TSTP Solution File: SYO462^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO462^2 : TPTP v8.2.0. Released v4.0.0.
% 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 : n017.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 09:04:53 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO462^2 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % 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 10:26:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (28192)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)
% 0.14/0.37 % (28190)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)
% 0.14/0.37 % (28185)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (28187)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)
% 0.14/0.37 % (28192)Instruction limit reached!
% 0.14/0.37 % (28192)------------------------------
% 0.14/0.37 % (28192)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28192)Termination reason: Unknown
% 0.14/0.37 % (28192)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (28192)Memory used [KB]: 1023
% 0.14/0.37 % (28192)Time elapsed: 0.003 s
% 0.14/0.37 % (28192)Instructions burned: 3 (million)
% 0.14/0.37 % (28192)------------------------------
% 0.14/0.37 % (28192)------------------------------
% 0.14/0.37 % (28191)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (28190)Refutation not found, incomplete strategy
% 0.14/0.37 % (28190)------------------------------
% 0.14/0.37 % (28190)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28190)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (28190)Memory used [KB]: 5628
% 0.14/0.37 % (28190)Time elapsed: 0.005 s
% 0.14/0.37 % (28190)Instructions burned: 7 (million)
% 0.14/0.37 % (28190)------------------------------
% 0.14/0.37 % (28190)------------------------------
% 0.14/0.37 % (28189)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)
% 0.14/0.37 % (28186)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)
% 0.14/0.37 % (28188)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (28189)Instruction limit reached!
% 0.14/0.37 % (28189)------------------------------
% 0.14/0.37 % (28189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28189)Termination reason: Unknown
% 0.14/0.37 % (28189)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (28189)Memory used [KB]: 1023
% 0.14/0.37 % (28189)Time elapsed: 0.003 s
% 0.14/0.37 % (28189)Instructions burned: 3 (million)
% 0.14/0.37 % (28189)------------------------------
% 0.14/0.37 % (28189)------------------------------
% 0.14/0.37 % (28188)Instruction limit reached!
% 0.14/0.37 % (28188)------------------------------
% 0.14/0.37 % (28188)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28188)Termination reason: Unknown
% 0.14/0.37 % (28188)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (28188)Memory used [KB]: 1023
% 0.14/0.37 % (28188)Time elapsed: 0.003 s
% 0.14/0.37 % (28188)Instructions burned: 2 (million)
% 0.14/0.37 % (28188)------------------------------
% 0.14/0.37 % (28188)------------------------------
% 0.14/0.38 % (28186)Instruction limit reached!
% 0.14/0.38 % (28186)------------------------------
% 0.14/0.38 % (28186)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (28186)Termination reason: Unknown
% 0.14/0.38 % (28186)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (28186)Memory used [KB]: 1023
% 0.14/0.38 % (28186)Time elapsed: 0.004 s
% 0.14/0.38 % (28186)Instructions burned: 4 (million)
% 0.14/0.38 % (28186)------------------------------
% 0.14/0.38 % (28186)------------------------------
% 0.14/0.38 % (28191)Instruction limit reached!
% 0.14/0.38 % (28191)------------------------------
% 0.14/0.38 % (28191)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (28191)Termination reason: Unknown
% 0.14/0.38 % (28191)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (28191)Memory used [KB]: 5756
% 0.14/0.38 % (28191)Time elapsed: 0.012 s
% 0.14/0.38 % (28191)Instructions burned: 18 (million)
% 0.14/0.38 % (28191)------------------------------
% 0.14/0.38 % (28191)------------------------------
% 0.20/0.38 % (28193)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)
% 0.20/0.38 % (28187)First to succeed.
% 0.20/0.39 % (28194)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)
% 0.20/0.39 % (28185)Also succeeded, but the first one will report.
% 0.20/0.39 % (28195)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)
% 0.20/0.39 % (28187)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% 0.20/0.39 thf(type_def_5, type, mu: $tType).
% 0.20/0.39 thf(func_def_0, type, mu: $tType).
% 0.20/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.39 thf(func_def_33, type, rel_d: $i > $i > $o).
% 0.20/0.39 thf(func_def_34, type, mbox_d: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_35, type, mdia_d: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_36, type, p: $i > $o).
% 0.20/0.39 thf(func_def_37, type, q: $i > $o).
% 0.20/0.39 thf(func_def_38, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.20/0.39 thf(func_def_55, type, sK1: $i > $i).
% 0.20/0.39 thf(f463,plain,(
% 0.20/0.39 $false),
% 0.20/0.39 inference(avatar_sat_refutation,[],[f240,f245,f249,f258,f263,f264,f272,f277,f278,f332,f368,f399,f420,f462])).
