TSTP Solution File: SYO458^4 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO458^4 : 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 : n032.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 09:04:46 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
% 0.03/0.13 % Problem : SYO458^4 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n032.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 09:00:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.38 % (24981)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.38 % (24977)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)
% 0.20/0.38 % (24976)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)
% 0.20/0.38 % (24980)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)
% 0.20/0.38 % (24978)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.38 % (24979)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)
% 0.20/0.38 % (24982)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)
% 0.20/0.38 % (24975)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.38 % (24978)Instruction limit reached!
% 0.20/0.38 % (24978)------------------------------
% 0.20/0.38 % (24978)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (24978)Termination reason: Unknown
% 0.20/0.38 % (24979)Instruction limit reached!
% 0.20/0.38 % (24979)------------------------------
% 0.20/0.38 % (24979)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (24978)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (24978)Memory used [KB]: 1023
% 0.20/0.38 % (24978)Time elapsed: 0.003 s
% 0.20/0.38 % (24978)Instructions burned: 2 (million)
% 0.20/0.38 % (24978)------------------------------
% 0.20/0.38 % (24978)------------------------------
% 0.20/0.38 % (24979)Termination reason: Unknown
% 0.20/0.38 % (24979)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (24979)Memory used [KB]: 1023
% 0.20/0.38 % (24979)Time elapsed: 0.003 s
% 0.20/0.38 % (24979)Instructions burned: 2 (million)
% 0.20/0.38 % (24979)------------------------------
% 0.20/0.38 % (24979)------------------------------
% 0.20/0.38 % (24982)Instruction limit reached!
% 0.20/0.38 % (24982)------------------------------
% 0.20/0.38 % (24982)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (24982)Termination reason: Unknown
% 0.20/0.38 % (24982)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (24982)Memory used [KB]: 1023
% 0.20/0.38 % (24982)Time elapsed: 0.003 s
% 0.20/0.38 % (24982)Instructions burned: 3 (million)
% 0.20/0.38 % (24982)------------------------------
% 0.20/0.38 % (24982)------------------------------
% 0.20/0.38 % (24976)Instruction limit reached!
% 0.20/0.38 % (24976)------------------------------
% 0.20/0.38 % (24976)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (24976)Termination reason: Unknown
% 0.20/0.38 % (24976)Termination phase: shuffling
% 0.20/0.38
% 0.20/0.38 % (24976)Memory used [KB]: 1023
% 0.20/0.38 % (24976)Time elapsed: 0.004 s
% 0.20/0.38 % (24976)Instructions burned: 4 (million)
% 0.20/0.38 % (24976)------------------------------
% 0.20/0.38 % (24976)------------------------------
% 0.20/0.39 % (24980)First to succeed.
% 0.20/0.39 % (24981)Also succeeded, but the first one will report.
% 0.20/0.39 % (24977)Also succeeded, but the first one will report.
% 0.20/0.39 % (24980)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_b: $i > $i > $o).
% 0.20/0.39 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.20/0.39 thf(func_def_35, type, mdia_b: ($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(f204,plain,(
% 0.20/0.39 $false),
% 0.20/0.39 inference(avatar_sat_refutation,[],[f176,f186,f202])).
% 0.20/0.39 thf(f202,plain,(
% 0.20/0.39 ~spl0_3),
% 0.20/0.39 inference(avatar_contradiction_clause,[],[f201])).
% 0.20/0.39 thf(f201,plain,(
% 0.20/0.39 $false | ~spl0_3),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f200])).
% 0.20/0.39 thf(f200,plain,(
% 0.20/0.39 ($true = $false) | ~spl0_3),
% 0.20/0.39 inference(forward_demodulation,[],[f189,f169])).
% 0.20/0.39 thf(f169,plain,(
% 0.20/0.39 ($false = (p @ sK2)) | ~spl0_3),
% 0.20/0.39 inference(avatar_component_clause,[],[f167])).
% 0.20/0.39 thf(f167,plain,(
% 0.20/0.39 spl0_3 <=> ($false = (p @ sK2))),
% 0.20/0.39 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.39 thf(f189,plain,(
% 0.20/0.39 ($true = (p @ sK2))),
% 0.20/0.39 inference(trivial_inequality_removal,[],[f187])).
% 0.20/0.39 thf(f187,plain,(
% 0.20/0.39 ($true = $false) | ($true = (p @ sK2))),
% 0.20/0.39 inference(superposition,[],[f156,f130])).
