TSTP Solution File: PLA053^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% 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 : n007.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 02:21:20 EDT 2024
% Result : Theorem 0.26s 0.43s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.15 % 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
% 0.15/0.39 % Computer : n007.cluster.edu
% 0.15/0.39 % Model : x86_64 x86_64
% 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.39 % Memory : 8042.1875MB
% 0.15/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat May 18 13:41:38 EDT 2024
% 0.15/0.40 % CPUTime :
% 0.15/0.40 This is a TH0_THM_EQU_NAR problem
% 0.15/0.40 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
% 0.15/0.42 % (5749)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.42 % (5748)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)
% 0.15/0.42 % (5747)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)
% 0.15/0.42 % (5750)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)
% 0.15/0.42 % (5751)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)
% 0.15/0.42 % (5753)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)
% 0.15/0.42 % (5749)Instruction limit reached!
% 0.15/0.42 % (5749)------------------------------
% 0.15/0.42 % (5749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (5749)Termination reason: Unknown
% 0.15/0.42 % (5749)Termination phase: shuffling
% 0.15/0.42 % (5750)Instruction limit reached!
% 0.15/0.42 % (5750)------------------------------
% 0.15/0.42 % (5750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (5750)Termination reason: Unknown
% 0.15/0.42 % (5750)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (5750)Memory used [KB]: 1023
% 0.15/0.42 % (5750)Time elapsed: 0.003 s
% 0.15/0.42 % (5750)Instructions burned: 2 (million)
% 0.15/0.42 % (5750)------------------------------
% 0.15/0.42 % (5750)------------------------------
% 0.15/0.42
% 0.15/0.42 % (5749)Memory used [KB]: 1023
% 0.15/0.42 % (5749)Time elapsed: 0.003 s
% 0.15/0.42 % (5749)Instructions burned: 2 (million)
% 0.15/0.42 % (5749)------------------------------
% 0.15/0.42 % (5749)------------------------------
% 0.15/0.42 % (5746)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.42 % (5752)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.42 % (5753)Instruction limit reached!
% 0.15/0.42 % (5753)------------------------------
% 0.15/0.42 % (5753)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (5753)Termination reason: Unknown
% 0.15/0.42 % (5753)Termination phase: Property scanning
% 0.15/0.42
% 0.15/0.42 % (5753)Memory used [KB]: 1023
% 0.15/0.42 % (5753)Time elapsed: 0.004 s
% 0.15/0.42 % (5753)Instructions burned: 4 (million)
% 0.15/0.42 % (5753)------------------------------
% 0.15/0.42 % (5753)------------------------------
% 0.15/0.42 % (5751)Refutation not found, incomplete strategy
% 0.15/0.42 % (5751)------------------------------
% 0.15/0.42 % (5751)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (5747)Instruction limit reached!
% 0.15/0.42 % (5747)------------------------------
% 0.15/0.42 % (5747)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (5747)Termination reason: Unknown
% 0.15/0.42 % (5747)Termination phase: Saturation
% 0.15/0.42
% 0.15/0.42 % (5747)Memory used [KB]: 5500
% 0.15/0.42 % (5747)Time elapsed: 0.005 s
% 0.15/0.42 % (5747)Instructions burned: 5 (million)
% 0.15/0.42 % (5747)------------------------------
% 0.15/0.42 % (5747)------------------------------
% 0.15/0.42 % (5751)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.42
% 0.15/0.42
% 0.15/0.42 % (5751)Memory used [KB]: 5500
% 0.15/0.42 % (5751)Time elapsed: 0.004 s
% 0.15/0.42 % (5751)Instructions burned: 4 (million)
% 0.15/0.42 % (5751)------------------------------
% 0.15/0.42 % (5751)------------------------------
% 0.26/0.43 % (5746)First to succeed.
% 0.26/0.43 % (5752)Instruction limit reached!
% 0.26/0.43 % (5752)------------------------------
% 0.26/0.43 % (5752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.43 % (5752)Termination reason: Unknown
% 0.26/0.43 % (5752)Termination phase: Saturation
% 0.26/0.43
% 0.26/0.43 % (5752)Memory used [KB]: 5628
% 0.26/0.43 % (5752)Time elapsed: 0.012 s
% 0.26/0.43 % (5752)Instructions burned: 18 (million)
% 0.26/0.43 % (5752)------------------------------
% 0.26/0.43 % (5752)------------------------------
% 0.26/0.43 % (5748)Also succeeded, but the first one will report.
