TSTP Solution File: PUZ085^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PUZ085^1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.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 : Sun May 5 08:49:08 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ085^1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 18:00:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650
% 0.21/0.37 % (18765)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.37 % (18759)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 Vampire---4 for (2999ds/4Mi)
% 0.21/0.37 % (18760)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 Vampire---4 for (2999ds/27Mi)
% 0.21/0.37 % (18761)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.21/0.37 % (18762)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.21/0.37 % (18765)Instruction limit reached!
% 0.21/0.37 % (18765)------------------------------
% 0.21/0.37 % (18765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (18765)Termination reason: Unknown
% 0.21/0.37 % (18765)Termination phase: shuffling
% 0.21/0.37 % (18758)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.21/0.37
% 0.21/0.37 % (18763)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.21/0.37 % (18765)Memory used [KB]: 1023
% 0.21/0.37 % (18765)Time elapsed: 0.003 s
% 0.21/0.37 % (18765)Instructions burned: 3 (million)
% 0.21/0.37 % (18765)------------------------------
% 0.21/0.37 % (18765)------------------------------
% 0.21/0.37 % (18764)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.21/0.37 % (18761)Instruction limit reached!
% 0.21/0.37 % (18761)------------------------------
% 0.21/0.37 % (18761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (18761)Termination reason: Unknown
% 0.21/0.37 % (18762)Instruction limit reached!
% 0.21/0.37 % (18762)------------------------------
% 0.21/0.37 % (18762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (18762)Termination reason: Unknown
% 0.21/0.37 % (18762)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (18762)Memory used [KB]: 1023
% 0.21/0.37 % (18762)Time elapsed: 0.003 s
% 0.21/0.37 % (18762)Instructions burned: 2 (million)
% 0.21/0.37 % (18762)------------------------------
% 0.21/0.37 % (18762)------------------------------
% 0.21/0.37 % (18761)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (18761)Memory used [KB]: 1023
% 0.21/0.37 % (18761)Time elapsed: 0.003 s
% 0.21/0.37 % (18761)Instructions burned: 2 (million)
% 0.21/0.37 % (18761)------------------------------
% 0.21/0.37 % (18761)------------------------------
% 0.21/0.37 % (18759)Instruction limit reached!
% 0.21/0.37 % (18759)------------------------------
% 0.21/0.37 % (18759)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (18759)Termination reason: Unknown
% 0.21/0.37 % (18759)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (18759)Memory used [KB]: 1023
% 0.21/0.37 % (18759)Time elapsed: 0.004 s
% 0.21/0.37 % (18759)Instructions burned: 4 (million)
% 0.21/0.37 % (18759)------------------------------
% 0.21/0.37 % (18759)------------------------------
% 0.21/0.38 % (18763)Refutation not found, incomplete strategy
% 0.21/0.38 % (18763)------------------------------
% 0.21/0.38 % (18763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (18763)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (18763)Memory used [KB]: 5628
% 0.21/0.38 % (18763)Time elapsed: 0.008 s
% 0.21/0.38 % (18763)Instructions burned: 10 (million)
% 0.21/0.38 % (18763)------------------------------
% 0.21/0.38 % (18763)------------------------------
% 0.21/0.38 % (18764)Instruction limit reached!
% 0.21/0.38 % (18764)------------------------------
% 0.21/0.38 % (18764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (18764)Termination reason: Unknown
% 0.21/0.38 % (18764)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (18764)Memory used [KB]: 5756
% 0.21/0.38 % (18764)Time elapsed: 0.013 s
% 0.21/0.38 % (18764)Instructions burned: 19 (million)
% 0.21/0.38 % (18764)------------------------------
% 0.21/0.38 % (18764)------------------------------
% 0.21/0.38 % (18758)First to succeed.
% 0.21/0.39 % (18766)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (2999ds/37Mi)
% 0.21/0.39 % (18760)Also succeeded, but the first one will report.