% 0.20/0.39 thf(f462,plain,(
% 0.20/0.39 ~spl0_5 | ~spl0_7 | ~spl0_8),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f461])).
% 0.20/0.39 thf(f461,plain,(
% 0.20/0.39 $false | (~spl0_5 | ~spl0_7 | ~spl0_8)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f460])).
% 0.20/0.39 thf(f460,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_5 | ~spl0_7 | ~spl0_8)),
% 0.20/0.39 inference(forward_demodulation,[],[f446,f262])).
% 0.20/0.39 thf(f262,plain,(
% 0.20/0.39 ((q @ sK5) = $false) | ~spl0_7),
% 0.20/0.39 inference(avatar_component_clause,[],[f260])).
% 0.20/0.39 thf(f260,plain,(
% 0.20/0.39 spl0_7 <=> ((q @ sK5) = $false)),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.20/0.39 thf(f446,plain,(
% 0.20/0.39 ($true = (q @ sK5)) | (~spl0_5 | ~spl0_8)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f441])).
% 0.20/0.39 thf(f441,plain,(
% 0.20/0.39 ($true = $false) | ($true = (q @ sK5)) | (~spl0_5 | ~spl0_8)),
% 0.20/0.39 inference(superposition,[],[f267,f253])).
% 0.20/0.39 thf(f253,plain,(
% 0.20/0.39 ((rel_d @ sK2 @ sK5) = $true) | ~spl0_5),
% 0.20/0.39 inference(avatar_component_clause,[],[f251])).
% 0.20/0.39 thf(f251,plain,(
% 0.20/0.39 spl0_5 <=> ((rel_d @ sK2 @ sK5) = $true)),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.20/0.39 thf(f267,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ($true = (q @ X1))) ) | ~spl0_8),
% 0.20/0.39 inference(avatar_component_clause,[],[f266])).
% 0.20/0.39 thf(f266,plain,(
% 0.20/0.39 spl0_8 <=> ! [X1] : (((rel_d @ sK2 @ X1) = $false) | ($true = (q @ X1)))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.20/0.39 thf(f420,plain,(
% 0.20/0.39 ~spl0_4 | ~spl0_9 | ~spl0_10),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f419])).
% 0.20/0.39 thf(f419,plain,(
% 0.20/0.39 $false | (~spl0_4 | ~spl0_9 | ~spl0_10)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f418])).
% 0.20/0.39 thf(f418,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_4 | ~spl0_9 | ~spl0_10)),
% 0.20/0.39 inference(forward_demodulation,[],[f388,f378])).
% 0.20/0.39 thf(f378,plain,(
% 0.20/0.39 ((p @ sK3) = $false) | (~spl0_9 | ~spl0_10)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f377])).
% 0.20/0.39 thf(f377,plain,(
% 0.20/0.39 ($true = $false) | ((p @ sK3) = $false) | (~spl0_9 | ~spl0_10)),
% 0.20/0.39 inference(forward_demodulation,[],[f375,f276])).
% 0.20/0.39 thf(f276,plain,(
% 0.20/0.39 ($false = (q @ sK3)) | ~spl0_10),
% 0.20/0.39 inference(avatar_component_clause,[],[f274])).
% 0.20/0.39 thf(f274,plain,(
% 0.20/0.39 spl0_10 <=> ($false = (q @ sK3))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.20/0.39 thf(f375,plain,(
% 0.20/0.39 ((p @ sK3) = $false) | ($true = (q @ sK3)) | ~spl0_9),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f370])).
% 0.20/0.39 thf(f370,plain,(
% 0.20/0.39 ($true = (q @ sK3)) | ((p @ sK3) = $false) | ($true = $false) | ~spl0_9),
% 0.20/0.39 inference(superposition,[],[f271,f171])).
% 0.20/0.39 thf(f171,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ($true = (q @ X1)) | ((p @ X1) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f170])).
% 0.20/0.39 thf(f170,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (p @ X1))) | ((rel_d @ sK2 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f169])).
% 0.20/0.39 thf(f169,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (q @ X1))) | ((rel_d @ sK2 @ X1) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f168])).
% 0.20/0.39 thf(f168,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ($false = (~ ((~ (p @ X1)) | (q @ X1))))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f166])).
% 0.20/0.39 thf(f166,plain,(
% 0.20/0.39 ( ! [X1 : $i] : ((((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1)))) = $false) | ((rel_d @ sK2 @ X1) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f165])).
% 0.20/0.39 thf(f165,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK2 @ X1))) | (((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1)))) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f164])).