% 0.20/0.39 thf(f130,plain,(
% 0.20/0.39 ($true = (rel_b @ sK1 @ sK2))),
% 0.20/0.40 inference(not_proxy_clausification,[],[f129])).
% 0.20/0.40 thf(f129,plain,(
% 0.20/0.40 ($false = (~ (rel_b @ sK1 @ sK2)))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f127])).
% 0.20/0.40 thf(f127,plain,(
% 0.20/0.40 (((~ (rel_b @ sK1 @ sK2)) | (~ ((~ ((p @ sK2) | (~ (q @ sK2)))) | (~ ((q @ sK2) | (~ (p @ sK2))))))) = $false)),
% 0.20/0.40 inference(beta_eta_normalization,[],[f126])).
% 0.20/0.40 thf(f126,plain,(
% 0.20/0.40 ($false = ((^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ ((q @ Y0) | (~ (p @ Y0)))))))) @ sK2))),
% 0.20/0.40 inference(sigma_clausification,[],[f125])).
% 0.20/0.40 thf(f125,plain,(
% 0.20/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ ((q @ Y0) | (~ (p @ Y0))))))))) = $false)),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f123])).
% 0.20/0.40 thf(f123,plain,(
% 0.20/0.40 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (~ ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ ((q @ Y0) | (~ (p @ Y0))))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (q @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (p @ Y0))))))))),
% 0.20/0.40 inference(beta_eta_normalization,[],[f122])).
% 0.20/0.40 thf(f122,plain,(
% 0.20/0.40 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ ((q @ Y1) | (~ (p @ Y1))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (q @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1)))))))) @ sK1))),
% 0.20/0.40 inference(sigma_clausification,[],[f121])).
% 0.20/0.40 thf(f121,plain,(
% 0.20/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ ((q @ Y1) | (~ (p @ Y1))))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (q @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))),
% 0.20/0.40 inference(boolean_simplification,[],[f120])).
% 0.20/0.40 thf(f120,plain,(
% 0.20/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (~ ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ ((q @ Y1) | (~ (p @ Y1))))))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (q @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_b @ Y0 @ Y1)) | (p @ Y1))))))))))))),
% 0.20/0.40 inference(beta_eta_normalization,[],[f119])).
% 0.20/0.40 thf(f119,plain,(
% 0.20/0.40 ($true != ((^[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 > $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)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ p @ q)))))),
% 0.20/0.40 inference(definition_unfolding,[],[f115,f110,f117,f116,f112,f112,f112,f118])).
% 0.20/0.40 thf(f118,plain,(
% 0.20/0.40 (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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.20/0.40 inference(definition_unfolding,[],[f111,f116,f117,f117])).
% 0.20/0.40 thf(f111,plain,(
% 0.20/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.40 inference(cnf_transformation,[],[f82])).
% 0.20/0.40 thf(f82,plain,(
% 0.20/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.40 inference(fool_elimination,[],[f81])).
% 0.20/0.40 thf(f81,plain,(
% 0.20/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.20/0.40 inference(rectify,[],[f8])).
% 0.20/0.40 thf(f8,axiom,(
% 0.20/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.20/0.40 thf(f112,plain,(
% 0.20/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.40 inference(cnf_transformation,[],[f40])).
% 0.20/0.40 thf(f40,plain,(
% 0.20/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_b @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.40 inference(fool_elimination,[],[f39])).
% 0.20/0.40 thf(f39,plain,(
% 0.20/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_b @ X1 @ X2)))) = mbox_b)),
% 0.20/0.40 inference(rectify,[],[f32])).
% 0.20/0.40 thf(f32,axiom,(
% 0.20/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_b @ X2 @ X7)))) = mbox_b)),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_b)).
% 0.20/0.40 thf(f116,plain,(
% 0.20/0.40 (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)))))))),
% 0.20/0.40 inference(definition_unfolding,[],[f113,f109,f114,f109,f109])).
% 0.20/0.40 thf(f114,plain,(
% 0.20/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.40 inference(cnf_transformation,[],[f53])).
% 0.20/0.40 thf(f53,plain,(
% 0.20/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.40 inference(fool_elimination,[],[f52])).
% 0.20/0.40 thf(f52,plain,(
% 0.20/0.40 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.20/0.40 inference(rectify,[],[f4])).
% 0.20/0.40 thf(f4,axiom,(
% 0.20/0.40 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.20/0.40 thf(f109,plain,(
% 0.20/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.40 inference(cnf_transformation,[],[f94])).
% 0.20/0.40 thf(f94,plain,(
% 0.20/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.40 inference(fool_elimination,[],[f93])).