% 0.21/0.39 % (18767)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.21/0.39 % (18768)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.21/0.39 % (18758)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for Vampire---4
% 0.21/0.39 % SZS output start Proof for Vampire---4
% 0.21/0.39 thf(type_def_5, type, mu: $tType).
% 0.21/0.39 thf(func_def_0, type, mu: $tType).
% 0.21/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_33, type, peter: $i > $i > $o).
% 0.21/0.39 thf(func_def_34, type, john: $i > $i > $o).
% 0.21/0.39 thf(func_def_35, type, wife: ($i > $i > $o) > $i > $i > $o).
% 0.21/0.39 thf(func_def_53, type, sK2: $i > $o).
% 0.21/0.39 thf(func_def_56, type, ph5: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(f272,plain,(
% 0.21/0.39 $false),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f270])).
% 0.21/0.39 thf(f270,plain,(
% 0.21/0.39 ($false = $true)),
% 0.21/0.39 inference(superposition,[],[f266,f203])).
% 0.21/0.39 thf(f203,plain,(
% 0.21/0.39 ($false = (sK2 @ sK4))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f202])).
% 0.21/0.39 thf(f202,plain,(
% 0.21/0.39 ($false = ((~ (wife @ peter @ sK3 @ sK4)) | (sK2 @ sK4)))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f201])).
% 0.21/0.39 thf(f201,plain,(
% 0.21/0.39 ($false = ((^[Y0 : $i]: ((~ (wife @ peter @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK4))),
% 0.21/0.39 inference(sigma_clausification,[],[f198])).
% 0.21/0.39 thf(f198,plain,(
% 0.21/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK3 @ Y0)) | (sK2 @ Y0)))))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f197])).
% 0.21/0.39 thf(f197,plain,(
% 0.21/0.39 ($false = ((~ (wife @ peter @ sK1 @ sK3)) | (!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK3 @ Y0)) | (sK2 @ Y0))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f196])).
% 0.21/0.39 thf(f196,plain,(
% 0.21/0.39 (((^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ Y0 @ Y1)) | (sK2 @ Y1)))))) @ sK3) = $false)),
% 0.21/0.39 inference(sigma_clausification,[],[f195])).
% 0.21/0.39 thf(f195,plain,(
% 0.21/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ Y0 @ Y1)) | (sK2 @ Y1))))))))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f193])).
% 0.21/0.39 thf(f193,plain,(
% 0.21/0.39 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ Y0 @ Y1)) | (sK2 @ Y1))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (sK2 @ Y0)))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f192])).
% 0.21/0.39 thf(f192,plain,(
% 0.21/0.39 ($false = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ sK1 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (wife @ peter @ Y1 @ Y2)) | (Y0 @ Y2))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ sK1 @ Y1)) | (Y0 @ Y1))))))) @ sK2))),
% 0.21/0.39 inference(sigma_clausification,[],[f191])).
% 0.21/0.39 thf(f191,plain,(
% 0.21/0.39 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ sK1 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (wife @ peter @ Y1 @ Y2)) | (Y0 @ Y2))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (wife @ peter @ sK1 @ Y1)) | (Y0 @ Y1)))))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f190])).
% 0.21/0.39 thf(f190,plain,(
% 0.21/0.39 ($false = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (wife @ peter @ Y0 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (wife @ peter @ Y2 @ Y3)) | (Y1 @ Y3))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (wife @ peter @ Y0 @ Y2)) | (Y1 @ Y2))))))))) @ sK1))),
% 0.21/0.39 inference(sigma_clausification,[],[f189])).
% 0.21/0.39 thf(f189,plain,(
% 0.21/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (wife @ peter @ Y0 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (wife @ peter @ Y2 @ Y3)) | (Y1 @ Y3))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (wife @ peter @ Y0 @ Y2)) | (Y1 @ Y2)))))))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f163])).