% 0.20/0.39 thf(f164,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ ((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1)))))) | ($true = (~ (rel_d @ sK2 @ X1)))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f163])).
% 0.20/0.39 thf(f163,plain,(
% 0.20/0.39 ( ! [X1 : $i] : ((((~ ((~ ((~ (p @ X1)) | (q @ X1))) | (~ ((~ (q @ X1)) | (p @ X1))))) | (~ (rel_d @ sK2 @ X1))) = $true)) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f162])).
% 0.20/0.39 thf(f162,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_d @ sK2 @ Y0)))) @ X1))) )),
% 0.20/0.39 inference(pi_clausification,[],[f161])).
% 0.20/0.39 thf(f161,plain,(
% 0.20/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_d @ sK2 @ Y0))))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f160])).
% 0.20/0.39 thf(f160,plain,(
% 0.20/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_d @ sK2 @ Y0)))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f158])).
% 0.20/0.39 thf(f158,plain,(
% 0.20/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((~ (p @ Y0)) | (q @ Y0))) | (~ ((~ (q @ Y0)) | (p @ Y0))))) | (~ (rel_d @ sK2 @ Y0)))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))))) = $false)),
% 0.20/0.39 inference(beta_eta_normalization,[],[f157])).
% 0.20/0.39 thf(f157,plain,(
% 0.20/0.39 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_d @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_d @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1))))))))))) @ sK2) = $false)),
% 0.20/0.39 inference(sigma_clausification,[],[f156])).
% 0.20/0.39 thf(f156,plain,(
% 0.20/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ ((~ (p @ Y1)) | (q @ Y1))) | (~ ((~ (q @ Y1)) | (p @ Y1))))) | (~ (rel_d @ Y0 @ Y1)))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_d @ Y0 @ Y1))))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_d @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_d @ Y0 @ Y1)))))))))))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f151])).
% 0.20/0.39 thf(f151,plain,(
% 0.20/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))) @ q)))))),
% 0.20/0.39 inference(definition_unfolding,[],[f137,f136,f141,f132,f143,f143,f132,f132])).
% 0.20/0.39 thf(f143,plain,(
% 0.20/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.20/0.39 inference(definition_unfolding,[],[f122,f140,f141,f141])).
% 0.20/0.39 thf(f140,plain,(
% 0.20/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.20/0.39 inference(definition_unfolding,[],[f139,f110,f124,f110,f110])).
% 0.20/0.39 thf(f124,plain,(
% 0.20/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f91])).
% 0.20/0.39 thf(f91,plain,(
% 0.20/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f90])).
% 0.20/0.39 thf(f90,plain,(
% 0.20/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.39 inference(rectify,[],[f4])).
% 0.20/0.39 thf(f4,axiom,(
% 0.20/0.39 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.39 thf(f110,plain,(
% 0.20/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f85])).
% 0.20/0.39 thf(f85,plain,(
% 0.20/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.39 inference(fool_elimination,[],[f84])).
% 0.20/0.39 thf(f84,plain,(
% 0.20/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.39 inference(rectify,[],[f3])).
% 0.20/0.39 thf(f3,axiom,(
% 0.20/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.39 thf(f139,plain,(
% 0.20/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f41])).
% 0.20/0.39 thf(f41,plain,(
% 0.20/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.39 inference(fool_elimination,[],[f40])).
% 0.20/0.39 thf(f40,plain,(
% 0.20/0.39 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.39 inference(rectify,[],[f5])).
% 0.20/0.39 thf(f5,axiom,(
% 0.20/0.39 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.39 thf(f122,plain,(
% 0.20/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f46])).
% 0.20/0.39 thf(f46,plain,(
% 0.20/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.39 inference(fool_elimination,[],[f45])).
% 0.20/0.39 thf(f45,plain,(
% 0.20/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.20/0.39 inference(rectify,[],[f8])).
% 0.20/0.39 thf(f8,axiom,(
% 0.20/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.20/0.39 thf(f132,plain,(
% 0.20/0.39 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))))),
% 0.20/0.39 inference(cnf_transformation,[],[f79])).
% 0.20/0.39 thf(f79,plain,(
% 0.20/0.39 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_d @ Y1 @ Y2)))))))))),
% 0.20/0.39 inference(fool_elimination,[],[f78])).
% 0.20/0.39 thf(f78,plain,(
% 0.20/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_d @ X1 @ X2) | (X0 @ X2)))) = mbox_d)),
% 0.20/0.39 inference(rectify,[],[f32])).