% 0.20/0.40 thf(f93,plain,(
% 0.20/0.40 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.20/0.40 inference(rectify,[],[f3])).
% 0.20/0.40 thf(f3,axiom,(
% 0.20/0.40 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.20/0.40 thf(f113,plain,(
% 0.20/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.40 inference(cnf_transformation,[],[f80])).
% 0.20/0.40 thf(f80,plain,(
% 0.20/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.40 inference(fool_elimination,[],[f79])).
% 0.20/0.40 thf(f79,plain,(
% 0.20/0.40 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.20/0.40 inference(rectify,[],[f5])).
% 0.20/0.40 thf(f5,axiom,(
% 0.20/0.40 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.20/0.40 thf(f117,plain,(
% 0.20/0.40 (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)))))),
% 0.20/0.40 inference(definition_unfolding,[],[f108,f114,f109])).
% 0.20/0.40 thf(f108,plain,(
% 0.20/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.40 inference(cnf_transformation,[],[f102])).
% 0.20/0.40 thf(f102,plain,(
% 0.20/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.40 inference(fool_elimination,[],[f101])).
% 0.20/0.40 thf(f101,plain,(
% 0.20/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.20/0.40 inference(rectify,[],[f6])).
% 0.20/0.40 thf(f6,axiom,(
% 0.20/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.40 thf(f110,plain,(
% 0.20/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.40 inference(cnf_transformation,[],[f57])).
% 0.20/0.40 thf(f57,plain,(
% 0.20/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.40 inference(fool_elimination,[],[f56])).
% 0.20/0.40 thf(f56,plain,(
% 0.20/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.40 inference(rectify,[],[f28])).
% 0.20/0.40 thf(f28,axiom,(
% 0.20/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.40 thf(f115,plain,(
% 0.20/0.40 ((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ q)) @ (mbox_b @ (mequiv @ p @ q)))) != $true)),
% 0.20/0.40 inference(cnf_transformation,[],[f107])).
% 0.20/0.40 thf(f107,plain,(
% 0.20/0.40 ((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ q)) @ (mbox_b @ (mequiv @ p @ q)))) != $true)),
% 0.20/0.40 inference(flattening,[],[f78])).
% 0.20/0.40 thf(f78,plain,(
% 0.20/0.40 ~((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ q)) @ (mbox_b @ (mequiv @ p @ q)))) = $true)),
% 0.20/0.40 inference(fool_elimination,[],[f77])).
% 0.20/0.40 thf(f77,plain,(
% 0.20/0.40 ~(mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ q)) @ (mbox_b @ (mequiv @ p @ q))))),
% 0.20/0.40 inference(rectify,[],[f37])).
% 0.20/0.40 thf(f37,negated_conjecture,(
% 0.20/0.40 ~(mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ q)) @ (mbox_b @ (mequiv @ p @ q))))),
% 0.20/0.40 inference(negated_conjecture,[],[f36])).
% 0.20/0.40 thf(f36,conjecture,(
% 0.20/0.40 (mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ q)) @ (mbox_b @ (mequiv @ p @ q))))),
% 0.20/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.20/0.40 thf(f156,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($true = (p @ X1))) )),
% 0.20/0.40 inference(not_proxy_clausification,[],[f155])).
% 0.20/0.40 thf(f155,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = (p @ X1)) | ($true = (~ (rel_b @ sK1 @ X1)))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f154])).
% 0.20/0.40 thf(f154,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_b @ sK1 @ X1)) | (p @ X1)))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f153])).
% 0.20/0.40 thf(f153,plain,(
% 0.20/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (p @ Y0))) @ X1) = $true)) )),
% 0.20/0.40 inference(pi_clausification,[],[f152])).
% 0.20/0.40 thf(f152,plain,(
% 0.20/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (p @ Y0)))))),
% 0.20/0.40 inference(not_proxy_clausification,[],[f145])).
% 0.20/0.40 thf(f145,plain,(
% 0.20/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (p @ Y0))))) = $false)),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f124])).
% 0.20/0.40 thf(f124,plain,(
% 0.20/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (q @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (p @ Y0)))))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f123])).
% 0.20/0.40 thf(f186,plain,(
% 0.20/0.40 ~spl0_4),
% 0.20/0.40 inference(avatar_contradiction_clause,[],[f185])).
% 0.20/0.40 thf(f185,plain,(
% 0.20/0.40 $false | ~spl0_4),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f184])).
