3,axiom,(
% 0.16/0.37 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.16/0.37 thf(f114,plain,(
% 0.16/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f41])).
% 0.16/0.37 thf(f41,plain,(
% 0.16/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.37 inference(fool_elimination,[],[f40])).
% 0.16/0.37 thf(f40,plain,(
% 0.16/0.37 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.16/0.37 inference(rectify,[],[f5])).
% 0.16/0.37 thf(f5,axiom,(
% 0.16/0.37 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.16/0.37 thf(f132,plain,(
% 0.16/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.16/0.37 inference(definition_unfolding,[],[f109,f99,f129])).
% 0.16/0.37 thf(f109,plain,(
% 0.16/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.37 inference(cnf_transformation,[],[f47])).
% 0.16/0.37 thf(f47,plain,(
% 0.16/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.37 inference(fool_elimination,[],[f46])).
% 0.16/0.37 thf(f46,plain,(
% 0.16/0.37 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.16/0.37 inference(rectify,[],[f6])).
% 0.16/0.37 thf(f6,axiom,(
% 0.16/0.37 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.37 thf(f112,plain,(
% 0.16/0.37 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f91])).
% 0.16/0.37 thf(f91,plain,(
% 0.16/0.37 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.16/0.37 inference(fool_elimination,[],[f90])).
% 0.16/0.37 thf(f90,plain,(
% 0.16/0.37 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))))),
% 0.16/0.37 inference(rectify,[],[f16])).
% 0.16/0.37 thf(f16,axiom,(
% 0.16/0.37 (mbox = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.16/0.37 thf(f99,plain,(
% 0.16/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f53])).
% 0.16/0.37 thf(f53,plain,(
% 0.16/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.37 inference(fool_elimination,[],[f52])).
% 0.16/0.37 thf(f52,plain,(
% 0.16/0.37 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.16/0.37 inference(rectify,[],[f4])).
% 0.16/0.37 thf(f4,axiom,(
% 0.16/0.37 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.16/0.37 thf(f98,plain,(
% 0.16/0.37 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f43])).
% 0.16/0.37 thf(f43,plain,(
% 0.16/0.37 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.16/0.37 inference(fool_elimination,[],[f42])).
% 0.16/0.37 thf(f42,plain,(
% 0.16/0.37 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))),
% 0.16/0.37 inference(rectify,[],[f11])).
% 0.16/0.37 thf(f11,axiom,(
% 0.16/0.37 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.16/0.37 thf(f104,plain,(
% 0.16/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.37 inference(cnf_transformation,[],[f49])).
% 0.16/0.37 thf(f49,plain,(
% 0.16/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.37 inference(fool_elimination,[],[f48])).
% 0.16/0.37 thf(f48,plain,(
% 0.16/0.37 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.16/0.37 inference(rectify,[],[f28])).
% 0.16/0.37 thf(f28,axiom,(
% 0.16/0.37 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.37 thf(f102,plain,(
% 0.16/0.37 ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mor @ (mbox @ sK0 @ (mimplies @ (mand @ Y0 @ (mbox @ sK0 @ Y0)) @ Y1)) @ (mbox @ sK0 @ (mimplies @ (mand @ Y1 @ (mbox @ sK0 @ Y1)) @ Y0)))))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f97])).
% 0.16/0.37 thf(f97,plain,(
% 0.16/0.37 ($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mor @ (mbox @ sK0 @ (mimplies @ (mand @ Y0 @ (mbox @ sK0 @ Y0)) @ Y1)) @ (mbox @ sK0 @ (mimplies @ (mand @ Y1 @ (mbox @ sK0 @ Y1)) @ Y0))))))))) & ($true = (mweakly_connected @ sK0))),
% 0.16/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.16/0.37 thf(f96,plain,(
% 0.16/0.37 ? [X0 : $i > $i > $o] : (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mor @ (mbox @ X0 @ (mimplies @ (mand @ Y0 @ (mbox @ X0 @ Y0)) @ Y1)) @ (mbox @ X0 @ (mimplies @ (mand @ Y1 @ (mbox @ X0 @ Y1)) @ Y0))))))))) & ($true = (mweakly_connected @ X0))) => (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mor @ (mbox @ sK0 @ (mimplies @ (mand @ Y0 @ (mbox @ sK0 @ Y0)) @ Y1)) @ (mbox @ sK0 @ (mimplies @ (mand @ Y1 @ (mbox @ sK0 @ Y1)) @ Y0))))))))) & ($true = (mweakly_connected @ sK0)))),
% 0.16/0.37 introduced(choice_axiom,[])).