% 0.20/0.39 thf(f32,axiom,(
% 0.20/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_d @ X2 @ X7) | (X3 @ X7)))) = mbox_d)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_d)).
% 0.20/0.39 thf(f141,plain,(
% 0.20/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.39 inference(definition_unfolding,[],[f111,f124,f110])).
% 0.20/0.39 thf(f111,plain,(
% 0.20/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.39 inference(cnf_transformation,[],[f97])).
% 0.20/0.39 thf(f97,plain,(
% 0.20/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.39 inference(fool_elimination,[],[f96])).
% 0.20/0.39 thf(f96,plain,(
% 0.20/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.20/0.39 inference(rectify,[],[f6])).
% 0.20/0.39 thf(f6,axiom,(
% 0.20/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.39 thf(f136,plain,(
% 0.20/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.39 inference(cnf_transformation,[],[f64])).
% 0.20/0.39 thf(f64,plain,(
% 0.20/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.39 inference(fool_elimination,[],[f63])).
% 0.20/0.39 thf(f63,plain,(
% 0.20/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.39 inference(rectify,[],[f28])).
% 0.20/0.39 thf(f28,axiom,(
% 0.20/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.39 thf(f137,plain,(
% 0.20/0.39 ((mvalid @ (mimplies @ (mbox_d @ (mequiv @ p @ q)) @ (mequiv @ (mbox_d @ p) @ (mbox_d @ q)))) != $true)),
% 0.20/0.39 inference(cnf_transformation,[],[f104])).
% 0.20/0.39 thf(f104,plain,(
% 0.20/0.39 ((mvalid @ (mimplies @ (mbox_d @ (mequiv @ p @ q)) @ (mequiv @ (mbox_d @ p) @ (mbox_d @ q)))) != $true)),
% 0.20/0.39 inference(flattening,[],[f68])).
% 0.20/0.39 thf(f68,plain,(
% 0.20/0.39 ~((mvalid @ (mimplies @ (mbox_d @ (mequiv @ p @ q)) @ (mequiv @ (mbox_d @ p) @ (mbox_d @ q)))) = $true)),
% 0.20/0.39 inference(fool_elimination,[],[f67])).
% 0.20/0.39 thf(f67,plain,(
% 0.20/0.39 ~(mvalid @ (mimplies @ (mbox_d @ (mequiv @ p @ q)) @ (mequiv @ (mbox_d @ p) @ (mbox_d @ q))))),
% 0.20/0.39 inference(rectify,[],[f36])).
% 0.20/0.39 thf(f36,negated_conjecture,(
% 0.20/0.39 ~(mvalid @ (mimplies @ (mbox_d @ (mequiv @ p @ q)) @ (mequiv @ (mbox_d @ p) @ (mbox_d @ q))))),
% 0.20/0.39 inference(negated_conjecture,[],[f35])).
% 0.20/0.39 thf(f35,conjecture,(
% 0.20/0.39 (mvalid @ (mimplies @ (mbox_d @ (mequiv @ p @ q)) @ (mequiv @ (mbox_d @ p) @ (mbox_d @ q))))),
% 0.20/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.20/0.39 thf(f271,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK3)) | ~spl0_9),
% 0.20/0.39 inference(avatar_component_clause,[],[f269])).
% 0.20/0.39 thf(f269,plain,(
% 0.20/0.39 spl0_9 <=> ($true = (rel_d @ sK2 @ sK3))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.20/0.39 thf(f388,plain,(
% 0.20/0.39 ((p @ sK3) = $true) | (~spl0_4 | ~spl0_9)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f385])).
% 0.20/0.39 thf(f385,plain,(
% 0.20/0.39 ($true = $false) | ((p @ sK3) = $true) | (~spl0_4 | ~spl0_9)),
% 0.20/0.39 inference(superposition,[],[f271,f248])).
% 0.20/0.39 thf(f248,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ((p @ X1) = $true)) ) | ~spl0_4),
% 0.20/0.39 inference(avatar_component_clause,[],[f247])).
% 0.20/0.39 thf(f247,plain,(
% 0.20/0.39 spl0_4 <=> ! [X1] : (((p @ X1) = $true) | ((rel_d @ sK2 @ X1) = $false))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.39 thf(f399,plain,(
% 0.20/0.39 ~spl0_1 | ~spl0_4 | ~spl0_6),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f398])).
% 0.20/0.39 thf(f398,plain,(
% 0.20/0.39 $false | (~spl0_1 | ~spl0_4 | ~spl0_6)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f397])).
% 0.20/0.39 thf(f397,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_1 | ~spl0_4 | ~spl0_6)),
% 0.20/0.39 inference(forward_demodulation,[],[f389,f257])).