% 0.26/0.43 % (5746)Refutation found. Thanks to Tanya!
% 0.26/0.43 % SZS status Theorem for theBenchmark
% 0.26/0.43 % SZS output start Proof for theBenchmark
% 0.26/0.43 thf(type_def_5, type, mworld: $tType).
% 0.26/0.43 thf(func_def_0, type, mworld: $tType).
% 0.26/0.43 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.26/0.43 thf(func_def_2, type, mactual: mworld).
% 0.26/0.43 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.26/0.43 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.26/0.43 thf(func_def_14, type, h: $i > mworld > $o).
% 0.26/0.43 thf(func_def_15, type, bomb: $i > mworld > $o).
% 0.26/0.43 thf(func_def_16, type, defused: $i > mworld > $o).
% 0.26/0.43 thf(func_def_34, type, sK2: mworld > $i).
% 0.26/0.43 thf(func_def_35, type, sK3: mworld > $i > $i).
% 0.26/0.43 thf(func_def_36, type, sK4: mworld).
% 0.26/0.43 thf(f167,plain,(
% 0.26/0.43 $false),
% 0.26/0.43 inference(avatar_sat_refutation,[],[f130,f143,f166])).
% 0.26/0.43 thf(f166,plain,(
% 0.26/0.43 ~spl0_1),
% 0.26/0.43 inference(avatar_contradiction_clause,[],[f165])).
% 0.26/0.43 thf(f165,plain,(
% 0.26/0.43 $false | ~spl0_1),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f157])).
% 0.26/0.43 thf(f157,plain,(
% 0.26/0.43 ($false = $true) | ~spl0_1),
% 0.26/0.43 inference(superposition,[],[f155,f109])).
% 0.26/0.43 thf(f109,plain,(
% 0.26/0.43 ((mrel @ mactual @ sK4) = $true)),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f107])).
% 0.26/0.43 thf(f107,plain,(
% 0.26/0.43 ($false = ((mrel @ mactual @ sK4) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4))))))))),
% 0.26/0.43 inference(beta_eta_normalization,[],[f106])).
% 0.26/0.43 thf(f106,plain,(
% 0.26/0.43 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((h @ Y2 @ Y0) & (bomb @ Y1 @ Y0)) => (defused @ Y1 @ Y0)))))))) @ sK4))),
% 0.26/0.43 inference(sigma_clausification,[],[f105])).
% 0.26/0.43 thf(f105,plain,(
% 0.26/0.43 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((h @ Y2 @ Y0) & (bomb @ Y1 @ Y0)) => (defused @ Y1 @ Y0))))))))))),
% 0.26/0.43 inference(beta_eta_normalization,[],[f71])).
% 0.26/0.43 thf(f71,plain,(
% 0.26/0.43 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 0.26/0.43 inference(definition_unfolding,[],[f62,f59,f55,f57,f67,f53,f56])).
% 0.26/0.43 thf(f56,plain,(
% 0.26/0.43 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f43])).
% 0.26/0.43 thf(f43,plain,(
% 0.26/0.43 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 0.26/0.43 inference(fool_elimination,[],[f42])).
% 0.26/0.43 thf(f42,plain,(
% 0.26/0.43 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))))),
% 0.26/0.43 inference(rectify,[],[f3])).
% 0.26/0.43 thf(f3,axiom,(
% 0.26/0.43 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def)).
% 0.26/0.43 thf(f53,plain,(
% 0.26/0.43 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f32])).
% 0.26/0.43 thf(f32,plain,(
% 0.26/0.43 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.26/0.43 inference(fool_elimination,[],[f31])).
% 0.26/0.43 thf(f31,plain,(
% 0.26/0.43 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.26/0.43 inference(rectify,[],[f5])).
% 0.26/0.43 thf(f5,axiom,(
% 0.26/0.43 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.26/0.43 thf(f67,plain,(
% 0.26/0.43 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f20])).
% 0.26/0.43 thf(f20,plain,(
% 0.26/0.43 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.26/0.43 inference(fool_elimination,[],[f19])).
% 0.26/0.43 thf(f19,plain,(
% 0.26/0.43 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2] : (X0 @ X2 @ X1))))),
% 0.26/0.43 inference(rectify,[],[f12])).
% 0.26/0.43 thf(f12,axiom,(
% 0.26/0.43 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6] : (X1 @ X6 @ X2))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def)).