% 0.16/0.37 thf(f95,plain,(
% 0.16/0.37 ? [X0 : $i > $i > $o] : (($true != (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mor @ (mbox @ X0 @ (mimplies @ (mand @ Y0 @ (mbox @ X0 @ Y0)) @ Y1)) @ (mbox @ X0 @ (mimplies @ (mand @ Y1 @ (mbox @ X0 @ Y1)) @ Y0))))))))) & ($true = (mweakly_connected @ X0)))),
% 0.16/0.37 inference(ennf_transformation,[],[f69])).
% 0.16/0.37 thf(f69,plain,(
% 0.16/0.37 ~! [X0 : $i > $i > $o] : (($true = (mweakly_connected @ X0)) => ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mor @ (mbox @ X0 @ (mimplies @ (mand @ Y0 @ (mbox @ X0 @ Y0)) @ Y1)) @ (mbox @ X0 @ (mimplies @ (mand @ Y1 @ (mbox @ X0 @ Y1)) @ Y0))))))))))),
% 0.16/0.37 inference(fool_elimination,[],[f68])).
% 0.16/0.37 thf(f68,plain,(
% 0.16/0.37 ~! [X0 : $i > $i > $o] : ((mweakly_connected @ X0) => (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mforall_prop @ (^[X2 : $i > $o] : (mor @ (mbox @ X0 @ (mimplies @ (mand @ X1 @ (mbox @ X0 @ X1)) @ X2)) @ (mbox @ X0 @ (mimplies @ (mand @ X2 @ (mbox @ X0 @ X2)) @ X1)))))))))),
% 0.16/0.37 inference(rectify,[],[f33])).
% 0.16/0.37 thf(f33,negated_conjecture,(
% 0.16/0.37 ~! [X6 : $i > $i > $o] : ((mweakly_connected @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mor @ (mbox @ X6 @ (mimplies @ (mand @ X11 @ (mbox @ X6 @ X11)) @ X12)) @ (mbox @ X6 @ (mimplies @ (mand @ X12 @ (mbox @ X6 @ X12)) @ X11)))))))))),
% 0.16/0.37 inference(negated_conjecture,[],[f32])).
% 0.16/0.37 thf(f32,conjecture,(
% 0.16/0.37 ! [X6 : $i > $i > $o] : ((mweakly_connected @ X6) => (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mor @ (mbox @ X6 @ (mimplies @ (mand @ X11 @ (mbox @ X6 @ X11)) @ X12)) @ (mbox @ X6 @ (mimplies @ (mand @ X12 @ (mbox @ X6 @ X12)) @ X11)))))))))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.16/0.37 thf(f287,plain,(
% 0.16/0.37 ~spl1_4),
% 0.16/0.37 inference(avatar_contradiction_clause,[],[f286])).
% 0.16/0.37 thf(f286,plain,(
% 0.16/0.37 $false | ~spl1_4),
% 0.16/0.37 inference(trivial_inequality_removal,[],[f283])).
% 0.16/0.37 thf(f283,plain,(
% 0.16/0.37 ($true = $false) | ~spl1_4),
% 0.16/0.37 inference(superposition,[],[f173,f231])).
% 0.16/0.37 thf(f231,plain,(
% 0.16/0.37 ($true = (sK4 @ sK6)) | ~spl1_4),
% 0.16/0.37 inference(avatar_component_clause,[],[f229])).
