TSTP Solution File: PLA053^5 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n006.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 : Mon Jun 24 13:38:51 EDT 2024
% Result : Theorem 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : PLA053^5 : TPTP v8.2.0. Released v8.1.0.
% 0.12/0.14 % Command : run_vampire %s %d THM
% 0.14/0.36 % Computer : n006.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 : Tue Jun 18 17:12:24 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.38 This is a TH0_THM_EQU_NAR problem
% 0.14/0.38 Running higher-order theorem proving
% 0.14/0.38 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.14/0.40 % (15235)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.40 % (15233)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)
% 0.14/0.40 % (15236)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)
% 0.14/0.40 % (15234)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)
% 0.14/0.40 % (15238)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.40 % (15237)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)
% 0.14/0.40 % (15232)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.40 % (15235)Instruction limit reached!
% 0.14/0.40 % (15235)------------------------------
% 0.14/0.40 % (15235)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.40 % (15235)Termination reason: Unknown
% 0.14/0.40 % (15235)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (15236)Instruction limit reached!
% 0.14/0.40 % (15236)------------------------------
% 0.14/0.40 % (15236)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.40 % (15236)Termination reason: Unknown
% 0.14/0.40 % (15236)Termination phase: Preprocessing 3
% 0.14/0.40
% 0.14/0.40 % (15236)Memory used [KB]: 1023
% 0.14/0.40 % (15236)Time elapsed: 0.003 s
% 0.14/0.40 % (15236)Instructions burned: 3 (million)
% 0.14/0.40 % (15236)------------------------------
% 0.14/0.40 % (15236)------------------------------
% 0.14/0.40 % (15235)Memory used [KB]: 1023
% 0.14/0.40 % (15235)Time elapsed: 0.003 s
% 0.14/0.40 % (15235)Instructions burned: 3 (million)
% 0.14/0.40 % (15235)------------------------------
% 0.14/0.40 % (15235)------------------------------
% 0.14/0.40 % (15233)Instruction limit reached!
% 0.14/0.40 % (15233)------------------------------
% 0.14/0.40 % (15233)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.40 % (15233)Termination reason: Unknown
% 0.14/0.40 % (15233)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (15233)Memory used [KB]: 1023
% 0.14/0.40 % (15233)Time elapsed: 0.004 s
% 0.14/0.40 % (15233)Instructions burned: 4 (million)
% 0.14/0.40 % (15233)------------------------------
% 0.14/0.40 % (15233)------------------------------
% 0.14/0.40 % (15237)Refutation not found, incomplete strategy
% 0.14/0.40 % (15237)------------------------------
% 0.14/0.40 % (15237)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.40 % (15237)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.40
% 0.14/0.40
% 0.14/0.40 % (15237)Memory used [KB]: 5500
% 0.14/0.40 % (15237)Time elapsed: 0.004 s
% 0.14/0.40 % (15237)Instructions burned: 3 (million)
% 0.14/0.40 % (15237)------------------------------
% 0.14/0.40 % (15237)------------------------------
% 0.14/0.41 % (15234)First to succeed.
% 0.14/0.41 % (15238)Instruction limit reached!
% 0.14/0.41 % (15238)------------------------------
% 0.14/0.41 % (15238)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.41 % (15238)Termination reason: Unknown
% 0.14/0.41 % (15238)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (15238)Memory used [KB]: 5628
% 0.14/0.41 % (15238)Time elapsed: 0.013 s
% 0.14/0.41 % (15238)Instructions burned: 18 (million)
% 0.14/0.41 % (15238)------------------------------
% 0.14/0.41 % (15238)------------------------------
% 0.14/0.41 % (15232)Also succeeded, but the first one will report.
% 0.14/0.42 % (15234)Refutation found. Thanks to Tanya!
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% 0.14/0.42 thf(type_def_5, type, mworld: $tType).
% 0.14/0.42 thf(func_def_0, type, mworld: $tType).
% 0.14/0.42 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.14/0.42 thf(func_def_2, type, mactual: mworld).
% 0.14/0.42 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.14/0.42 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.14/0.42 thf(func_def_14, type, h: $i > mworld > $o).
% 0.14/0.42 thf(func_def_15, type, bomb: $i > mworld > $o).
