TSTP Solution File: SYO469^5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO469^5 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n016.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 09:05:08 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO469^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14 % 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
% 0.14/0.34 % Computer : n016.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
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 08:57:22 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (2389)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 % (2391)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)
% 0.14/0.38 % (2390)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)
% 0.14/0.38 % (2392)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (2392)Instruction limit reached!
% 0.14/0.38 % (2392)------------------------------
% 0.14/0.38 % (2392)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (2392)Termination reason: Unknown
% 0.14/0.38 % (2392)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (2392)Memory used [KB]: 1023
% 0.14/0.38 % (2392)Time elapsed: 0.003 s
% 0.14/0.38 % (2392)Instructions burned: 2 (million)
% 0.14/0.38 % (2392)------------------------------
% 0.14/0.38 % (2392)------------------------------
% 0.14/0.38 % (2390)Instruction limit reached!
% 0.14/0.38 % (2390)------------------------------
% 0.14/0.38 % (2390)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (2390)Termination reason: Unknown
% 0.14/0.38 % (2390)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (2390)Memory used [KB]: 1023
% 0.14/0.38 % (2390)Time elapsed: 0.005 s
% 0.14/0.38 % (2390)Instructions burned: 4 (million)
% 0.14/0.38 % (2390)------------------------------
% 0.14/0.38 % (2390)------------------------------
% 0.14/0.38 % (2394)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)
% 0.14/0.38 % (2396)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)
% 0.14/0.38 % (2393)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)
% 0.14/0.38 % (2395)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (2393)Instruction limit reached!
% 0.14/0.38 % (2393)------------------------------
% 0.14/0.38 % (2393)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (2393)Termination reason: Unknown
% 0.14/0.38 % (2393)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (2393)Memory used [KB]: 1023
% 0.14/0.38 % (2393)Time elapsed: 0.004 s
% 0.14/0.38 % (2393)Instructions burned: 2 (million)
% 0.14/0.38 % (2393)------------------------------
% 0.14/0.38 % (2393)------------------------------
% 0.14/0.38 % (2391)Instruction limit reached!
% 0.14/0.38 % (2391)------------------------------
% 0.14/0.38 % (2391)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (2391)Termination reason: Unknown
% 0.14/0.38 % (2391)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (2391)Memory used [KB]: 5756
% 0.14/0.38 % (2391)Time elapsed: 0.019 s
% 0.14/0.38 % (2391)Instructions burned: 27 (million)
% 0.14/0.38 % (2391)------------------------------
% 0.14/0.38 % (2391)------------------------------
% 0.14/0.39 % (2389)First to succeed.
% 0.14/0.39 % (2396)Instruction limit reached!
% 0.14/0.39 % (2396)------------------------------
% 0.14/0.39 % (2396)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2396)Termination reason: Unknown
% 0.14/0.39 % (2396)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (2396)Memory used [KB]: 1023
% 0.14/0.39 % (2396)Time elapsed: 0.006 s
% 0.14/0.39 % (2396)Instructions burned: 4 (million)
% 0.14/0.39 % (2396)------------------------------
% 0.14/0.39 % (2396)------------------------------
% 0.14/0.39 % (2394)Refutation not found, incomplete strategy
% 0.14/0.39 % (2394)------------------------------
% 0.14/0.39 % (2394)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2389)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% 0.14/0.39 thf(type_def_5, type, mu: $tType).
% 0.14/0.39 thf(func_def_0, type, mu: $tType).
% 0.14/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.39 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.14/0.39 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.39 thf(func_def_36, type, p: $i > $o).
% 0.14/0.39 thf(func_def_37, type, q: $i > $o).
% 0.14/0.39 thf(func_def_57, type, sK4: $i > $i).
% 0.14/0.39 thf(f422,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(avatar_sat_refutation,[],[f336,f343,f376,f384,f392,f421])).