% 0.21/0.39 thf(f163,plain,(
% 0.21/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ (wife @ peter) @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ (wife @ peter) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ (wife @ peter) @ Y0)))))))),
% 0.21/0.39 inference(definition_unfolding,[],[f133,f118,f117,f153,f114,f114,f114])).
% 0.21/0.39 thf(f114,plain,(
% 0.21/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f93])).
% 0.21/0.39 thf(f93,plain,(
% 0.21/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f92])).
% 0.21/0.39 thf(f92,plain,(
% 0.21/0.39 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))),
% 0.21/0.39 inference(rectify,[],[f16])).
% 0.21/0.39 thf(f16,axiom,(
% 0.21/0.39 (mbox = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))))),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mbox)).
% 0.21/0.39 thf(f153,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.39 inference(definition_unfolding,[],[f141,f128,f130])).
% 0.21/0.39 thf(f130,plain,(
% 0.21/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f78])).
% 0.21/0.39 thf(f78,plain,(
% 0.21/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.39 inference(fool_elimination,[],[f77])).
% 0.21/0.39 thf(f77,plain,(
% 0.21/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.21/0.39 inference(rectify,[],[f3])).
% 0.21/0.39 thf(f3,axiom,(
% 0.21/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mnot)).
% 0.21/0.39 thf(f128,plain,(
% 0.21/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f83])).
% 0.21/0.39 thf(f83,plain,(
% 0.21/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f82])).
% 0.21/0.39 thf(f82,plain,(
% 0.21/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.21/0.39 inference(rectify,[],[f4])).
% 0.21/0.39 thf(f4,axiom,(
% 0.21/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mor)).
% 0.21/0.39 thf(f141,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.39 inference(cnf_transformation,[],[f81])).
% 0.21/0.39 thf(f81,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f80])).
% 0.21/0.39 thf(f80,plain,(
% 0.21/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.39 inference(rectify,[],[f6])).
% 0.21/0.39 thf(f6,axiom,(
% 0.21/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mimplies)).
% 0.21/0.39 thf(f117,plain,(
% 0.21/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f54])).
% 0.21/0.39 thf(f54,plain,(
% 0.21/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.39 inference(fool_elimination,[],[f53])).
% 0.21/0.39 thf(f53,plain,(
% 0.21/0.39 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.21/0.39 inference(rectify,[],[f11])).
% 0.21/0.39 thf(f11,axiom,(
% 0.21/0.39 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mforall_prop)).
% 0.21/0.39 thf(f118,plain,(
% 0.21/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.39 inference(cnf_transformation,[],[f112])).
% 0.21/0.39 thf(f112,plain,(
% 0.21/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f111])).
% 0.21/0.39 thf(f111,plain,(
% 0.21/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.39 inference(rectify,[],[f28])).
% 0.21/0.39 thf(f28,axiom,(
% 0.21/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mvalid)).
% 0.21/0.39 thf(f133,plain,(
% 0.21/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ (wife @ peter) @ Y0) @ (mbox @ (wife @ peter) @ (mbox @ (wife @ peter) @ Y0)))))) != $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f113])).
% 0.21/0.39 thf(f113,plain,(
% 0.21/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ (wife @ peter) @ Y0) @ (mbox @ (wife @ peter) @ (mbox @ (wife @ peter) @ Y0)))))) != $true)),
% 0.21/0.39 inference(flattening,[],[f48])).
% 0.21/0.39 thf(f48,plain,(
% 0.21/0.39 ~((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ (wife @ peter) @ Y0) @ (mbox @ (wife @ peter) @ (mbox @ (wife @ peter) @ Y0)))))) = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f47])).
% 0.21/0.39 thf(f47,plain,(
% 0.21/0.39 ~(mvalid @ (mforall_prop @ (^[X0 : $i > $o] : (mimplies @ (mbox @ (wife @ peter) @ X0) @ (mbox @ (wife @ peter) @ (mbox @ (wife @ peter) @ X0))))))),
% 0.21/0.39 inference(rectify,[],[f39])).