% 0.26/0.43 thf(f57,plain,(
% 0.26/0.43 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f24])).
% 0.26/0.43 thf(f24,plain,(
% 0.26/0.43 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.26/0.43 inference(fool_elimination,[],[f23])).
% 0.26/0.43 thf(f23,plain,(
% 0.26/0.43 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : (X0 @ X2 @ X1))) = mforall_di)),
% 0.26/0.43 inference(rectify,[],[f11])).
% 0.26/0.43 thf(f11,axiom,(
% 0.26/0.43 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6] : (X1 @ X6 @ X2))) = mforall_di)),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def)).
% 0.26/0.43 thf(f55,plain,(
% 0.26/0.43 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f38])).
% 0.26/0.43 thf(f38,plain,(
% 0.26/0.43 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.26/0.43 inference(fool_elimination,[],[f37])).
% 0.26/0.43 thf(f37,plain,(
% 0.26/0.43 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.26/0.43 inference(rectify,[],[f7])).
% 0.26/0.43 thf(f7,axiom,(
% 0.26/0.43 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def)).
% 0.26/0.43 thf(f59,plain,(
% 0.26/0.43 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.26/0.43 inference(cnf_transformation,[],[f41])).
% 0.26/0.43 thf(f41,plain,(
% 0.26/0.43 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.26/0.43 inference(fool_elimination,[],[f1])).
% 0.26/0.43 thf(f1,axiom,(
% 0.26/0.43 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.26/0.43 thf(f62,plain,(
% 0.26/0.43 ($true != (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f50])).
% 0.26/0.43 thf(f50,plain,(
% 0.26/0.43 ($true != (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))),
% 0.26/0.43 inference(flattening,[],[f40])).
% 0.26/0.43 thf(f40,plain,(
% 0.26/0.43 ~($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))))),
% 0.26/0.43 inference(fool_elimination,[],[f39])).
% 0.26/0.43 thf(f39,plain,(
% 0.26/0.43 ~(mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))),
% 0.26/0.43 inference(rectify,[],[f17])).
% 0.26/0.43 thf(f17,negated_conjecture,(
% 0.26/0.43 ~(mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6))))))))),
% 0.26/0.43 inference(negated_conjecture,[],[f16])).
% 0.26/0.43 thf(f16,conjecture,(
% 0.26/0.43 (mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6))))))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.26/0.43 thf(f155,plain,(
% 0.26/0.43 ((mrel @ mactual @ sK4) = $false) | ~spl0_1),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f149])).
% 0.26/0.43 thf(f149,plain,(
% 0.26/0.43 ((mrel @ mactual @ sK4) = $false) | ($false = $true) | ~spl0_1),
% 0.26/0.43 inference(superposition,[],[f66,f125])).
% 0.26/0.43 thf(f125,plain,(
% 0.26/0.43 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK4))) ) | ~spl0_1),
% 0.26/0.43 inference(avatar_component_clause,[],[f124])).
% 0.26/0.43 thf(f124,plain,(
% 0.26/0.43 spl0_1 <=> ! [X0 : mworld] : (($false = (mrel @ X0 @ sK4)) | ($false = (mrel @ mactual @ X0)))),
% 0.26/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.26/0.43 thf(f66,plain,(
% 0.26/0.43 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 0.26/0.43 inference(cnf_transformation,[],[f36])).
% 0.26/0.43 thf(f36,plain,(
% 0.26/0.43 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 0.26/0.43 inference(fool_elimination,[],[f35])).
% 0.26/0.43 thf(f35,plain,(
% 0.26/0.43 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.26/0.43 inference(rectify,[],[f9])).
% 0.26/0.43 thf(f9,axiom,(
% 0.26/0.43 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive)).
% 0.26/0.43 thf(f143,plain,(
% 0.26/0.43 ~spl0_2),
% 0.26/0.43 inference(avatar_contradiction_clause,[],[f142])).
% 0.26/0.43 thf(f142,plain,(
% 0.26/0.43 $false | ~spl0_2),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f137])).
% 0.26/0.43 thf(f137,plain,(
% 0.26/0.43 ($false = $true) | ~spl0_2),
% 0.26/0.43 inference(superposition,[],[f116,f134])).
% 0.26/0.43 thf(f134,plain,(
% 0.26/0.43 ($false = (bomb @ sK5 @ sK4)) | ~spl0_2),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f132])).