% 0.14/0.39 thf(f421,plain,(
% 0.14/0.39 spl0_6 | ~spl0_9),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f420])).
% 0.14/0.39 thf(f420,plain,(
% 0.14/0.39 $false | (spl0_6 | ~spl0_9)),
% 0.14/0.39 inference(subsumption_resolution,[],[f413,f314])).
% 0.14/0.39 thf(f314,plain,(
% 0.14/0.39 ($false != (rel_s4 @ sK1 @ sK2)) | spl0_6),
% 0.14/0.39 inference(avatar_component_clause,[],[f313])).
% 0.14/0.39 thf(f313,plain,(
% 0.14/0.39 spl0_6 <=> ($false = (rel_s4 @ sK1 @ sK2))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.14/0.39 thf(f413,plain,(
% 0.14/0.39 ($false = (rel_s4 @ sK1 @ sK2)) | ~spl0_9),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f409])).
% 0.14/0.39 thf(f409,plain,(
% 0.14/0.39 ($true = $false) | ($false = (rel_s4 @ sK1 @ sK2)) | ~spl0_9),
% 0.14/0.39 inference(superposition,[],[f172,f405])).
% 0.14/0.39 thf(f405,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (($false = (rel_s4 @ X0 @ sK3)) | ((rel_s4 @ sK1 @ X0) = $false)) ) | ~spl0_9),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f403])).
% 0.14/0.39 thf(f403,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (($true = $false) | ($false = (rel_s4 @ X0 @ sK3)) | ((rel_s4 @ sK1 @ X0) = $false)) ) | ~spl0_9),
% 0.14/0.39 inference(superposition,[],[f199,f328])).
% 0.14/0.39 thf(f328,plain,(
% 0.14/0.39 ((rel_s4 @ sK1 @ sK3) = $false) | ~spl0_9),
% 0.14/0.39 inference(avatar_component_clause,[],[f326])).
% 0.14/0.39 thf(f326,plain,(
% 0.14/0.39 spl0_9 <=> ((rel_s4 @ sK1 @ sK3) = $false)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.14/0.39 thf(f199,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X3)) | ((rel_s4 @ X1 @ X2) = $false) | ((rel_s4 @ X2 @ X3) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f198])).
% 0.14/0.39 thf(f198,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((rel_s4 @ X1 @ X2) & (rel_s4 @ X2 @ X3))) | ($true = (rel_s4 @ X1 @ X3))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f197])).
% 0.14/0.39 thf(f197,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s4 @ X1 @ X2) & (rel_s4 @ X2 @ X3)) => (rel_s4 @ X1 @ X3)))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f196])).
% 0.14/0.39 thf(f196,plain,(
% 0.14/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s4 @ X1 @ X2) & (rel_s4 @ X2 @ Y0)) => (rel_s4 @ X1 @ Y0))) @ X3) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f195])).
% 0.14/0.39 thf(f195,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ X1 @ X2) & (rel_s4 @ X2 @ Y0)) => (rel_s4 @ X1 @ Y0)))) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f194])).
% 0.14/0.39 thf(f194,plain,(
% 0.14/0.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ X1 @ Y1))))) @ X2))) )),
% 0.14/0.39 inference(pi_clausification,[],[f193])).
% 0.14/0.39 thf(f193,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ X1 @ Y1)))))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f192])).
% 0.14/0.39 thf(f192,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y1) & (rel_s4 @ Y1 @ Y2)) => (rel_s4 @ Y0 @ Y2))))))) @ X1) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f191])).
% 0.14/0.39 thf(f191,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y1) & (rel_s4 @ Y1 @ Y2)) => (rel_s4 @ Y0 @ Y2)))))))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.39 thf(f156,plain,(
% 0.14/0.39 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ rel_s4) = $true)),
% 0.14/0.39 inference(definition_unfolding,[],[f140,f141])).
% 0.14/0.39 thf(f141,plain,(
% 0.14/0.39 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f75])).