% 0.21/0.39 thf(f39,negated_conjecture,(
% 0.21/0.39 ~(mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ (wife @ peter) @ X11) @ (mbox @ (wife @ peter) @ (mbox @ (wife @ peter) @ X11))))))),
% 0.21/0.39 inference(negated_conjecture,[],[f38])).
% 0.21/0.39 thf(f38,conjecture,(
% 0.21/0.39 (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ (wife @ peter) @ X11) @ (mbox @ (wife @ peter) @ (mbox @ (wife @ peter) @ X11))))))),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',conj)).
% 0.21/0.39 thf(f266,plain,(
% 0.21/0.39 ((sK2 @ sK4) = $true)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f260])).
% 0.21/0.39 thf(f260,plain,(
% 0.21/0.39 ((sK2 @ sK4) = $true) | ($false = $true)),
% 0.21/0.39 inference(superposition,[],[f252,f205])).
% 0.21/0.39 thf(f205,plain,(
% 0.21/0.39 ($true = (wife @ peter @ sK3 @ sK4))),
% 0.21/0.39 inference(not_proxy_clausification,[],[f204])).
% 0.21/0.39 thf(f204,plain,(
% 0.21/0.39 ($false = (~ (wife @ peter @ sK3 @ sK4)))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f202])).
% 0.21/0.39 thf(f252,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($false = (wife @ peter @ sK3 @ X0)) | ($true = (sK2 @ X0))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f246])).
% 0.21/0.39 thf(f246,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($false = $true) | ($false = (wife @ peter @ sK3 @ X0)) | ($true = (sK2 @ X0))) )),
% 0.21/0.39 inference(superposition,[],[f243,f200])).
% 0.21/0.39 thf(f200,plain,(
% 0.21/0.39 ($true = (wife @ peter @ sK1 @ sK3))),
% 0.21/0.39 inference(not_proxy_clausification,[],[f199])).
% 0.21/0.39 thf(f199,plain,(
% 0.21/0.39 ($false = (~ (wife @ peter @ sK1 @ sK3)))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f197])).
% 0.21/0.39 thf(f243,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (($false = (wife @ peter @ sK1 @ X1)) | ($false = (wife @ peter @ X1 @ X0)) | ($true = (sK2 @ X0))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f239])).
% 0.21/0.39 thf(f239,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = (wife @ peter @ sK1 @ X1)) | ($false = (wife @ peter @ X1 @ X0)) | ($true = (sK2 @ X0))) )),
% 0.21/0.39 inference(superposition,[],[f210,f225])).
% 0.21/0.39 thf(f225,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (wife @ peter @ X3 @ X1)) | ($false = (wife @ peter @ X2 @ X1)) | ($false = (wife @ peter @ X3 @ X2))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f224])).
% 0.21/0.39 thf(f224,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((wife @ peter @ X3 @ X2) & (wife @ peter @ X2 @ X1))) | ($true = (wife @ peter @ X3 @ X1))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f223])).
% 0.21/0.39 thf(f223,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((wife @ peter @ X3 @ X2) & (wife @ peter @ X2 @ X1)) => (wife @ peter @ X3 @ X1)))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f222])).
% 0.21/0.39 thf(f222,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((wife @ peter @ Y0 @ X2) & (wife @ peter @ X2 @ X1)) => (wife @ peter @ Y0 @ X1))) @ X3))) )),
% 0.21/0.39 inference(pi_clausification,[],[f221])).
% 0.21/0.39 thf(f221,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((wife @ peter @ Y0 @ X2) & (wife @ peter @ X2 @ X1)) => (wife @ peter @ Y0 @ X1)))))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f220])).
% 0.21/0.39 thf(f220,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((wife @ peter @ Y1 @ Y0) & (wife @ peter @ Y0 @ X1)) => (wife @ peter @ Y1 @ X1))))) @ X2))) )),
% 0.21/0.39 inference(pi_clausification,[],[f219])).
