TSTP Solution File: LCL624^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL624^1 : TPTP v8.2.0. Released v3.6.0.
% 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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:16:14 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : LCL624^1 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.11 % 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
% 0.11/0.31 % Computer : n023.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 01:38:38 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 This is a TH0_THM_EQU_NAR problem
% 0.11/0.31 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
% 0.16/0.32 % (11453)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.32 % (11456)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.16/0.32 % (11455)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 (3000ds/275Mi)
% 0.16/0.32 % (11453)Instruction limit reached!
% 0.16/0.32 % (11453)------------------------------
% 0.16/0.32 % (11453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (11453)Termination reason: Unknown
% 0.16/0.32 % (11453)Termination phase: Property scanning
% 0.16/0.32
% 0.16/0.32 % (11453)Memory used [KB]: 1023
% 0.16/0.32 % (11452)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 (3000ds/27Mi)
% 0.16/0.32 % (11453)Time elapsed: 0.003 s
% 0.16/0.32 % (11453)Instructions burned: 4 (million)
% 0.16/0.32 % (11453)------------------------------
% 0.16/0.32 % (11453)------------------------------
% 0.16/0.32 % (11455)Refutation not found, incomplete strategy
% 0.16/0.32 % (11455)------------------------------
% 0.16/0.32 % (11455)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.32 % (11455)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.32
% 0.16/0.32
% 0.16/0.32 % (11455)Memory used [KB]: 5500
% 0.16/0.32 % (11455)Time elapsed: 0.003 s
% 0.16/0.32 % (11455)Instructions burned: 4 (million)
% 0.16/0.32 % (11455)------------------------------
% 0.16/0.32 % (11455)------------------------------
% 0.16/0.33 % (11450)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.16/0.33 % (11456)First to succeed.
% 0.16/0.33 % (11457)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.16/0.33 % (11456)Refutation found. Thanks to Tanya!
% 0.16/0.33 % SZS status Theorem for theBenchmark
% 0.16/0.33 % SZS output start Proof for theBenchmark
% 0.16/0.33 thf(type_def_6, type, individuals: $tType).
% 0.16/0.33 thf(func_def_1, type, prop_a: $i > $o).
% 0.16/0.33 thf(func_def_2, type, prop_b: $i > $o).
% 0.16/0.33 thf(func_def_3, type, prop_c: $i > $o).
% 0.16/0.33 thf(func_def_4, type, mfalse: $i > $o).
% 0.16/0.33 thf(func_def_5, type, mtrue: $i > $o).
% 0.16/0.33 thf(func_def_6, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_8, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_9, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_10, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_11, type, miff: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_12, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_13, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_14, type, individuals: $tType).
% 0.16/0.33 thf(func_def_15, type, mall: (individuals > $i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_16, type, mexists: (individuals > $i > $o) > $i > $o).
% 0.16/0.33 thf(func_def_17, type, mvalid: ($i > $o) > $o).
% 0.16/0.33 thf(func_def_18, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.33 thf(func_def_19, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.33 thf(func_def_20, type, minvalid: ($i > $o) > $o).
% 0.16/0.33 thf(func_def_34, type, sK0: $i > $o).
% 0.16/0.33 thf(func_def_35, type, sK1: $i > $o).
% 0.16/0.33 thf(func_def_36, type, sK2: $i > $i > $o).
% 0.16/0.33 thf(func_def_40, type, sK6: $i > $i).
% 0.16/0.33 thf(f150,plain,(
% 0.16/0.33 $false),
% 0.16/0.33 inference(avatar_sat_refutation,[],[f146,f149])).
% 0.16/0.33 thf(f149,plain,(
% 0.16/0.33 ~spl3_5),
% 0.16/0.33 inference(avatar_contradiction_clause,[],[f148])).
% 0.16/0.33 thf(f148,plain,(
% 0.16/0.33 $false | ~spl3_5),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f147])).
% 0.16/0.33 thf(f147,plain,(
% 0.16/0.33 ($false = $true) | ~spl3_5),
% 0.16/0.33 inference(backward_demodulation,[],[f122,f142])).