% 0.16/0.37 thf(f229,plain,(
% 0.16/0.37 spl1_4 <=> ($true = (sK4 @ sK6))),
% 0.16/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.16/0.37 thf(f173,plain,(
% 0.16/0.37 ($false = (sK4 @ sK6))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f171])).
% 0.16/0.37 thf(f280,plain,(
% 0.16/0.37 ~spl1_3),
% 0.16/0.37 inference(avatar_contradiction_clause,[],[f279])).
% 0.16/0.37 thf(f279,plain,(
% 0.16/0.37 $false | ~spl1_3),
% 0.16/0.37 inference(trivial_inequality_removal,[],[f275])).
% 0.16/0.37 thf(f275,plain,(
% 0.16/0.37 ($true = $false) | ~spl1_3),
% 0.16/0.37 inference(superposition,[],[f227,f158])).
% 0.16/0.37 thf(f158,plain,(
% 0.16/0.37 ((sK3 @ sK5) = $false)),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f156])).
% 0.16/0.37 thf(f156,plain,(
% 0.16/0.37 ($false = ((sK3 @ sK5) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK5 @ Y0)))))) | (~ (sK4 @ sK5)))))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f154])).
% 0.16/0.37 thf(f154,plain,(
% 0.16/0.37 ($false = (((sK3 @ sK5) | ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK5 @ Y0)))))) | (~ (sK4 @ sK5)))) | (~ (sK0 @ sK2 @ sK5))))),
% 0.16/0.37 inference(beta_eta_normalization,[],[f153])).
% 0.16/0.37 thf(f153,plain,(
% 0.16/0.37 ($false = ((^[Y0 : $i]: (((sK3 @ Y0) | ((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK4 @ Y0)))) | (~ (sK0 @ sK2 @ Y0)))) @ sK5))),
% 0.16/0.37 inference(sigma_clausification,[],[f152])).
% 0.16/0.37 thf(f152,plain,(
% 0.16/0.37 ((!! @ $i @ (^[Y0 : $i]: (((sK3 @ Y0) | ((~ (!! @ $i @ (^[Y1 : $i]: ((sK4 @ Y1) | (~ (sK0 @ Y0 @ Y1)))))) | (~ (sK4 @ Y0)))) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f150])).
% 0.16/0.37 thf(f227,plain,(
% 0.16/0.37 ($true = (sK3 @ sK5)) | ~spl1_3),
% 0.16/0.37 inference(avatar_component_clause,[],[f225])).
% 0.16/0.37 thf(f254,plain,(
% 0.16/0.37 ~spl1_2),
% 0.16/0.37 inference(avatar_contradiction_clause,[],[f253])).
% 0.16/0.37 thf(f253,plain,(
% 0.16/0.37 $false | ~spl1_2),
% 0.16/0.37 inference(trivial_inequality_removal,[],[f245])).
% 0.16/0.37 thf(f245,plain,(
% 0.16/0.37 ($true = $false) | ~spl1_2),
% 0.16/0.37 inference(superposition,[],[f167,f239])).
% 0.16/0.37 thf(f239,plain,(
% 0.16/0.37 ((sK0 @ sK2 @ sK5) = $false) | ~spl1_2),
% 0.16/0.37 inference(trivial_inequality_removal,[],[f234])).
% 0.16/0.37 thf(f234,plain,(
% 0.16/0.37 ($true = $false) | ((sK0 @ sK2 @ sK5) = $false) | ~spl1_2),
% 0.16/0.37 inference(superposition,[],[f223,f182])).
% 0.16/0.37 thf(f182,plain,(
% 0.16/0.37 ($true = (sK0 @ sK2 @ sK6))),
% 0.16/0.37 inference(not_proxy_clausification,[],[f170])).
% 0.16/0.37 thf(f170,plain,(
% 0.16/0.37 ($false = (~ (sK0 @ sK2 @ sK6)))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f169])).