% 0.20/0.40 thf(f184,plain,(
% 0.20/0.40 ($true = $false) | ~spl0_4),
% 0.20/0.40 inference(forward_demodulation,[],[f179,f174])).
% 0.20/0.40 thf(f174,plain,(
% 0.20/0.40 ((q @ sK2) = $false) | ~spl0_4),
% 0.20/0.40 inference(avatar_component_clause,[],[f172])).
% 0.20/0.40 thf(f172,plain,(
% 0.20/0.40 spl0_4 <=> ((q @ sK2) = $false)),
% 0.20/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.40 thf(f179,plain,(
% 0.20/0.40 ((q @ sK2) = $true)),
% 0.20/0.40 inference(trivial_inequality_removal,[],[f177])).
% 0.20/0.40 thf(f177,plain,(
% 0.20/0.40 ($true = $false) | ((q @ sK2) = $true)),
% 0.20/0.40 inference(superposition,[],[f151,f130])).
% 0.20/0.40 thf(f151,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.20/0.40 inference(not_proxy_clausification,[],[f150])).
% 0.20/0.40 thf(f150,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = (~ (rel_b @ sK1 @ X1))) | ($true = (q @ X1))) )),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f149])).
% 0.20/0.40 thf(f149,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_b @ sK1 @ X1)) | (q @ X1)))) )),
% 0.20/0.40 inference(beta_eta_normalization,[],[f148])).
% 0.20/0.40 thf(f148,plain,(
% 0.20/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (q @ Y0))) @ X1))) )),
% 0.20/0.40 inference(pi_clausification,[],[f147])).
% 0.20/0.40 thf(f147,plain,(
% 0.20/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (q @ Y0)))))),
% 0.20/0.40 inference(not_proxy_clausification,[],[f146])).
% 0.20/0.40 thf(f146,plain,(
% 0.20/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_b @ sK1 @ Y0)) | (q @ Y0))))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f124])).
% 0.20/0.40 thf(f176,plain,(
% 0.20/0.40 spl0_3 | spl0_4),
% 0.20/0.40 inference(avatar_split_clause,[],[f138,f172,f167])).
% 0.20/0.40 thf(f138,plain,(
% 0.20/0.40 ($false = (p @ sK2)) | ((q @ sK2) = $false)),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f136])).
% 0.20/0.40 thf(f136,plain,(
% 0.20/0.40 ((q @ sK2) = $false) | ($false = ((p @ sK2) | (~ (q @ sK2))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f134])).
% 0.20/0.40 thf(f134,plain,(
% 0.20/0.40 (((q @ sK2) | (~ (p @ sK2))) = $false) | ($false = ((p @ sK2) | (~ (q @ sK2))))),
% 0.20/0.40 inference(not_proxy_clausification,[],[f133])).
% 0.20/0.40 thf(f133,plain,(
% 0.20/0.40 ($true = (~ ((q @ sK2) | (~ (p @ sK2))))) | ($false = ((p @ sK2) | (~ (q @ sK2))))),
% 0.20/0.40 inference(not_proxy_clausification,[],[f132])).
% 0.20/0.40 thf(f132,plain,(
% 0.20/0.40 ($true = (~ ((p @ sK2) | (~ (q @ sK2))))) | ($true = (~ ((q @ sK2) | (~ (p @ sK2)))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f131])).
% 0.20/0.40 thf(f131,plain,(
% 0.20/0.40 ($true = ((~ ((p @ sK2) | (~ (q @ sK2)))) | (~ ((q @ sK2) | (~ (p @ sK2))))))),
% 0.20/0.40 inference(not_proxy_clausification,[],[f128])).
% 0.20/0.40 thf(f128,plain,(
% 0.20/0.40 ($false = (~ ((~ ((p @ sK2) | (~ (q @ sK2)))) | (~ ((q @ sK2) | (~ (p @ sK2)))))))),
% 0.20/0.40 inference(binary_proxy_clausification,[],[f127])).
% 0.20/0.40 % SZS output end Proof for theBenchmark
% 0.20/0.40 % (24980)------------------------------
% 0.20/0.40 % (24980)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (24980)Termination reason: Refutation
% 0.20/0.40
% 0.20/0.40 % (24980)Memory used [KB]: 5628
% 0.20/0.40 % (24980)Time elapsed: 0.012 s
% 0.20/0.40 % (24980)Instructions burned: 11 (million)
% 0.20/0.40 % (24980)------------------------------
% 0.20/0.40 % (24980)------------------------------
% 0.20/0.40 % (24974)Success in time 0.018 s
% 0.20/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------