% 0.14/0.42 thf(func_def_16, type, defused: $i > mworld > $o).
% 0.14/0.42 thf(func_def_17, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.14/0.42 thf(func_def_34, type, sK1: mworld > $i > $i).
% 0.14/0.42 thf(func_def_36, type, sK3: mworld > $i).
% 0.14/0.42 thf(func_def_37, type, sK4: mworld).
% 0.14/0.42 thf(f181,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(avatar_sat_refutation,[],[f134,f158,f180])).
% 0.14/0.42 thf(f180,plain,(
% 0.14/0.42 ~spl0_1),
% 0.14/0.42 inference(avatar_contradiction_clause,[],[f179])).
% 0.14/0.42 thf(f179,plain,(
% 0.14/0.42 $false | ~spl0_1),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f172])).
% 0.14/0.42 thf(f172,plain,(
% 0.14/0.42 ($false = $true) | ~spl0_1),
% 0.14/0.42 inference(superposition,[],[f168,f54])).
% 0.14/0.42 thf(f54,plain,(
% 0.14/0.42 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 0.14/0.42 inference(cnf_transformation,[],[f43])).
% 0.14/0.42 thf(f43,plain,(
% 0.14/0.42 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 0.14/0.42 inference(fool_elimination,[],[f42])).
% 0.14/0.42 thf(f42,plain,(
% 0.14/0.42 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.14/0.42 inference(rectify,[],[f9])).
% 0.14/0.42 thf(f9,axiom,(
% 0.14/0.42 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive)).
% 0.14/0.42 thf(f168,plain,(
% 0.14/0.42 ($false = (mrel @ sK4 @ sK4)) | ~spl0_1),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f161])).
% 0.14/0.42 thf(f161,plain,(
% 0.14/0.42 ($false = (mrel @ sK4 @ sK4)) | ($false = $true) | ~spl0_1),
% 0.14/0.42 inference(superposition,[],[f129,f109])).
% 0.14/0.42 thf(f109,plain,(
% 0.14/0.42 ($true = (mrel @ mactual @ sK4))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f107])).
% 0.14/0.42 thf(f107,plain,(
% 0.14/0.42 ($false = ((mrel @ mactual @ sK4) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((bomb @ Y0 @ sK4) & (h @ Y1 @ sK4)) => (defused @ Y0 @ sK4))))))))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f106])).
% 0.14/0.42 thf(f106,plain,(
% 0.14/0.42 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((bomb @ Y1 @ Y0) & (h @ Y2 @ Y0)) => (defused @ Y1 @ Y0)))))))) @ sK4))),
% 0.14/0.42 inference(sigma_clausification,[],[f105])).
% 0.14/0.42 thf(f105,plain,(
% 0.14/0.42 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((bomb @ Y1 @ Y0) & (h @ Y2 @ Y0)) => (defused @ Y1 @ Y0))))))))) != $true)),
% 0.14/0.42 inference(beta_eta_normalization,[],[f69])).
% 0.14/0.42 thf(f69,plain,(
% 0.14/0.42 (((^[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]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 0.14/0.42 inference(definition_unfolding,[],[f57,f60,f62,f68,f64,f66,f65])).
% 0.14/0.42 thf(f65,plain,(
% 0.14/0.42 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f45])).
% 0.14/0.42 thf(f45,plain,(
% 0.14/0.42 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f44])).
% 0.14/0.42 thf(f44,plain,(
% 0.14/0.42 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 0.14/0.42 inference(rectify,[],[f3])).
% 0.14/0.42 thf(f3,axiom,(
% 0.14/0.42 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def)).
% 0.14/0.42 thf(f66,plain,(
% 0.14/0.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f27])).
% 0.14/0.42 thf(f27,plain,(
% 0.14/0.42 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f26])).
% 0.14/0.42 thf(f26,plain,(
% 0.14/0.42 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.14/0.42 inference(rectify,[],[f5])).
% 0.14/0.42 thf(f5,axiom,(
% 0.14/0.42 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.14/0.42 thf(f64,plain,(
% 0.14/0.42 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f31])).
% 0.14/0.42 thf(f31,plain,(
% 0.14/0.42 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.42 inference(fool_elimination,[],[f30])).