% 0.14/0.39 thf(f75,plain,(
% 0.14/0.39 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f74])).
% 0.14/0.39 thf(f74,plain,(
% 0.14/0.39 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X1) & (X0 @ X3 @ X2)) => (X0 @ X3 @ X1)))))),
% 0.14/0.39 inference(rectify,[],[f21])).
% 0.14/0.39 thf(f21,axiom,(
% 0.14/0.39 (mtransitive = (^[X6 : $i > $i > $o] : (! [X10,X9,X8] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.14/0.39 thf(f140,plain,(
% 0.14/0.39 ((mtransitive @ rel_s4) = $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f97])).
% 0.14/0.39 thf(f97,plain,(
% 0.14/0.39 ((mtransitive @ rel_s4) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f96])).
% 0.14/0.39 thf(f96,plain,(
% 0.14/0.39 (mtransitive @ rel_s4)),
% 0.14/0.39 inference(rectify,[],[f35])).
% 0.14/0.39 thf(f35,axiom,(
% 0.14/0.39 (mtransitive @ rel_s4)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.14/0.39 thf(f172,plain,(
% 0.14/0.39 ($true = (rel_s4 @ sK2 @ sK3))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f170])).
% 0.14/0.39 thf(f170,plain,(
% 0.14/0.39 ($false = (~ (rel_s4 @ sK2 @ sK3)))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.39 thf(f169,plain,(
% 0.14/0.39 (((q @ sK3) | (~ (rel_s4 @ sK2 @ sK3))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f168])).
% 0.14/0.39 thf(f168,plain,(
% 0.14/0.39 ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK2 @ Y0)))) @ sK3))),
% 0.14/0.39 inference(sigma_clausification,[],[f167])).
% 0.14/0.39 thf(f167,plain,(
% 0.14/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK2 @ Y0))))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f165])).
% 0.14/0.39 thf(f165,plain,(
% 0.14/0.39 (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK2 @ Y0))))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f163])).
% 0.14/0.39 thf(f163,plain,(
% 0.14/0.39 ($false = (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK2 @ Y0))))))) | (~ (rel_s4 @ sK1 @ sK2))))),
% 0.14/0.39 inference(beta_eta_normalization,[],[f162])).
% 0.14/0.39 thf(f162,plain,(
% 0.14/0.39 (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f161])).
% 0.14/0.39 thf(f161,plain,(
% 0.14/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.39 thf(f159,plain,(
% 0.14/0.39 (((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0))))))) = $false)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.39 thf(f158,plain,(
% 0.14/0.39 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.14/0.39 inference(sigma_clausification,[],[f157])).
% 0.14/0.39 thf(f157,plain,(
% 0.14/0.39 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f155])).
% 0.14/0.39 thf(f155,plain,(
% 0.14/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ p) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ q))))) != $true)),
% 0.14/0.39 inference(definition_unfolding,[],[f129,f134,f145,f117,f145,f117,f117,f145,f117,f117])).
% 0.14/0.39 thf(f117,plain,(
% 0.14/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f50])).
% 0.14/0.39 thf(f50,plain,(
% 0.14/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f49])).
% 0.14/0.39 thf(f49,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))) = mbox_s4)),
% 0.14/0.39 inference(rectify,[],[f32])).
% 0.14/0.39 thf(f32,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s4 @ X2 @ X7) | (X3 @ X7)))) = mbox_s4)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.39 thf(f145,plain,(
% 0.14/0.39 (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)))))),
% 0.14/0.39 inference(definition_unfolding,[],[f109,f121,f123])).
% 0.14/0.39 thf(f123,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f44])).
% 0.14/0.39 thf(f44,plain,(
% 0.14/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.39 inference(fool_elimination,[],[f43])).
% 0.14/0.39 thf(f43,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.14/0.39 inference(rectify,[],[f3])).