% 0.26/0.43 thf(f132,plain,(
% 0.26/0.43 ($false = (bomb @ sK5 @ sK4)) | ($false = $true) | ~spl0_2),
% 0.26/0.43 inference(superposition,[],[f114,f128])).
% 0.26/0.43 thf(f128,plain,(
% 0.26/0.43 ( ! [X1 : $i] : (($true = (defused @ X1 @ sK4)) | ($false = (bomb @ X1 @ sK4))) ) | ~spl0_2),
% 0.26/0.43 inference(avatar_component_clause,[],[f127])).
% 0.26/0.43 thf(f127,plain,(
% 0.26/0.43 spl0_2 <=> ! [X1] : (($true = (defused @ X1 @ sK4)) | ($false = (bomb @ X1 @ sK4)))),
% 0.26/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.26/0.43 thf(f114,plain,(
% 0.26/0.43 ($false = (defused @ sK5 @ sK4))),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f113])).
% 0.26/0.43 thf(f113,plain,(
% 0.26/0.43 ( ! [X1 : $i] : (($false = (((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))) )),
% 0.26/0.43 inference(beta_eta_normalization,[],[f112])).
% 0.26/0.43 thf(f112,plain,(
% 0.26/0.43 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4))) @ X1))) )),
% 0.26/0.43 inference(pi_clausification,[],[f111])).
% 0.26/0.43 thf(f111,plain,(
% 0.26/0.43 ($false = (?? @ $i @ (^[Y0 : $i]: (((h @ Y0 @ sK4) & (bomb @ sK5 @ sK4)) => (defused @ sK5 @ sK4)))))),
% 0.26/0.43 inference(beta_eta_normalization,[],[f110])).
% 0.26/0.43 thf(f110,plain,(
% 0.26/0.43 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4))))) @ sK5))),
% 0.26/0.43 inference(sigma_clausification,[],[f108])).
% 0.26/0.43 thf(f108,plain,(
% 0.26/0.43 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((h @ Y1 @ sK4) & (bomb @ Y0 @ sK4)) => (defused @ Y0 @ sK4)))))) = $false)),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f107])).
% 0.26/0.43 thf(f116,plain,(
% 0.26/0.43 ((bomb @ sK5 @ sK4) = $true)),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f115])).
% 0.26/0.43 thf(f115,plain,(
% 0.26/0.43 ( ! [X1 : $i] : (($true = ((h @ X1 @ sK4) & (bomb @ sK5 @ sK4)))) )),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f113])).
% 0.26/0.43 thf(f130,plain,(
% 0.26/0.43 spl0_1 | spl0_2),
% 0.26/0.43 inference(avatar_split_clause,[],[f121,f127,f124])).
% 0.26/0.43 thf(f121,plain,(
% 0.26/0.43 ( ! [X0 : mworld,X1 : $i] : (($false = (bomb @ X1 @ sK4)) | ($true = (defused @ X1 @ sK4)) | ($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK4))) )),
% 0.26/0.43 inference(trivial_inequality_removal,[],[f119])).
% 0.26/0.43 thf(f119,plain,(
% 0.26/0.43 ( ! [X0 : mworld,X1 : $i] : (($false = $true) | ($false = (mrel @ mactual @ X0)) | ($false = (bomb @ X1 @ sK4)) | ($true = (defused @ X1 @ sK4)) | ($false = (mrel @ X0 @ sK4))) )),
% 0.26/0.43 inference(superposition,[],[f104,f117])).
% 0.26/0.43 thf(f117,plain,(
% 0.26/0.43 ( ! [X1 : $i] : (($true = (h @ X1 @ sK4))) )),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f115])).
% 0.26/0.43 thf(f104,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (h @ (sK3 @ X1 @ X2) @ X3)) | ((mrel @ X1 @ X3) = $false) | ($false = (bomb @ X2 @ X3)) | ($false = (mrel @ mactual @ X1)) | ($true = (defused @ X2 @ X3))) )),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f103])).
% 0.26/0.43 thf(f103,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (((mrel @ X1 @ X3) = $false) | ($false = ((h @ (sK3 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3))) | ($true = (defused @ X2 @ X3)) | ($false = (mrel @ mactual @ X1))) )),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f102])).
% 0.26/0.43 thf(f102,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (((mrel @ X1 @ X3) = $false) | ($false = (mrel @ mactual @ X1)) | ($true = (((h @ (sK3 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3)) => (defused @ X2 @ X3)))) )),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f101])).