% 0.14/0.42 thf(f30,plain,(
% 0.14/0.42 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2] : (X0 @ X2 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f12])).
% 0.14/0.42 thf(f12,axiom,(
% 0.14/0.42 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6] : (X1 @ X6 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def)).
% 0.14/0.42 thf(f68,plain,(
% 0.14/0.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f20])).
% 0.14/0.42 thf(f20,plain,(
% 0.14/0.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.42 inference(fool_elimination,[],[f19])).
% 0.14/0.42 thf(f19,plain,(
% 0.14/0.42 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : (X0 @ X2 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f11])).
% 0.14/0.42 thf(f11,axiom,(
% 0.14/0.42 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6] : (X1 @ X6 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def)).
% 0.14/0.42 thf(f62,plain,(
% 0.14/0.42 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f25])).
% 0.14/0.42 thf(f25,plain,(
% 0.14/0.42 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f24])).
% 0.14/0.42 thf(f24,plain,(
% 0.14/0.42 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 0.14/0.42 inference(rectify,[],[f7])).
% 0.14/0.42 thf(f7,axiom,(
% 0.14/0.42 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def)).
% 0.14/0.42 thf(f60,plain,(
% 0.14/0.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.14/0.42 inference(cnf_transformation,[],[f21])).
% 0.14/0.42 thf(f21,plain,(
% 0.14/0.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.14/0.42 inference(fool_elimination,[],[f1])).
% 0.14/0.42 thf(f1,axiom,(
% 0.14/0.42 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.14/0.42 thf(f57,plain,(
% 0.14/0.42 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 0.14/0.42 inference(cnf_transformation,[],[f50])).
% 0.14/0.42 thf(f50,plain,(
% 0.14/0.42 ((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) != $true)),
% 0.14/0.42 inference(flattening,[],[f47])).
% 0.14/0.42 thf(f47,plain,(
% 0.14/0.42 ~((mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0)))))))) = $true)),
% 0.14/0.42 inference(fool_elimination,[],[f46])).
% 0.14/0.42 thf(f46,plain,(
% 0.14/0.42 ~(mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0))))))))),
% 0.14/0.42 inference(rectify,[],[f17])).
% 0.14/0.42 thf(f17,negated_conjecture,(
% 0.14/0.42 ~(mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6))))))))),
% 0.14/0.42 inference(negated_conjecture,[],[f16])).
% 0.14/0.42 thf(f16,conjecture,(
% 0.14/0.42 (mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6))))))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.14/0.42 thf(f129,plain,(
% 0.14/0.42 ( ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK4))) ) | ~spl0_1),
% 0.14/0.42 inference(avatar_component_clause,[],[f128])).
% 0.14/0.42 thf(f128,plain,(
% 0.14/0.42 spl0_1 <=> ! [X0 : mworld] : (($false = (mrel @ mactual @ X0)) | ($false = (mrel @ X0 @ sK4)))),
% 0.14/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.42 thf(f158,plain,(
% 0.14/0.42 ~spl0_2),
% 0.14/0.42 inference(avatar_contradiction_clause,[],[f157])).
% 0.14/0.42 thf(f157,plain,(
% 0.14/0.42 $false | ~spl0_2),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f154])).
% 0.14/0.42 thf(f154,plain,(
% 0.14/0.42 ($false = $true) | ~spl0_2),
% 0.14/0.42 inference(backward_demodulation,[],[f117,f152])).
% 0.14/0.42 thf(f152,plain,(
% 0.14/0.42 ($false = (bomb @ sK5 @ sK4)) | ~spl0_2),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f151])).
% 0.14/0.42 thf(f151,plain,(
% 0.14/0.42 ($false = (bomb @ sK5 @ sK4)) | ($false = $true) | ~spl0_2),
% 0.14/0.42 inference(superposition,[],[f114,f132])).
% 0.14/0.42 thf(f132,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($true = (defused @ X1 @ sK4)) | ($false = (bomb @ X1 @ sK4))) ) | ~spl0_2),
% 0.14/0.42 inference(avatar_component_clause,[],[f131])).
% 0.14/0.42 thf(f131,plain,(
% 0.14/0.42 spl0_2 <=> ! [X1] : (($true = (defused @ X1 @ sK4)) | ($false = (bomb @ X1 @ sK4)))),
% 0.14/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.42 thf(f114,plain,(
% 0.14/0.42 ($false = (defused @ sK5 @ sK4))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f113])).