% 0.14/0.39 thf(f3,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.39 thf(f121,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f62])).
% 0.14/0.39 thf(f62,plain,(
% 0.14/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f61])).
% 0.14/0.39 thf(f61,plain,(
% 0.14/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.14/0.39 inference(rectify,[],[f4])).
% 0.14/0.39 thf(f4,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.39 thf(f109,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f99])).
% 0.14/0.39 thf(f99,plain,(
% 0.14/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f98])).
% 0.14/0.39 thf(f98,plain,(
% 0.14/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.39 inference(rectify,[],[f6])).
% 0.14/0.39 thf(f6,axiom,(
% 0.14/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.39 thf(f134,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(cnf_transformation,[],[f79])).
% 0.14/0.39 thf(f79,plain,(
% 0.14/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.39 inference(fool_elimination,[],[f78])).
% 0.14/0.39 thf(f78,plain,(
% 0.14/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.39 inference(rectify,[],[f28])).
% 0.14/0.39 thf(f28,axiom,(
% 0.14/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.39 thf(f129,plain,(
% 0.14/0.39 ((mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ q)) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ q))))) != $true)),
% 0.14/0.39 inference(cnf_transformation,[],[f107])).
% 0.14/0.39 thf(f107,plain,(
% 0.14/0.39 ((mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ q)) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ q))))) != $true)),
% 0.14/0.39 inference(flattening,[],[f64])).
% 0.14/0.39 thf(f64,plain,(
% 0.14/0.39 ~((mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ q)) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ q))))) = $true)),
% 0.14/0.39 inference(fool_elimination,[],[f63])).
% 0.14/0.39 thf(f63,plain,(
% 0.14/0.39 ~(mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ q)) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ q)))))),
% 0.14/0.39 inference(rectify,[],[f37])).
% 0.14/0.39 thf(f37,negated_conjecture,(
% 0.14/0.39 ~(mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ q)) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ q)))))),
% 0.14/0.39 inference(negated_conjecture,[],[f36])).
% 0.14/0.39 thf(f36,conjecture,(
% 0.14/0.39 (mvalid @ (mimplies @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ q)) @ (mbox_s4 @ (mimplies @ (mbox_s4 @ p) @ (mbox_s4 @ q)))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.39 thf(f392,plain,(
% 0.14/0.39 ~spl0_8 | ~spl0_11),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f391])).
% 0.14/0.39 thf(f391,plain,(
% 0.14/0.39 $false | (~spl0_8 | ~spl0_11)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f387])).
% 0.14/0.39 thf(f387,plain,(
% 0.14/0.39 ($true = $false) | (~spl0_8 | ~spl0_11)),
% 0.14/0.39 inference(superposition,[],[f373,f324])).
% 0.14/0.39 thf(f324,plain,(
% 0.14/0.39 ($true = (p @ (sK4 @ sK3))) | ~spl0_8),
% 0.14/0.39 inference(avatar_component_clause,[],[f322])).
% 0.14/0.39 thf(f322,plain,(
% 0.14/0.39 spl0_8 <=> ($true = (p @ (sK4 @ sK3)))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.14/0.39 thf(f373,plain,(
% 0.14/0.39 ((p @ (sK4 @ sK3)) = $false) | ~spl0_11),
% 0.14/0.39 inference(avatar_component_clause,[],[f371])).
% 0.14/0.39 thf(f371,plain,(
% 0.14/0.39 spl0_11 <=> ((p @ (sK4 @ sK3)) = $false)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.14/0.39 thf(f384,plain,(
% 0.14/0.39 ~spl0_6),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f383])).
% 0.14/0.39 thf(f383,plain,(
% 0.14/0.39 $false | ~spl0_6),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f377])).
% 0.14/0.39 thf(f377,plain,(
% 0.14/0.39 ($true = $false) | ~spl0_6),
% 0.14/0.39 inference(superposition,[],[f315,f178])).