% 0.26/0.43 thf(f101,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((mrel @ X1 @ X3) => (((h @ (sK3 @ X1 @ X2) @ X3) & (bomb @ X2 @ X3)) => (defused @ X2 @ X3))))) )),
% 0.26/0.43 inference(beta_eta_normalization,[],[f100])).
% 0.26/0.43 thf(f100,plain,(
% 0.26/0.43 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK3 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0)))) @ X3) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 0.26/0.43 inference(pi_clausification,[],[f99])).
% 0.26/0.43 thf(f99,plain,(
% 0.26/0.43 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((h @ (sK3 @ X1 @ X2) @ Y0) & (bomb @ X2 @ Y0)) => (defused @ X2 @ Y0))))))) )),
% 0.26/0.43 inference(beta_eta_normalization,[],[f98])).
% 0.26/0.43 thf(f98,plain,(
% 0.26/0.43 ( ! [X2 : $i,X1 : mworld] : (($true = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1)))))) @ (sK3 @ X1 @ X2))) | ($false = (mrel @ mactual @ X1))) )),
% 0.26/0.43 inference(sigma_clausification,[],[f97])).
% 0.26/0.43 thf(f97,plain,(
% 0.26/0.43 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((h @ Y0 @ Y1) & (bomb @ X2 @ Y1)) => (defused @ X2 @ Y1))))))))) )),
% 0.26/0.43 inference(beta_eta_normalization,[],[f96])).
% 0.26/0.43 thf(f96,plain,(
% 0.26/0.43 ( ! [X2 : $i,X1 : mworld] : (($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))) @ X2)) | ($false = (mrel @ mactual @ X1))) )),
% 0.26/0.43 inference(pi_clausification,[],[f95])).
% 0.26/0.43 thf(f95,plain,(
% 0.26/0.43 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2))))))))) = $true)) )),
% 0.26/0.43 inference(binary_proxy_clausification,[],[f94])).
% 0.26/0.43 thf(f94,plain,(
% 0.26/0.43 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((h @ Y1 @ Y2) & (bomb @ Y0 @ Y2)) => (defused @ Y0 @ Y2)))))))))))) )),
% 0.26/0.43 inference(beta_eta_normalization,[],[f93])).
% 0.26/0.43 thf(f93,plain,(
% 0.26/0.43 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((h @ Y2 @ Y3) & (bomb @ Y1 @ Y3)) => (defused @ Y1 @ Y3))))))))))) @ X1))) )),
% 0.26/0.43 inference(pi_clausification,[],[f92])).
% 0.26/0.43 thf(f92,plain,(
% 0.26/0.43 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((h @ Y2 @ Y3) & (bomb @ Y1 @ Y3)) => (defused @ Y1 @ Y3)))))))))))))),
% 0.26/0.43 inference(beta_eta_normalization,[],[f70])).
% 0.26/0.43 thf(f70,plain,(
% 0.26/0.43 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (?? @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))) = $true)),
% 0.26/0.43 inference(definition_unfolding,[],[f60,f59,f55,f57,f67,f55,f53,f56])).
% 0.26/0.43 thf(f60,plain,(
% 0.26/0.43 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 0.26/0.43 inference(cnf_transformation,[],[f28])).
% 0.26/0.43 thf(f28,plain,(
% 0.26/0.43 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 0.26/0.43 inference(fool_elimination,[],[f27])).
% 0.26/0.43 thf(f27,plain,(
% 0.26/0.43 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))),
% 0.26/0.43 inference(rectify,[],[f15])).
% 0.26/0.43 thf(f15,axiom,(
% 0.26/0.43 (mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6)))))))))),
% 0.26/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 0.26/0.43 % SZS output end Proof for theBenchmark
% 0.26/0.43 % (5746)------------------------------
% 0.26/0.43 % (5746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.26/0.43 % (5746)Termination reason: Refutation
% 0.26/0.43
% 0.26/0.43 % (5746)Memory used [KB]: 5628
% 0.26/0.43 % (5746)Time elapsed: 0.013 s
% 0.26/0.43 % (5746)Instructions burned: 15 (million)
% 0.26/0.43 % (5746)------------------------------
% 0.26/0.43 % (5746)------------------------------
% 0.26/0.43 % (5745)Success in time 0.017 s
% 0.26/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------