% 0.20/0.39 thf(f257,plain,(
% 0.20/0.39 ($false = (p @ sK4)) | ~spl0_6),
% 0.20/0.39 inference(avatar_component_clause,[],[f255])).
% 0.20/0.39 thf(f255,plain,(
% 0.20/0.39 spl0_6 <=> ($false = (p @ sK4))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.20/0.39 thf(f389,plain,(
% 0.20/0.39 ($true = (p @ sK4)) | (~spl0_1 | ~spl0_4)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f383])).
% 0.20/0.39 thf(f383,plain,(
% 0.20/0.39 ($true = (p @ sK4)) | ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.20/0.39 inference(superposition,[],[f248,f235])).
% 0.20/0.39 thf(f235,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK4)) | ~spl0_1),
% 0.20/0.39 inference(avatar_component_clause,[],[f233])).
% 0.20/0.39 thf(f233,plain,(
% 0.20/0.39 spl0_1 <=> ($true = (rel_d @ sK2 @ sK4))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.39 thf(f368,plain,(
% 0.20/0.39 ~spl0_1 | ~spl0_6 | ~spl0_8),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f367])).
% 0.20/0.39 thf(f367,plain,(
% 0.20/0.39 $false | (~spl0_1 | ~spl0_6 | ~spl0_8)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f366])).
% 0.20/0.39 thf(f366,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_1 | ~spl0_6 | ~spl0_8)),
% 0.20/0.39 inference(backward_demodulation,[],[f355,f360])).
% 0.20/0.39 thf(f360,plain,(
% 0.20/0.39 ((q @ sK4) = $false) | (~spl0_1 | ~spl0_6)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f359])).
% 0.20/0.39 thf(f359,plain,(
% 0.20/0.39 ((q @ sK4) = $false) | ($true = $false) | (~spl0_1 | ~spl0_6)),
% 0.20/0.39 inference(forward_demodulation,[],[f357,f257])).
% 0.20/0.39 thf(f357,plain,(
% 0.20/0.39 ((q @ sK4) = $false) | ($true = (p @ sK4)) | ~spl0_1),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f351])).
% 0.20/0.39 thf(f351,plain,(
% 0.20/0.39 ($true = $false) | ((q @ sK4) = $false) | ($true = (p @ sK4)) | ~spl0_1),
% 0.20/0.39 inference(superposition,[],[f174,f235])).
% 0.20/0.39 thf(f174,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ((p @ X1) = $true) | ((q @ X1) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f173])).
% 0.20/0.39 thf(f173,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (q @ X1))) | ((p @ X1) = $true) | ((rel_d @ sK2 @ X1) = $false)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f172])).
% 0.20/0.39 thf(f172,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | (((~ (q @ X1)) | (p @ X1)) = $true)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f167])).
% 0.20/0.39 thf(f167,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ((~ ((~ (q @ X1)) | (p @ X1))) = $false)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f166])).
% 0.20/0.39 thf(f355,plain,(
% 0.20/0.39 ($true = (q @ sK4)) | (~spl0_1 | ~spl0_8)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f347])).
% 0.20/0.39 thf(f347,plain,(
% 0.20/0.39 ($true = (q @ sK4)) | ($true = $false) | (~spl0_1 | ~spl0_8)),
% 0.20/0.39 inference(superposition,[],[f235,f267])).
% 0.20/0.39 thf(f332,plain,(
% 0.20/0.39 ~spl0_2 | ~spl0_3 | ~spl0_4),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f331])).
% 0.20/0.39 thf(f331,plain,(
% 0.20/0.39 $false | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f330])).
% 0.20/0.39 thf(f330,plain,(
% 0.20/0.39 ($true = $false) | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 0.20/0.39 inference(forward_demodulation,[],[f323,f298])).
% 0.20/0.39 thf(f298,plain,(
% 0.20/0.39 ((p @ sK6) = $false) | (~spl0_2 | ~spl0_3)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f297])).
% 0.20/0.39 thf(f297,plain,(
% 0.20/0.39 ($true = $false) | ((p @ sK6) = $false) | (~spl0_2 | ~spl0_3)),
% 0.20/0.39 inference(forward_demodulation,[],[f296,f244])).
% 0.20/0.39 thf(f244,plain,(
% 0.20/0.39 ($false = (q @ sK6)) | ~spl0_3),
% 0.20/0.39 inference(avatar_component_clause,[],[f242])).