% 0.14/0.39 thf(f178,plain,(
% 0.14/0.39 ($true = (rel_s4 @ sK1 @ sK2))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f164])).
% 0.14/0.39 thf(f164,plain,(
% 0.14/0.39 ($false = (~ (rel_s4 @ sK1 @ sK2)))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f163])).
% 0.14/0.39 thf(f315,plain,(
% 0.14/0.39 ($false = (rel_s4 @ sK1 @ sK2)) | ~spl0_6),
% 0.14/0.39 inference(avatar_component_clause,[],[f313])).
% 0.14/0.39 thf(f376,plain,(
% 0.14/0.39 spl0_6 | spl0_11 | spl0_7),
% 0.14/0.39 inference(avatar_split_clause,[],[f375,f318,f371,f313])).
% 0.14/0.39 thf(f318,plain,(
% 0.14/0.39 spl0_7 <=> ($true = (q @ sK3))),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.14/0.39 thf(f375,plain,(
% 0.14/0.39 ((p @ (sK4 @ sK3)) = $false) | ($false = (rel_s4 @ sK1 @ sK2)) | spl0_7),
% 0.14/0.39 inference(subsumption_resolution,[],[f360,f319])).
% 0.14/0.39 thf(f319,plain,(
% 0.14/0.39 ($true != (q @ sK3)) | spl0_7),
% 0.14/0.39 inference(avatar_component_clause,[],[f318])).
% 0.14/0.39 thf(f360,plain,(
% 0.14/0.39 ($false = (rel_s4 @ sK1 @ sK2)) | ((p @ (sK4 @ sK3)) = $false) | ($true = (q @ sK3))),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f354])).
% 0.14/0.39 thf(f354,plain,(
% 0.14/0.39 ((p @ (sK4 @ sK3)) = $false) | ($true = $false) | ($false = (rel_s4 @ sK1 @ sK2)) | ($true = (q @ sK3))),
% 0.14/0.39 inference(superposition,[],[f172,f247])).
% 0.14/0.39 thf(f247,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s4 @ X1 @ X0)) | ((p @ (sK4 @ X0)) = $false) | ((rel_s4 @ sK1 @ X1) = $false) | ($true = (q @ X0))) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f240])).
% 0.14/0.39 thf(f240,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = (rel_s4 @ X1 @ X0)) | ((p @ (sK4 @ X0)) = $false) | ($true = (q @ X0)) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.39 inference(superposition,[],[f199,f189])).
% 0.14/0.39 thf(f189,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((q @ X1) = $true) | ($false = (p @ (sK4 @ X1)))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f187])).
% 0.14/0.39 thf(f187,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($false = ((p @ (sK4 @ X1)) | (~ (rel_s4 @ X1 @ (sK4 @ X1))))) | ((q @ X1) = $true)) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f186])).
% 0.14/0.39 thf(f186,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((q @ X1) = $true) | ((rel_s4 @ sK1 @ X1) = $false) | (((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK4 @ X1)) = $false)) )),
% 0.14/0.39 inference(sigma_clausification,[],[f185])).
% 0.14/0.39 thf(f185,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((q @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.39 thf(f184,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((q @ X1) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f183])).
% 0.14/0.39 thf(f183,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = ((q @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f182])).
% 0.14/0.39 thf(f182,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((~ (rel_s4 @ sK1 @ X1)) = $true) | ($true = ((q @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f181])).
% 0.14/0.39 thf(f181,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (((q @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | (~ (rel_s4 @ sK1 @ X1))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f180])).
% 0.14/0.39 thf(f180,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.39 inference(pi_clausification,[],[f179])).
% 0.14/0.39 thf(f179,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f160])).
% 0.14/0.39 thf(f160,plain,(
% 0.14/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.39 thf(f343,plain,(
% 0.14/0.39 ~spl0_7),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f342])).