% 0.14/0.42 thf(f113,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($false = (((bomb @ sK5 @ sK4) & (h @ X1 @ sK4)) => (defused @ sK5 @ sK4)))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f112])).
% 0.14/0.42 thf(f112,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (((bomb @ sK5 @ sK4) & (h @ Y0 @ sK4)) => (defused @ sK5 @ sK4))) @ X1))) )),
% 0.14/0.42 inference(pi_clausification,[],[f111])).
% 0.14/0.42 thf(f111,plain,(
% 0.14/0.42 ($false = (?? @ $i @ (^[Y0 : $i]: (((bomb @ sK5 @ sK4) & (h @ Y0 @ sK4)) => (defused @ sK5 @ sK4)))))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f110])).
% 0.14/0.42 thf(f110,plain,(
% 0.14/0.42 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((bomb @ Y0 @ sK4) & (h @ Y1 @ sK4)) => (defused @ Y0 @ sK4))))) @ sK5))),
% 0.14/0.42 inference(sigma_clausification,[],[f108])).
% 0.14/0.42 thf(f108,plain,(
% 0.14/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((bomb @ Y0 @ sK4) & (h @ Y1 @ sK4)) => (defused @ Y0 @ sK4)))))))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f107])).
% 0.14/0.42 thf(f117,plain,(
% 0.14/0.42 ($true = (bomb @ sK5 @ sK4))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f115])).
% 0.14/0.42 thf(f115,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($true = ((bomb @ sK5 @ sK4) & (h @ X1 @ sK4)))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f113])).
% 0.14/0.42 thf(f134,plain,(
% 0.14/0.42 spl0_2 | spl0_1),
% 0.14/0.42 inference(avatar_split_clause,[],[f125,f128,f131])).
% 0.14/0.42 thf(f125,plain,(
% 0.14/0.42 ( ! [X0 : mworld,X1 : $i] : (($false = (mrel @ mactual @ X0)) | ($false = (bomb @ X1 @ sK4)) | ($false = (mrel @ X0 @ sK4)) | ($true = (defused @ X1 @ sK4))) )),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f123])).
% 0.14/0.42 thf(f123,plain,(
% 0.14/0.42 ( ! [X0 : mworld,X1 : $i] : (($false = (mrel @ X0 @ sK4)) | ($true = (defused @ X1 @ sK4)) | ($false = (bomb @ X1 @ sK4)) | ($false = (mrel @ mactual @ X0)) | ($false = $true)) )),
% 0.14/0.42 inference(superposition,[],[f85,f116])).
% 0.14/0.42 thf(f116,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($true = (h @ X1 @ sK4))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f115])).
% 0.14/0.42 thf(f85,plain,(
% 0.14/0.42 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (h @ (sK1 @ X1 @ X2) @ X3)) | ($false = (mrel @ X1 @ X3)) | ($false = (mrel @ mactual @ X1)) | ((defused @ X2 @ X3) = $true) | ($false = (bomb @ X2 @ X3))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f84])).
% 0.14/0.42 thf(f84,plain,(
% 0.14/0.42 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (mrel @ X1 @ X3)) | ((defused @ X2 @ X3) = $true) | ($false = ((bomb @ X2 @ X3) & (h @ (sK1 @ X1 @ X2) @ X3)))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f83])).
% 0.14/0.42 thf(f83,plain,(
% 0.14/0.42 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($true = (((bomb @ X2 @ X3) & (h @ (sK1 @ X1 @ X2) @ X3)) => (defused @ X2 @ X3))) | ($false = (mrel @ X1 @ X3)) | ($false = (mrel @ mactual @ X1))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f82])).
% 0.14/0.42 thf(f82,plain,(
% 0.14/0.42 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : ((((mrel @ X1 @ X3) => (((bomb @ X2 @ X3) & (h @ (sK1 @ X1 @ X2) @ X3)) => (defused @ X2 @ X3))) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f81])).