% 0.20/0.39 thf(f242,plain,(
% 0.20/0.39 spl0_3 <=> ($false = (q @ sK6))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.39 thf(f296,plain,(
% 0.20/0.39 ((p @ sK6) = $false) | ($true = (q @ sK6)) | ~spl0_2),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f293])).
% 0.20/0.39 thf(f293,plain,(
% 0.20/0.39 ($true = $false) | ((p @ sK6) = $false) | ($true = (q @ sK6)) | ~spl0_2),
% 0.20/0.39 inference(superposition,[],[f239,f171])).
% 0.20/0.39 thf(f239,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK6)) | ~spl0_2),
% 0.20/0.39 inference(avatar_component_clause,[],[f237])).
% 0.20/0.39 thf(f237,plain,(
% 0.20/0.39 spl0_2 <=> ($true = (rel_d @ sK2 @ sK6))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.39 thf(f323,plain,(
% 0.20/0.39 ($true = (p @ sK6)) | (~spl0_2 | ~spl0_4)),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f320])).
% 0.20/0.39 thf(f320,plain,(
% 0.20/0.39 ($true = $false) | ($true = (p @ sK6)) | (~spl0_2 | ~spl0_4)),
% 0.20/0.39 inference(superposition,[],[f248,f239])).
% 0.20/0.39 thf(f278,plain,(
% 0.20/0.39 spl0_8 | spl0_4),
% 0.20/0.39 inference(avatar_split_clause,[],[f192,f247,f266])).
% 0.20/0.39 thf(f192,plain,(
% 0.20/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (p @ X2)) | ((rel_d @ sK2 @ X1) = $false) | ($true = (q @ X1)) | ((rel_d @ sK2 @ X2) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f191])).
% 0.20/0.39 thf(f191,plain,(
% 0.20/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (q @ X1)) | ((rel_d @ sK2 @ X1) = $false) | ($true = (~ (rel_d @ sK2 @ X2))) | ($true = (p @ X2))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f190])).
% 0.20/0.39 thf(f190,plain,(
% 0.20/0.39 ( ! [X2 : $i,X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ($true = ((p @ X2) | (~ (rel_d @ sK2 @ X2)))) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f189])).
% 0.20/0.39 thf(f189,plain,(
% 0.20/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_d @ sK2 @ X1))) | ($true = (q @ X1)) | ($true = ((p @ X2) | (~ (rel_d @ sK2 @ X2))))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f188])).
% 0.20/0.39 thf(f188,plain,(
% 0.20/0.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ X2)) | ($true = (~ (rel_d @ sK2 @ X1))) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(pi_clausification,[],[f187])).
% 0.20/0.39 thf(f187,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))) = $true) | ($true = (~ (rel_d @ sK2 @ X1))) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f186])).
% 0.20/0.39 thf(f186,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | ($true = (q @ X1)) | ($true = (~ (rel_d @ sK2 @ X1)))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f185])).
% 0.20/0.39 thf(f185,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((q @ X1) | (~ (rel_d @ sK2 @ X1)))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f183])).
% 0.20/0.39 thf(f183,plain,(
% 0.20/0.39 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | ($true = ((q @ X1) | (~ (rel_d @ sK2 @ X1))))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f182])).
% 0.20/0.39 thf(f182,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false)) )),
% 0.20/0.39 inference(pi_clausification,[],[f181])).
% 0.20/0.39 thf(f181,plain,(
% 0.20/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false)),
% 0.20/0.39 inference(not_proxy_clausification,[],[f180])).
% 0.20/0.39 thf(f180,plain,(
% 0.20/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false)),
% 0.20/0.39 inference(not_proxy_clausification,[],[f179])).
% 0.20/0.39 thf(f179,plain,(
% 0.20/0.39 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f177])).
% 0.20/0.39 thf(f177,plain,(
% 0.20/0.39 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))))) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f176])).
% 0.20/0.39 thf(f176,plain,(
% 0.20/0.39 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f175])).
% 0.20/0.39 thf(f175,plain,(
% 0.20/0.39 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f159])).
% 0.20/0.39 thf(f159,plain,(
% 0.20/0.39 ($false = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f158])).
% 0.20/0.39 thf(f277,plain,(
% 0.20/0.39 spl0_8 | spl0_10),
% 0.20/0.39 inference(avatar_split_clause,[],[f198,f274,f266])).
% 0.20/0.39 thf(f198,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((rel_d @ sK2 @ X1) = $false) | ($false = (q @ sK3)) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f197])).
% 0.20/0.39 thf(f197,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK2 @ X1))) | ($false = (q @ sK3)) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f195])).