% 0.14/0.39 thf(f342,plain,(
% 0.14/0.39 $false | ~spl0_7),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f339])).
% 0.14/0.39 thf(f339,plain,(
% 0.14/0.39 ($true = $false) | ~spl0_7),
% 0.14/0.39 inference(superposition,[],[f171,f320])).
% 0.14/0.39 thf(f320,plain,(
% 0.14/0.39 ($true = (q @ sK3)) | ~spl0_7),
% 0.14/0.39 inference(avatar_component_clause,[],[f318])).
% 0.14/0.39 thf(f171,plain,(
% 0.14/0.39 ($false = (q @ sK3))),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.39 thf(f336,plain,(
% 0.14/0.39 spl0_8 | spl0_7 | spl0_9),
% 0.14/0.39 inference(avatar_split_clause,[],[f301,f326,f318,f322])).
% 0.14/0.39 thf(f301,plain,(
% 0.14/0.39 ($true = (p @ (sK4 @ sK3))) | ($true = (q @ sK3)) | ((rel_s4 @ sK1 @ sK3) = $false)),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f297])).
% 0.14/0.39 thf(f297,plain,(
% 0.14/0.39 ($true = (q @ sK3)) | ($true = (p @ (sK4 @ sK3))) | ((rel_s4 @ sK1 @ sK3) = $false) | ($true = $false)),
% 0.14/0.39 inference(superposition,[],[f260,f190])).
% 0.14/0.39 thf(f190,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ (sK4 @ X1))) | ((q @ X1) = $true) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f188])).
% 0.14/0.39 thf(f188,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((~ (rel_s4 @ X1 @ (sK4 @ X1))) = $false) | ((q @ X1) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f187])).
% 0.14/0.39 thf(f260,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (((rel_s4 @ sK3 @ X0) = $false) | ((p @ X0) = $true)) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f254])).
% 0.14/0.39 thf(f254,plain,(
% 0.14/0.39 ( ! [X0 : $i] : (((p @ X0) = $true) | ((rel_s4 @ sK3 @ X0) = $false) | ($true = $false)) )),
% 0.14/0.39 inference(superposition,[],[f172,f248])).
% 0.14/0.39 thf(f248,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s4 @ sK2 @ X1)) | ((p @ X0) = $true) | ($false = (rel_s4 @ X1 @ X0))) )),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f239])).
% 0.14/0.39 thf(f239,plain,(
% 0.14/0.39 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s4 @ sK2 @ X1)) | ($true = $false) | ((p @ X0) = $true) | ($false = (rel_s4 @ X1 @ X0))) )),
% 0.14/0.39 inference(superposition,[],[f199,f177])).
% 0.14/0.39 thf(f177,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = (rel_s4 @ sK2 @ X1)) | ($true = (p @ X1))) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f176])).
% 0.14/0.39 thf(f176,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (p @ X1)) | ((~ (rel_s4 @ sK2 @ X1)) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f175])).
% 0.14/0.39 thf(f175,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((p @ X1) | (~ (rel_s4 @ sK2 @ X1))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f174])).
% 0.14/0.39 thf(f174,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK2 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.39 inference(pi_clausification,[],[f173])).
% 0.14/0.39 thf(f173,plain,(
% 0.14/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK2 @ Y0))))))),
% 0.14/0.39 inference(not_proxy_clausification,[],[f166])).
% 0.14/0.39 thf(f166,plain,(
% 0.14/0.39 ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s4 @ sK2 @ Y0)))))) = $false)),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f165])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (2389)------------------------------
% 0.14/0.39 % (2389)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (2389)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (2389)Memory used [KB]: 5756
% 0.14/0.39 % (2389)Time elapsed: 0.024 s
% 0.14/0.39 % (2389)Instructions burned: 28 (million)
% 0.14/0.39 % (2389)------------------------------
% 0.14/0.39 % (2389)------------------------------
% 0.14/0.39 % (2388)Success in time 0.036 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------