% 0.16/0.37 thf(f223,plain,(
% 0.16/0.37 ( ! [X0 : $i] : (((sK0 @ X0 @ sK6) = $false) | ((sK0 @ X0 @ sK5) = $false)) ) | ~spl1_2),
% 0.16/0.37 inference(avatar_component_clause,[],[f222])).
% 0.16/0.37 thf(f222,plain,(
% 0.16/0.37 spl1_2 <=> ! [X0] : (((sK0 @ X0 @ sK5) = $false) | ((sK0 @ X0 @ sK6) = $false))),
% 0.16/0.37 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.16/0.37 thf(f167,plain,(
% 0.16/0.37 ($true = (sK0 @ sK2 @ sK5))),
% 0.16/0.37 inference(not_proxy_clausification,[],[f155])).
% 0.16/0.37 thf(f155,plain,(
% 0.16/0.37 ((~ (sK0 @ sK2 @ sK5)) = $false)),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f154])).
% 0.16/0.37 thf(f233,plain,(
% 0.16/0.37 spl1_2 | spl1_4 | spl1_3 | spl1_1),
% 0.16/0.37 inference(avatar_split_clause,[],[f215,f218,f225,f229,f222])).
% 0.16/0.37 thf(f215,plain,(
% 0.16/0.37 ( ! [X0 : $i] : (($true = (sK4 @ sK6)) | ((sK0 @ X0 @ sK5) = $false) | ((sK0 @ X0 @ sK6) = $false) | (sK6 = sK5) | ($true = (sK3 @ sK5))) )),
% 0.16/0.37 inference(trivial_inequality_removal,[],[f209])).
% 0.16/0.37 thf(f209,plain,(
% 0.16/0.37 ( ! [X0 : $i] : (($true = (sK3 @ sK5)) | ((sK0 @ X0 @ sK6) = $false) | (sK6 = sK5) | ((sK0 @ X0 @ sK5) = $false) | ($true = (sK4 @ sK6)) | ($true = $false)) )),
% 0.16/0.37 inference(superposition,[],[f203,f180])).
% 0.16/0.37 thf(f180,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (((sK0 @ sK6 @ X1) = $false) | ($true = (sK3 @ X1))) )),
% 0.16/0.37 inference(not_proxy_clausification,[],[f179])).
% 0.16/0.37 thf(f179,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = (sK3 @ X1)) | ($true = (~ (sK0 @ sK6 @ X1)))) )),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f178])).
% 0.16/0.37 thf(f178,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = ((sK3 @ X1) | (~ (sK0 @ sK6 @ X1))))) )),
% 0.16/0.37 inference(beta_eta_normalization,[],[f177])).
% 0.16/0.37 thf(f177,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK6 @ Y0)))) @ X1))) )),
% 0.16/0.37 inference(pi_clausification,[],[f176])).
% 0.16/0.37 thf(f176,plain,(
% 0.16/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK6 @ Y0))))))),
% 0.16/0.37 inference(not_proxy_clausification,[],[f175])).
% 0.16/0.37 thf(f175,plain,(
% 0.16/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((sK3 @ Y0) | (~ (sK0 @ sK6 @ Y0)))))) = $false)),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.16/0.37 thf(f203,plain,(
% 0.16/0.37 ( ! [X0 : $i,X1 : $i] : (($true = (sK0 @ X0 @ sK5)) | ($false = (sK0 @ X1 @ X0)) | ($true = (sK4 @ X0)) | ($false = (sK0 @ X1 @ sK5)) | (sK5 = X0)) )),
% 0.16/0.37 inference(trivial_inequality_removal,[],[f201])).
% 0.16/0.37 thf(f201,plain,(
% 0.16/0.37 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X0)) | ($false = (sK0 @ X1 @ sK5)) | ($true = (sK0 @ X0 @ sK5)) | (sK5 = X0) | ($true = (sK4 @ X0)) | ($true = $false)) )),
% 0.16/0.37 inference(superposition,[],[f194,f165])).