% 0.21/0.39 thf(f219,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((wife @ peter @ Y1 @ Y0) & (wife @ peter @ Y0 @ X1)) => (wife @ peter @ Y1 @ X1)))))) = $true)) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f218])).
% 0.21/0.39 thf(f218,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((wife @ peter @ Y2 @ Y1) & (wife @ peter @ Y1 @ Y0)) => (wife @ peter @ Y2 @ Y0))))))) @ X1))) )),
% 0.21/0.39 inference(pi_clausification,[],[f217])).
% 0.21/0.39 thf(f217,plain,(
% 0.21/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((wife @ peter @ Y2 @ Y1) & (wife @ peter @ Y1 @ Y0)) => (wife @ peter @ Y2 @ Y0)))))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.39 thf(f164,plain,(
% 0.21/0.39 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))) @ (wife @ peter)))),
% 0.21/0.39 inference(definition_unfolding,[],[f138,f129])).
% 0.21/0.39 thf(f129,plain,(
% 0.21/0.39 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f62])).
% 0.21/0.39 thf(f62,plain,(
% 0.21/0.39 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f61])).
% 0.21/0.39 thf(f61,plain,(
% 0.21/0.39 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X1 @ X2)) => (X0 @ X1 @ X3)))) = mtransitive)),
% 0.21/0.39 inference(rectify,[],[f21])).
% 0.21/0.39 thf(f21,axiom,(
% 0.21/0.39 ((^[X6 : $i > $i > $o] : (! [X8,X9,X10] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',mtransitive)).
% 0.21/0.39 thf(f138,plain,(
% 0.21/0.39 ((mtransitive @ (wife @ peter)) = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f64])).
% 0.21/0.39 thf(f64,plain,(
% 0.21/0.39 ((mtransitive @ (wife @ peter)) = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f63])).
% 0.21/0.39 thf(f63,plain,(
% 0.21/0.39 (mtransitive @ (wife @ peter))),
% 0.21/0.39 inference(rectify,[],[f37])).
% 0.21/0.39 thf(f37,axiom,(
% 0.21/0.39 (mtransitive @ (wife @ peter))),
% 0.21/0.39 file('/export/starexec/sandbox/tmp/tmp.Cnv3vMfqyw/Vampire---4.8_18650',trans_wife_peter)).
% 0.21/0.39 thf(f210,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (($false = (wife @ peter @ sK1 @ X1)) | ((sK2 @ X1) = $true)) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f209])).
% 0.21/0.39 thf(f209,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (((sK2 @ X1) = $true) | ($true = (~ (wife @ peter @ sK1 @ X1)))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f208])).
% 0.21/0.39 thf(f208,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (($true = ((~ (wife @ peter @ sK1 @ X1)) | (sK2 @ X1)))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f207])).
% 0.21/0.39 thf(f207,plain,(
% 0.21/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (sK2 @ Y0))) @ X1))) )),
% 0.21/0.39 inference(pi_clausification,[],[f206])).
% 0.21/0.39 thf(f206,plain,(
% 0.21/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (sK2 @ Y0)))))),
% 0.21/0.39 inference(not_proxy_clausification,[],[f194])).
% 0.21/0.39 thf(f194,plain,(
% 0.21/0.39 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (wife @ peter @ sK1 @ Y0)) | (sK2 @ Y0))))))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f193])).
% 0.21/0.39 % SZS output end Proof for Vampire---4
% 0.21/0.39 % (18758)------------------------------
% 0.21/0.39 % (18758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (18758)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (18758)Memory used [KB]: 5756
% 0.21/0.39 % (18758)Time elapsed: 0.016 s
% 0.21/0.39 % (18758)Instructions burned: 18 (million)
% 0.21/0.39 % (18758)------------------------------
% 0.21/0.39 % (18758)------------------------------
% 0.21/0.39 % (18757)Success in time 0.018 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------