% 0.20/0.39 thf(f195,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = ((q @ sK3) | (~ (rel_d @ sK2 @ sK3)))) | ($true = (~ (rel_d @ sK2 @ X1))) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f194])).
% 0.20/0.39 thf(f194,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((q @ X1) | (~ (rel_d @ sK2 @ X1)))) | ($false = ((q @ sK3) | (~ (rel_d @ sK2 @ sK3))))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f193])).
% 0.20/0.39 thf(f193,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ sK3)) | ($true = ((q @ X1) | (~ (rel_d @ sK2 @ X1))))) )),
% 0.20/0.39 inference(sigma_clausification,[],[f184])).
% 0.20/0.39 thf(f184,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | ($true = ((q @ X1) | (~ (rel_d @ sK2 @ X1))))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f183])).
% 0.20/0.39 thf(f272,plain,(
% 0.20/0.39 spl0_8 | spl0_9),
% 0.20/0.39 inference(avatar_split_clause,[],[f200,f269,f266])).
% 0.20/0.39 thf(f200,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (rel_d @ sK2 @ sK3)) | ((rel_d @ sK2 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f199])).
% 0.20/0.39 thf(f199,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK2 @ X1))) | ($true = (q @ X1)) | ($true = (rel_d @ sK2 @ sK3))) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f196])).
% 0.20/0.39 thf(f196,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((~ (rel_d @ sK2 @ sK3)) = $false) | ($true = (q @ X1)) | ($true = (~ (rel_d @ sK2 @ X1)))) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f195])).
% 0.20/0.39 thf(f264,plain,(
% 0.20/0.39 spl0_4 | spl0_6),
% 0.20/0.39 inference(avatar_split_clause,[],[f212,f255,f247])).
% 0.20/0.39 thf(f212,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = (p @ sK4)) | ((rel_d @ sK2 @ X1) = $false) | ((p @ X1) = $true)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f211])).
% 0.20/0.39 thf(f211,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (~ (rel_d @ sK2 @ X1))) | ($false = (p @ sK4)) | ((p @ X1) = $true)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f210])).
% 0.20/0.39 thf(f210,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = (p @ sK4)) | ($true = ((p @ X1) | (~ (rel_d @ sK2 @ X1))))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f209])).
% 0.20/0.39 thf(f209,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($false = (p @ sK4)) | ($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ X1))) )),
% 0.20/0.39 inference(pi_clausification,[],[f208])).
% 0.20/0.39 thf(f208,plain,(
% 0.20/0.39 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))) = $true) | ($false = (p @ sK4))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f207])).
% 0.20/0.39 thf(f207,plain,(
% 0.20/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | ($false = (p @ sK4))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f205])).
% 0.20/0.39 thf(f205,plain,(
% 0.20/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | ($false = (p @ sK4))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f204])).
% 0.20/0.39 thf(f204,plain,(
% 0.20/0.39 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))) | ($false = (p @ sK4))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f202])).
% 0.20/0.39 thf(f202,plain,(
% 0.20/0.39 (((p @ sK4) | (~ (rel_d @ sK2 @ sK4))) = $false) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f201])).
% 0.20/0.39 thf(f201,plain,(
% 0.20/0.39 ($false = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ sK4)) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))),
% 0.20/0.39 inference(sigma_clausification,[],[f178])).
% 0.20/0.39 thf(f178,plain,(
% 0.20/0.39 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))) = $false) | ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f177])).
% 0.20/0.39 thf(f263,plain,(
% 0.20/0.39 spl0_7 | spl0_6),
% 0.20/0.39 inference(avatar_split_clause,[],[f216,f255,f260])).
% 0.20/0.39 thf(f216,plain,(
% 0.20/0.39 ($false = (p @ sK4)) | ((q @ sK5) = $false)),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f214])).
% 0.20/0.39 thf(f214,plain,(
% 0.20/0.39 ($false = ((q @ sK5) | (~ (rel_d @ sK2 @ sK5)))) | ($false = (p @ sK4))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f213])).
% 0.20/0.39 thf(f213,plain,(
% 0.20/0.39 ($false = (p @ sK4)) | ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ sK5))),
% 0.20/0.39 inference(sigma_clausification,[],[f206])).
% 0.20/0.39 thf(f206,plain,(
% 0.20/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | ($false = (p @ sK4))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f205])).
% 0.20/0.39 thf(f258,plain,(
% 0.20/0.39 spl0_5 | spl0_6),
% 0.20/0.39 inference(avatar_split_clause,[],[f217,f255,f251])).
% 0.20/0.39 thf(f217,plain,(
% 0.20/0.39 ($false = (p @ sK4)) | ((rel_d @ sK2 @ sK5) = $true)),
% 0.20/0.39 inference(not_proxy_clausification,[],[f215])).