% 0.16/0.33 thf(f142,plain,(
% 0.16/0.33 ($false = (sK1 @ (sK6 @ sK5))) | ~spl3_5),
% 0.16/0.33 inference(avatar_component_clause,[],[f140])).
% 0.16/0.33 thf(f140,plain,(
% 0.16/0.33 spl3_5 <=> ($false = (sK1 @ (sK6 @ sK5)))),
% 0.16/0.33 introduced(avatar_definition,[new_symbols(naming,[spl3_5])])).
% 0.16/0.33 thf(f122,plain,(
% 0.16/0.33 ((sK1 @ (sK6 @ sK5)) = $true)),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f120])).
% 0.16/0.33 thf(f120,plain,(
% 0.16/0.33 ((sK1 @ (sK6 @ sK5)) = $true) | ($false = $true)),
% 0.16/0.33 inference(superposition,[],[f89,f98])).
% 0.16/0.33 thf(f98,plain,(
% 0.16/0.33 ( ! [X1 : $i] : (((sK2 @ sK4 @ X1) = $false) | ((sK1 @ (sK6 @ X1)) = $true)) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f97])).
% 0.16/0.33 thf(f97,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((sK2 @ X1 @ (sK6 @ X1)) & (sK1 @ (sK6 @ X1))) = $true) | ((sK2 @ sK4 @ X1) = $false)) )),
% 0.16/0.33 inference(beta_eta_normalization,[],[f96])).
% 0.16/0.33 thf(f96,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ X1 @ Y0) & (sK1 @ Y0))) @ (sK6 @ X1)) = $true) | ((sK2 @ sK4 @ X1) = $false)) )),
% 0.16/0.33 inference(sigma_clausification,[],[f95])).
% 0.16/0.33 thf(f95,plain,(
% 0.16/0.33 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) & (sK1 @ Y0)))) = $true) | ((sK2 @ sK4 @ X1) = $false)) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f94])).
% 0.16/0.33 thf(f94,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((sK2 @ sK4 @ X1) => (?? @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) & (sK1 @ Y0))))) = $true)) )),
% 0.16/0.33 inference(beta_eta_normalization,[],[f93])).
% 0.16/0.33 thf(f93,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (sK1 @ Y1)))))) @ X1) = $true)) )),
% 0.16/0.33 inference(pi_clausification,[],[f84])).
% 0.16/0.33 thf(f84,plain,(
% 0.16/0.33 ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (sK1 @ Y1))))))) = $true)),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f83])).
% 0.16/0.33 thf(f83,plain,(
% 0.16/0.33 (((?? @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (sK1 @ Y1)))))))) = $true)),
% 0.16/0.33 inference(not_proxy_clausification,[],[f74])).
% 0.16/0.33 thf(f74,plain,(
% 0.16/0.33 ((~ ((?? @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (sK1 @ Y1))))))))) = $false)),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f73])).
% 0.16/0.33 thf(f73,plain,(
% 0.16/0.33 (((?? @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & ((sK0 @ Y1) & (sK1 @ Y1)))))))) | (~ ((?? @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (sK1 @ Y1)))))))))) = $false)),
% 0.16/0.33 inference(beta_eta_normalization,[],[f72])).
% 0.16/0.33 thf(f72,plain,(
% 0.16/0.33 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) & ((sK0 @ Y2) & (sK1 @ Y2)))))))) | (~ ((?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (sK0 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) & (sK1 @ Y2))))))))))) @ sK4) = $false)),
% 0.16/0.33 inference(sigma_clausification,[],[f71])).
% 0.16/0.33 thf(f71,plain,(
% 0.16/0.33 ($true != (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) & ((sK0 @ Y2) & (sK1 @ Y2)))))))) | (~ ((?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) => (sK0 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (?? @ $i @ (^[Y2 : $i]: ((sK2 @ Y1 @ Y2) & (sK1 @ Y2)))))))))))))),
% 0.16/0.33 inference(beta_eta_normalization,[],[f70])).