% 0.16/0.37 thf(f165,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($false = (sK0 @ sK5 @ X1)) | ($true = (sK4 @ X1))) )),
% 0.16/0.37 inference(not_proxy_clausification,[],[f164])).
% 0.16/0.37 thf(f164,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = (sK4 @ X1)) | ($true = (~ (sK0 @ sK5 @ X1)))) )),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f163])).
% 0.16/0.37 thf(f163,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = ((sK4 @ X1) | (~ (sK0 @ sK5 @ X1))))) )),
% 0.16/0.37 inference(beta_eta_normalization,[],[f162])).
% 0.16/0.37 thf(f162,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK5 @ Y0)))) @ X1))) )),
% 0.16/0.37 inference(pi_clausification,[],[f161])).
% 0.16/0.37 thf(f161,plain,(
% 0.16/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK5 @ Y0))))))),
% 0.16/0.37 inference(not_proxy_clausification,[],[f160])).
% 0.16/0.37 thf(f160,plain,(
% 0.16/0.37 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK5 @ Y0)))))))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f157])).
% 0.16/0.37 thf(f157,plain,(
% 0.16/0.37 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK4 @ Y0) | (~ (sK0 @ sK5 @ Y0)))))) | (~ (sK4 @ sK5))))),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f156])).
% 0.16/0.37 thf(f194,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X3 @ X1)) | ($false = (sK0 @ X2 @ X1)) | ((sK0 @ X2 @ X3) = $false) | (X1 = X3) | ($true = (sK0 @ X1 @ X3))) )),
% 0.16/0.37 inference(equality_proxy_clausification,[],[f193])).
% 0.16/0.37 thf(f193,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (sK0 @ X3 @ X1)) | ((sK0 @ X2 @ X3) = $false) | ($true = (X3 = X1)) | ($false = (sK0 @ X2 @ X1)) | ($true = (sK0 @ X1 @ X3))) )),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f192])).
% 0.16/0.37 thf(f192,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK0 @ X1 @ X3) | (sK0 @ X3 @ X1))) | ($false = (sK0 @ X2 @ X1)) | ((sK0 @ X2 @ X3) = $false) | ($true = (X3 = X1))) )),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f191])).
% 0.16/0.37 thf(f191,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((sK0 @ X2 @ X3) & (sK0 @ X2 @ X1))) | ($true = ((sK0 @ X1 @ X3) | (sK0 @ X3 @ X1))) | ($true = (X3 = X1))) )),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f190])).
% 0.16/0.37 thf(f190,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK0 @ X1 @ X3) | (sK0 @ X3 @ X1)) | (X3 = X1))) | ($false = ((sK0 @ X2 @ X3) & (sK0 @ X2 @ X1)))) )),
% 0.16/0.37 inference(binary_proxy_clausification,[],[f189])).
% 0.16/0.37 thf(f189,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK0 @ X2 @ X3) & (sK0 @ X2 @ X1)) => (((sK0 @ X1 @ X3) | (sK0 @ X3 @ X1)) | (X3 = X1))))) )),
% 0.16/0.37 inference(beta_eta_normalization,[],[f188])).
% 0.16/0.37 thf(f188,plain,(
% 0.16/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK0 @ X2 @ Y0) & (sK0 @ X2 @ X1)) => (((sK0 @ X1 @ Y0) | (sK0 @ Y0 @ X1)) | (Y0 = X1)))) @ X3))) )),
% 0.16/0.37 inference(pi_clausification,[],[f187])).
% 0.16/0.37 thf(f187,plain,(
% 0.16/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ X2 @ Y0) & (sK0 @ X2 @ X1)) => (((sK0 @ X1 @ Y0) | (sK0 @ Y0 @ X1)) | (Y0 = X1))))))) )),
% 0.16/0.37 inference(beta_eta_normalization,[],[f186])).