% 0.20/0.39 thf(f215,plain,(
% 0.20/0.39 ($false = (p @ sK4)) | ($false = (~ (rel_d @ sK2 @ sK5)))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f214])).
% 0.20/0.39 thf(f249,plain,(
% 0.20/0.39 spl0_4 | spl0_1),
% 0.20/0.39 inference(avatar_split_clause,[],[f226,f233,f247])).
% 0.20/0.39 thf(f226,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (((p @ X1) = $true) | ($true = (rel_d @ sK2 @ sK4)) | ((rel_d @ sK2 @ X1) = $false)) )),
% 0.20/0.39 inference(not_proxy_clausification,[],[f225])).
% 0.20/0.39 thf(f225,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = (rel_d @ sK2 @ sK4)) | ($true = (~ (rel_d @ sK2 @ X1))) | ((p @ X1) = $true)) )),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f224])).
% 0.20/0.39 thf(f224,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((p @ X1) | (~ (rel_d @ sK2 @ X1)))) | ($true = (rel_d @ sK2 @ sK4))) )),
% 0.20/0.39 inference(beta_eta_normalization,[],[f223])).
% 0.20/0.39 thf(f223,plain,(
% 0.20/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ X1)) | ($true = (rel_d @ sK2 @ sK4))) )),
% 0.20/0.39 inference(pi_clausification,[],[f222])).
% 0.20/0.39 thf(f222,plain,(
% 0.20/0.39 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0))))) = $true) | ($true = (rel_d @ sK2 @ sK4))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f221])).
% 0.20/0.39 thf(f221,plain,(
% 0.20/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | ($true = (rel_d @ sK2 @ sK4))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f219])).
% 0.20/0.39 thf(f219,plain,(
% 0.20/0.39 (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false) | ($true = (rel_d @ sK2 @ sK4))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f218])).
% 0.20/0.39 thf(f218,plain,(
% 0.20/0.39 ($false = (~ (rel_d @ sK2 @ sK4))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) = $false)),
% 0.20/0.39 inference(not_proxy_clausification,[],[f203])).
% 0.20/0.39 thf(f203,plain,(
% 0.20/0.39 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_d @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))))))) | ($false = (~ (rel_d @ sK2 @ sK4)))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f202])).
% 0.20/0.39 thf(f245,plain,(
% 0.20/0.39 spl0_1 | spl0_3),
% 0.20/0.39 inference(avatar_split_clause,[],[f230,f242,f233])).
% 0.20/0.39 thf(f230,plain,(
% 0.20/0.39 ($false = (q @ sK6)) | ($true = (rel_d @ sK2 @ sK4))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f228])).
% 0.20/0.39 thf(f228,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK4)) | ($false = ((q @ sK6) | (~ (rel_d @ sK2 @ sK6))))),
% 0.20/0.39 inference(beta_eta_normalization,[],[f227])).
% 0.20/0.39 thf(f227,plain,(
% 0.20/0.39 (((^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0)))) @ sK6) = $false) | ($true = (rel_d @ sK2 @ sK4))),
% 0.20/0.39 inference(sigma_clausification,[],[f220])).
% 0.20/0.39 thf(f220,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK4)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_d @ sK2 @ Y0))))))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f219])).
% 0.20/0.39 thf(f240,plain,(
% 0.20/0.39 spl0_1 | spl0_2),
% 0.20/0.39 inference(avatar_split_clause,[],[f231,f237,f233])).
% 0.20/0.39 thf(f231,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK4)) | ($true = (rel_d @ sK2 @ sK6))),
% 0.20/0.39 inference(not_proxy_clausification,[],[f229])).
% 0.20/0.39 thf(f229,plain,(
% 0.20/0.39 ($true = (rel_d @ sK2 @ sK4)) | ($false = (~ (rel_d @ sK2 @ sK6)))),
% 0.20/0.39 inference(binary_proxy_clausification,[],[f228])).
% 0.20/0.39 % SZS output end Proof for theBenchmark
% 0.20/0.39 % (28187)------------------------------
% 0.20/0.39 % (28187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (28187)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (28187)Memory used [KB]: 5884
% 0.20/0.39 % (28187)Time elapsed: 0.021 s
% 0.20/0.39 % (28187)Instructions burned: 25 (million)
% 0.20/0.39 % (28187)------------------------------
% 0.20/0.39 % (28187)------------------------------
% 0.20/0.39 % (28184)Success in time 0.031 s
% 0.20/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------