% 0.16/0.33 thf(f70,plain,(
% 0.16/0.33 ($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]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ sK2 @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ sK2 @ sK0)) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ sK2 @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ sK2 @ sK1))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ sK2 @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ sK2 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ sK0 @ sK1))))))),
% 0.16/0.33 inference(definition_unfolding,[],[f67,f64,f68,f60,f61,f55,f55,f61,f61,f61,f60])).
% 0.16/0.33 thf(f55,plain,(
% 0.16/0.33 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.16/0.33 inference(cnf_transformation,[],[f40])).
% 0.16/0.33 thf(f40,plain,(
% 0.16/0.33 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.16/0.33 inference(fool_elimination,[],[f39])).
% 0.16/0.33 thf(f39,plain,(
% 0.16/0.33 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X0 @ X2 @ X3) => (X1 @ X3)))))),
% 0.16/0.33 inference(rectify,[],[f8])).
% 0.16/0.33 thf(f8,axiom,(
% 0.16/0.33 (mbox = (^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (! [X2] : ((X4 @ X0 @ X2) => (X5 @ X2)))))),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.16/0.33 thf(f61,plain,(
% 0.16/0.33 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.16/0.33 inference(cnf_transformation,[],[f33])).
% 0.16/0.33 thf(f33,plain,(
% 0.16/0.33 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.16/0.33 inference(fool_elimination,[],[f32])).
% 0.16/0.33 thf(f32,plain,(
% 0.16/0.33 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X1 @ X3) & (X0 @ X2 @ X3)))) = mdia)),
% 0.16/0.33 inference(rectify,[],[f9])).
% 0.16/0.33 thf(f9,axiom,(
% 0.16/0.33 ((^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (? [X2] : ((X5 @ X2) & (X4 @ X0 @ X2)))) = mdia)),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.16/0.33 thf(f60,plain,(
% 0.16/0.33 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.16/0.33 inference(cnf_transformation,[],[f35])).
% 0.16/0.33 thf(f35,plain,(
% 0.16/0.33 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.16/0.33 inference(fool_elimination,[],[f34])).
% 0.16/0.33 thf(f34,plain,(
% 0.16/0.33 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 0.16/0.33 inference(rectify,[],[f5])).
% 0.16/0.33 thf(f5,axiom,(
% 0.16/0.33 ((^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X2 @ X1) & (X0 @ X1))) = mand)),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.16/0.33 thf(f68,plain,(
% 0.16/0.33 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.16/0.33 inference(definition_unfolding,[],[f57,f65,f62])).
% 0.16/0.33 thf(f62,plain,(
% 0.16/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.33 inference(cnf_transformation,[],[f38])).
% 0.16/0.33 thf(f38,plain,(
% 0.16/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.33 inference(fool_elimination,[],[f37])).
% 0.16/0.33 thf(f37,plain,(
% 0.16/0.33 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.16/0.33 inference(rectify,[],[f3])).
% 0.16/0.33 thf(f3,axiom,(
% 0.16/0.33 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.16/0.33 thf(f65,plain,(
% 0.16/0.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.33 inference(cnf_transformation,[],[f42])).
% 0.16/0.33 thf(f42,plain,(
% 0.16/0.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.33 inference(fool_elimination,[],[f41])).
% 0.16/0.33 thf(f41,plain,(
% 0.16/0.33 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.16/0.33 inference(rectify,[],[f4])).
% 0.16/0.33 thf(f4,axiom,(
% 0.16/0.33 ((^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X0 @ X1) | (X2 @ X1))) = mor)),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.16/0.33 thf(f57,plain,(
% 0.16/0.33 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.33 inference(cnf_transformation,[],[f29])).
% 0.16/0.33 thf(f29,plain,(
% 0.16/0.33 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.33 inference(fool_elimination,[],[f28])).
% 0.16/0.33 thf(f28,plain,(
% 0.16/0.33 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimpl)),
% 0.16/0.33 inference(rectify,[],[f6])).
% 0.16/0.33 thf(f6,axiom,(
% 0.16/0.33 ((^[X1 : $i > $o, X3 : $i > $o] : (mor @ (mnot @ X1) @ X3)) = mimpl)),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimpl)).