% 0.16/0.37 thf(f186,plain,(
% 0.16/0.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ Y1) & (sK0 @ Y0 @ X1)) => (((sK0 @ X1 @ Y1) | (sK0 @ Y1 @ X1)) | (Y1 = X1)))))) @ X2))) )),
% 0.16/0.37 inference(pi_clausification,[],[f185])).
% 0.16/0.37 thf(f185,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ Y1) & (sK0 @ Y0 @ X1)) => (((sK0 @ X1 @ Y1) | (sK0 @ Y1 @ X1)) | (Y1 = X1))))))))) )),
% 0.16/0.37 inference(beta_eta_normalization,[],[f184])).
% 0.16/0.37 thf(f184,plain,(
% 0.16/0.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y2) & (sK0 @ Y1 @ Y0)) => (((sK0 @ Y0 @ Y2) | (sK0 @ Y2 @ Y0)) | (Y2 = Y0)))))))) @ X1))) )),
% 0.16/0.37 inference(pi_clausification,[],[f183])).
% 0.16/0.37 thf(f183,plain,(
% 0.16/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y2) & (sK0 @ Y1 @ Y0)) => (((sK0 @ Y0 @ Y2) | (sK0 @ Y2 @ Y0)) | (Y2 = Y0))))))))))),
% 0.16/0.37 inference(beta_eta_normalization,[],[f141])).
% 0.16/0.37 thf(f141,plain,(
% 0.16/0.37 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (((Y0 @ Y1 @ Y3) | (Y0 @ Y3 @ Y1)) | (Y3 = Y1)))))))))) @ sK0))),
% 0.16/0.37 inference(definition_unfolding,[],[f101,f126])).
% 0.16/0.37 thf(f126,plain,(
% 0.16/0.37 (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (((Y0 @ Y1 @ Y3) | (Y0 @ Y3 @ Y1)) | (Y3 = Y1)))))))))))),
% 0.16/0.37 inference(cnf_transformation,[],[f67])).
% 0.16/0.37 thf(f67,plain,(
% 0.16/0.37 (mweakly_connected = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y2 @ Y1)) => (((Y0 @ Y1 @ Y3) | (Y0 @ Y3 @ Y1)) | (Y3 = Y1)))))))))))),
% 0.16/0.37 inference(fool_elimination,[],[f66])).
% 0.16/0.37 thf(f66,plain,(
% 0.16/0.37 (mweakly_connected = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X2 @ X1)) => ((X1 = X3) | (X0 @ X1 @ X3) | (X0 @ X3 @ X1))))))),
% 0.16/0.37 inference(rectify,[],[f26])).
% 0.16/0.37 thf(f26,axiom,(
% 0.16/0.37 (mweakly_connected = (^[X6 : $i > $i > $o] : (! [X10,X8,X9] : (((X6 @ X8 @ X9) & (X6 @ X8 @ X10)) => ((X9 = X10) | (X6 @ X10 @ X9) | (X6 @ X9 @ X10))))))),
% 0.16/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_connected)).
% 0.16/0.37 thf(f101,plain,(
% 0.16/0.37 ($true = (mweakly_connected @ sK0))),
% 0.16/0.37 inference(cnf_transformation,[],[f97])).
% 0.16/0.37 % SZS output end Proof for theBenchmark
% 0.16/0.37 % (19192)------------------------------
% 0.16/0.37 % (19192)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.16/0.37 % (19192)Termination reason: Refutation
% 0.16/0.37
% 0.16/0.37 % (19192)Memory used [KB]: 5884
% 0.16/0.37 % (19192)Time elapsed: 0.020 s
% 0.16/0.37 % (19192)Instructions burned: 22 (million)
% 0.16/0.37 % (19192)------------------------------
% 0.16/0.37 % (19192)------------------------------
% 0.16/0.37 % (19191)Success in time 0.035 s
%------------------------------------------------------------------------------