% 0.14/0.42 thf(f81,plain,(
% 0.14/0.42 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((bomb @ X2 @ Y0) & (h @ (sK1 @ X1 @ X2) @ Y0)) => (defused @ X2 @ Y0)))) @ X3)) | ($false = (mrel @ mactual @ X1))) )),
% 0.14/0.42 inference(pi_clausification,[],[f80])).
% 0.14/0.42 thf(f80,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (((bomb @ X2 @ Y0) & (h @ (sK1 @ X1 @ X2) @ Y0)) => (defused @ X2 @ Y0))))))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f79])).
% 0.14/0.42 thf(f79,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((bomb @ X2 @ Y1) & (h @ Y0 @ Y1)) => (defused @ X2 @ Y1)))))) @ (sK1 @ X1 @ X2)) = $true)) )),
% 0.14/0.42 inference(sigma_clausification,[],[f78])).
% 0.14/0.42 thf(f78,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : mworld] : (((?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) => (((bomb @ X2 @ Y1) & (h @ Y0 @ Y1)) => (defused @ X2 @ Y1))))))) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f77])).
% 0.14/0.42 thf(f77,plain,(
% 0.14/0.42 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((bomb @ Y0 @ Y2) & (h @ Y1 @ Y2)) => (defused @ Y0 @ Y2)))))))) @ X2))) )),
% 0.14/0.42 inference(pi_clausification,[],[f76])).
% 0.14/0.42 thf(f76,plain,(
% 0.14/0.42 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((bomb @ Y0 @ Y2) & (h @ Y1 @ Y2)) => (defused @ Y0 @ Y2))))))))))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f75])).
% 0.14/0.42 thf(f75,plain,(
% 0.14/0.42 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ X1 @ Y2) => (((bomb @ Y0 @ Y2) & (h @ Y1 @ Y2)) => (defused @ Y0 @ Y2)))))))))))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f74])).
% 0.14/0.42 thf(f74,plain,(
% 0.14/0.42 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((bomb @ Y1 @ Y3) & (h @ Y2 @ Y3)) => (defused @ Y1 @ Y3))))))))))) @ X1))) )),
% 0.14/0.42 inference(pi_clausification,[],[f73])).
% 0.14/0.42 thf(f73,plain,(
% 0.14/0.42 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y0 @ Y3) => (((bomb @ Y1 @ Y3) & (h @ Y2 @ Y3)) => (defused @ Y1 @ Y3)))))))))))) = $true)),
% 0.14/0.42 inference(beta_eta_normalization,[],[f72])).
% 0.14/0.42 thf(f72,plain,(
% 0.14/0.42 ($true = ((^[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 > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f67,f60,f62,f68,f64,f62,f66,f65])).
% 0.14/0.42 thf(f67,plain,(
% 0.14/0.42 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f37])).
% 0.14/0.42 thf(f37,plain,(
% 0.14/0.42 ($true = (mlocal @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mexists_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mand @ (bomb @ Y0) @ (h @ Y1)) @ (defused @ Y0))))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f36])).
% 0.14/0.42 thf(f36,plain,(
% 0.14/0.42 (mlocal @ (mbox @ (mforall_di @ (^[X0 : $i] : (mexists_di @ (^[X1 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X0) @ (h @ X1)) @ (defused @ X0)))))))))),
% 0.14/0.42 inference(rectify,[],[f15])).
% 0.14/0.42 thf(f15,axiom,(
% 0.14/0.42 (mlocal @ (mbox @ (mforall_di @ (^[X6 : $i] : (mexists_di @ (^[X7 : $i] : (mbox @ (mimplies @ (mand @ (bomb @ X6) @ (h @ X7)) @ (defused @ X6)))))))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3)).
% 0.14/0.42 % SZS output end Proof for theBenchmark
% 0.14/0.42 % (15234)------------------------------
% 0.14/0.42 % (15234)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.14/0.42 % (15234)Termination reason: Refutation
% 0.14/0.42
% 0.14/0.42 % (15234)Memory used [KB]: 5756
% 0.14/0.42 % (15234)Time elapsed: 0.015 s
% 0.14/0.42 % (15234)Instructions burned: 16 (million)
% 0.14/0.42 % (15234)------------------------------
% 0.14/0.42 % (15234)------------------------------
% 0.14/0.42 % (15231)Success in time 0.028 s
%------------------------------------------------------------------------------