% 0.16/0.33 thf(f64,plain,(
% 0.16/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.33 inference(cnf_transformation,[],[f22])).
% 0.16/0.33 thf(f22,plain,(
% 0.16/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.33 inference(fool_elimination,[],[f21])).
% 0.16/0.33 thf(f21,plain,(
% 0.16/0.33 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.16/0.33 inference(rectify,[],[f12])).
% 0.16/0.33 thf(f12,axiom,(
% 0.16/0.33 ((^[X5 : $i > $o] : (! [X6] : (X5 @ X6))) = mvalid)),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.33 thf(f67,plain,(
% 0.16/0.33 ((mvalid @ (mimpl @ (mand @ (mdia @ sK2 @ (mbox @ sK2 @ sK0)) @ (mbox @ sK2 @ (mdia @ sK2 @ sK1))) @ (mdia @ sK2 @ (mdia @ sK2 @ (mand @ sK0 @ sK1))))) != $true)),
% 0.16/0.33 inference(cnf_transformation,[],[f51])).
% 0.16/0.33 thf(f51,plain,(
% 0.16/0.33 ((mvalid @ (mimpl @ (mand @ (mdia @ sK2 @ (mbox @ sK2 @ sK0)) @ (mbox @ sK2 @ (mdia @ sK2 @ sK1))) @ (mdia @ sK2 @ (mdia @ sK2 @ (mand @ sK0 @ sK1))))) != $true)),
% 0.16/0.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f49,f50])).
% 0.16/0.33 thf(f50,plain,(
% 0.16/0.33 ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o] : ((mvalid @ (mimpl @ (mand @ (mdia @ X2 @ (mbox @ X2 @ X0)) @ (mbox @ X2 @ (mdia @ X2 @ X1))) @ (mdia @ X2 @ (mdia @ X2 @ (mand @ X0 @ X1))))) != $true) => ((mvalid @ (mimpl @ (mand @ (mdia @ sK2 @ (mbox @ sK2 @ sK0)) @ (mbox @ sK2 @ (mdia @ sK2 @ sK1))) @ (mdia @ sK2 @ (mdia @ sK2 @ (mand @ sK0 @ sK1))))) != $true)),
% 0.16/0.33 introduced(choice_axiom,[])).
% 0.16/0.33 thf(f49,plain,(
% 0.16/0.33 ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o] : ((mvalid @ (mimpl @ (mand @ (mdia @ X2 @ (mbox @ X2 @ X0)) @ (mbox @ X2 @ (mdia @ X2 @ X1))) @ (mdia @ X2 @ (mdia @ X2 @ (mand @ X0 @ X1))))) != $true)),
% 0.16/0.33 inference(ennf_transformation,[],[f20])).
% 0.16/0.33 thf(f20,plain,(
% 0.16/0.33 ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o] : ((mvalid @ (mimpl @ (mand @ (mdia @ X2 @ (mbox @ X2 @ X0)) @ (mbox @ X2 @ (mdia @ X2 @ X1))) @ (mdia @ X2 @ (mdia @ X2 @ (mand @ X0 @ X1))))) = $true)),
% 0.16/0.33 inference(fool_elimination,[],[f19])).
% 0.16/0.33 thf(f19,plain,(
% 0.16/0.33 ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i > $o] : (mvalid @ (mimpl @ (mand @ (mdia @ X2 @ (mbox @ X2 @ X0)) @ (mbox @ X2 @ (mdia @ X2 @ X1))) @ (mdia @ X2 @ (mdia @ X2 @ (mand @ X0 @ X1)))))),
% 0.16/0.33 inference(rectify,[],[f17])).
% 0.16/0.33 thf(f17,negated_conjecture,(
% 0.16/0.33 ~! [X5 : $i > $o,X7 : $i > $o,X4 : $i > $i > $o] : (mvalid @ (mimpl @ (mand @ (mdia @ X4 @ (mbox @ X4 @ X5)) @ (mbox @ X4 @ (mdia @ X4 @ X7))) @ (mdia @ X4 @ (mdia @ X4 @ (mand @ X5 @ X7)))))),
% 0.16/0.33 inference(negated_conjecture,[],[f16])).
% 0.16/0.33 thf(f16,conjecture,(
% 0.16/0.33 ! [X5 : $i > $o,X7 : $i > $o,X4 : $i > $i > $o] : (mvalid @ (mimpl @ (mand @ (mdia @ X4 @ (mbox @ X4 @ X5)) @ (mbox @ X4 @ (mdia @ X4 @ X7))) @ (mdia @ X4 @ (mdia @ X4 @ (mand @ X5 @ X7)))))),
% 0.16/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.16/0.33 thf(f89,plain,(
% 0.16/0.33 ((sK2 @ sK4 @ sK5) = $true)),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f87])).
% 0.16/0.33 thf(f87,plain,(
% 0.16/0.33 (((sK2 @ sK4 @ sK5) & (!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK0 @ Y0))))) = $true)),
% 0.16/0.33 inference(beta_eta_normalization,[],[f86])).
% 0.16/0.33 thf(f86,plain,(
% 0.16/0.33 (((^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK0 @ Y1)))))) @ sK5) = $true)),
% 0.16/0.33 inference(sigma_clausification,[],[f85])).
% 0.16/0.33 thf(f85,plain,(
% 0.16/0.33 ($true = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) => (sK0 @ Y1))))))))),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f83])).
% 0.16/0.33 thf(f146,plain,(
% 0.16/0.33 spl3_5),
% 0.16/0.33 inference(avatar_split_clause,[],[f145,f140])).
% 0.16/0.33 thf(f145,plain,(
% 0.16/0.33 ($false = (sK1 @ (sK6 @ sK5)))),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f144])).
% 0.16/0.33 thf(f144,plain,(
% 0.16/0.33 ($false = $true) | ($false = (sK1 @ (sK6 @ sK5)))),
% 0.16/0.33 inference(forward_demodulation,[],[f132,f133])).
% 0.16/0.33 thf(f133,plain,(
% 0.16/0.33 ((sK0 @ (sK6 @ sK5)) = $true)),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f128])).
% 0.16/0.33 thf(f128,plain,(
% 0.16/0.33 ((sK0 @ (sK6 @ sK5)) = $true) | ($false = $true)),
% 0.16/0.33 inference(superposition,[],[f126,f92])).
% 0.16/0.33 thf(f92,plain,(
% 0.16/0.33 ( ! [X1 : $i] : (((sK2 @ sK5 @ X1) = $false) | ((sK0 @ X1) = $true)) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f91])).
% 0.16/0.33 thf(f91,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((sK2 @ sK5 @ X1) => (sK0 @ X1)) = $true)) )),
% 0.16/0.33 inference(beta_eta_normalization,[],[f90])).
% 0.16/0.33 thf(f90,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK0 @ Y0))) @ X1) = $true)) )),
% 0.16/0.33 inference(pi_clausification,[],[f88])).
% 0.16/0.33 thf(f88,plain,(
% 0.16/0.33 ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ sK5 @ Y0) => (sK0 @ Y0)))) = $true)),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f87])).
% 0.16/0.33 thf(f126,plain,(
% 0.16/0.33 ((sK2 @ sK5 @ (sK6 @ sK5)) = $true)),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f123])).
% 0.16/0.33 thf(f123,plain,(
% 0.16/0.33 ((sK2 @ sK5 @ (sK6 @ sK5)) = $true) | ($false = $true)),
% 0.16/0.33 inference(superposition,[],[f99,f89])).
% 0.16/0.33 thf(f99,plain,(
% 0.16/0.33 ( ! [X1 : $i] : (((sK2 @ sK4 @ X1) = $false) | ($true = (sK2 @ X1 @ (sK6 @ X1)))) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f97])).
% 0.16/0.33 thf(f132,plain,(
% 0.16/0.33 ((sK0 @ (sK6 @ sK5)) = $false) | ($false = (sK1 @ (sK6 @ sK5)))),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f129])).
% 0.16/0.33 thf(f129,plain,(
% 0.16/0.33 ($false = $true) | ($false = (sK1 @ (sK6 @ sK5))) | ((sK0 @ (sK6 @ sK5)) = $false)),
% 0.16/0.33 inference(superposition,[],[f118,f126])).
% 0.16/0.33 thf(f118,plain,(
% 0.16/0.33 ( ! [X0 : $i] : (((sK2 @ sK5 @ X0) = $false) | ((sK1 @ X0) = $false) | ((sK0 @ X0) = $false)) )),
% 0.16/0.33 inference(trivial_inequality_removal,[],[f115])).
% 0.16/0.33 thf(f115,plain,(
% 0.16/0.33 ( ! [X0 : $i] : (((sK0 @ X0) = $false) | ($false = $true) | ((sK2 @ sK5 @ X0) = $false) | ((sK1 @ X0) = $false)) )),
% 0.16/0.33 inference(superposition,[],[f89,f82])).
% 0.16/0.33 thf(f82,plain,(
% 0.16/0.33 ( ! [X2 : $i,X1 : $i] : (((sK2 @ sK4 @ X1) = $false) | ($false = (sK0 @ X2)) | ((sK2 @ X1 @ X2) = $false) | ((sK1 @ X2) = $false)) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f81])).
% 0.16/0.33 thf(f81,plain,(
% 0.16/0.33 ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1 @ X2) = $false) | ((sK2 @ sK4 @ X1) = $false) | (((sK0 @ X2) & (sK1 @ X2)) = $false)) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f80])).
% 0.16/0.33 thf(f80,plain,(
% 0.16/0.33 ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1 @ X2) & ((sK0 @ X2) & (sK1 @ X2))) = $false) | ((sK2 @ sK4 @ X1) = $false)) )),
% 0.16/0.33 inference(beta_eta_normalization,[],[f79])).
% 0.16/0.33 thf(f79,plain,(
% 0.16/0.33 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ X1 @ Y0) & ((sK0 @ Y0) & (sK1 @ Y0)))) @ X2) = $false) | ((sK2 @ sK4 @ X1) = $false)) )),
% 0.16/0.33 inference(pi_clausification,[],[f78])).
% 0.16/0.33 thf(f78,plain,(
% 0.16/0.33 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) & ((sK0 @ Y0) & (sK1 @ Y0))))) = $false) | ((sK2 @ sK4 @ X1) = $false)) )),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f77])).
% 0.16/0.33 thf(f77,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((sK2 @ sK4 @ X1) & (?? @ $i @ (^[Y0 : $i]: ((sK2 @ X1 @ Y0) & ((sK0 @ Y0) & (sK1 @ Y0)))))) = $false)) )),
% 0.16/0.33 inference(beta_eta_normalization,[],[f76])).
% 0.16/0.33 thf(f76,plain,(
% 0.16/0.33 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & ((sK0 @ Y1) & (sK1 @ Y1))))))) @ X1) = $false)) )),
% 0.16/0.33 inference(pi_clausification,[],[f75])).
% 0.16/0.33 thf(f75,plain,(
% 0.16/0.33 ($false = (?? @ $i @ (^[Y0 : $i]: ((sK2 @ sK4 @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y0 @ Y1) & ((sK0 @ Y1) & (sK1 @ Y1)))))))))),
% 0.16/0.33 inference(binary_proxy_clausification,[],[f73])).
% 0.16/0.33 % SZS output end Proof for theBenchmark
% 0.16/0.33 % (11456)------------------------------
% 0.16/0.33 % (11456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.33 % (11456)Termination reason: Refutation
% 0.16/0.33
% 0.16/0.33 % (11456)Memory used [KB]: 5628
% 0.16/0.33 % (11456)Time elapsed: 0.007 s
% 0.16/0.33 % (11456)Instructions burned: 10 (million)
% 0.16/0.33 % (11456)------------------------------
% 0.16/0.33 % (11456)------------------------------
% 0.16/0.33 % (11449)Success in time 0.012 s
% 0.16/0.33 % Vampire---4.8 exiting
%------------------------------------------------------------------------------