TSTP Solution File: SYO478^6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO478^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:05:22 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO478^6 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 09:47:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.37 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
% 0.22/0.39 % (9952)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (9951)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)
% 0.22/0.39 % (9953)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)
% 0.22/0.39 % (9946)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39 % (9949)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (9950)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)
% 0.22/0.39 % (9947)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)
% 0.22/0.39 % (9949)Instruction limit reached!
% 0.22/0.39 % (9949)------------------------------
% 0.22/0.39 % (9949)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (9949)Termination reason: Unknown
% 0.22/0.39 % (9949)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (9949)Memory used [KB]: 1023
% 0.22/0.39 % (9949)Time elapsed: 0.002 s
% 0.22/0.39 % (9949)Instructions burned: 2 (million)
% 0.22/0.39 % (9949)------------------------------
% 0.22/0.39 % (9949)------------------------------
% 0.22/0.39 % (9953)Instruction limit reached!
% 0.22/0.39 % (9953)------------------------------
% 0.22/0.39 % (9953)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (9953)Termination reason: Unknown
% 0.22/0.39 % (9953)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (9953)Memory used [KB]: 1023
% 0.22/0.39 % (9953)Time elapsed: 0.003 s
% 0.22/0.39 % (9953)Instructions burned: 4 (million)
% 0.22/0.39 % (9953)------------------------------
% 0.22/0.39 % (9953)------------------------------
% 0.22/0.39 % (9950)Instruction limit reached!
% 0.22/0.39 % (9950)------------------------------
% 0.22/0.39 % (9950)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (9950)Termination reason: Unknown
% 0.22/0.39 % (9950)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (9950)Memory used [KB]: 1023
% 0.22/0.39 % (9950)Time elapsed: 0.003 s
% 0.22/0.39 % (9950)Instructions burned: 4 (million)
% 0.22/0.39 % (9950)------------------------------
% 0.22/0.39 % (9950)------------------------------
% 0.22/0.39 % (9948)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)
% 0.22/0.39 % (9947)Instruction limit reached!
% 0.22/0.39 % (9947)------------------------------
% 0.22/0.39 % (9947)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (9947)Termination reason: Unknown
% 0.22/0.39 % (9947)Termination phase: Property scanning
% 0.22/0.39
% 0.22/0.39 % (9947)Memory used [KB]: 1023
% 0.22/0.39 % (9947)Time elapsed: 0.004 s
% 0.22/0.39 % (9947)Instructions burned: 5 (million)
% 0.22/0.39 % (9947)------------------------------
% 0.22/0.39 % (9947)------------------------------
% 0.22/0.39 % (9951)First to succeed.
% 0.22/0.39 % (9952)Also succeeded, but the first one will report.
% 0.22/0.39 % (9946)Also succeeded, but the first one will report.
% 0.22/0.39 % (9951)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% 0.22/0.39 thf(type_def_5, type, mu: $tType).
% 0.22/0.39 thf(func_def_0, type, mu: $tType).
% 0.22/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.39 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.22/0.39 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.22/0.39 thf(func_def_36, type, f: mu > $i > $o).
% 0.22/0.39 thf(func_def_55, type, sK3: mu).
% 0.22/0.39 thf(f150,plain,(
% 0.22/0.39 $false),
% 0.22/0.39 inference(trivial_inequality_removal,[],[f148])).
% 0.22/0.39 thf(f148,plain,(
% 0.22/0.39 ($true = $false)),
% 0.22/0.39 inference(superposition,[],[f147,f136])).
% 0.22/0.39 thf(f136,plain,(
% 0.22/0.39 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.22/0.39 inference(not_proxy_clausification,[],[f130])).
% 0.22/0.39 thf(f130,plain,(
% 0.22/0.39 ((~ (rel_s5 @ sK1 @ sK2)) = $false)),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f129])).
% 0.22/0.39 thf(f129,plain,(
% 0.22/0.39 (((~ (!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK2))))) | (~ (rel_s5 @ sK1 @ sK2))) = $false)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f128])).
% 0.22/0.39 thf(f128,plain,(
% 0.22/0.39 ($false = ((^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2))),
% 0.22/0.39 inference(sigma_clausification,[],[f127])).
% 0.22/0.39 thf(f127,plain,(
% 0.22/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0))))))),
% 0.22/0.39 inference(binary_proxy_clausification,[],[f125])).
% 0.22/0.39 thf(f125,plain,(
% 0.22/0.39 (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ mu @ (^[Y1 : mu]: (~ (f @ Y1 @ Y0))))) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ mu @ (^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))))))) = $false)),
% 0.22/0.39 inference(beta_eta_normalization,[],[f124])).
% 0.22/0.39 thf(f124,plain,(
% 0.22/0.39 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2)))))))))) @ sK1) = $false)),
% 0.22/0.39 inference(sigma_clausification,[],[f123])).
% 0.22/0.39 thf(f123,plain,(
% 0.22/0.39 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))))))))) != $true)),
% 0.22/0.39 inference(boolean_simplification,[],[f122])).
% 0.22/0.39 thf(f122,plain,(
% 0.22/0.39 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ mu @ (^[Y2 : mu]: (~ (f @ Y2 @ Y1))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (~ (!! @ mu @ (^[Y1 : mu]: (~ (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))))))))))))),
% 0.22/0.39 inference(beta_eta_normalization,[],[f121])).
% 0.22/0.39 thf(f121,plain,(
% 0.22/0.39 (((^[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 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ (f @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))) @ (^[Y0 : mu]: (f @ Y0)))))) != $true)),
% 0.22/0.39 inference(definition_unfolding,[],[f117,f111,f120,f119,f115,f115,f119])).
% 0.22/0.39 thf(f115,plain,(
% 0.22/0.39 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f77])).
% 0.22/0.39 thf(f77,plain,(
% 0.22/0.39 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f76])).
% 0.22/0.39 thf(f76,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))) = mbox_s5)),
% 0.22/0.39 inference(rectify,[],[f32])).
% 0.22/0.39 thf(f32,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))) = mbox_s5)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.22/0.39 thf(f119,plain,(
% 0.22/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.22/0.39 inference(definition_unfolding,[],[f112,f113,f118,f113])).
% 0.22/0.39 thf(f118,plain,(
% 0.22/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f65])).
% 0.22/0.39 thf(f65,plain,(
% 0.22/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f64])).
% 0.22/0.39 thf(f64,plain,(
% 0.22/0.39 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.22/0.39 inference(rectify,[],[f10])).
% 0.22/0.39 thf(f10,axiom,(
% 0.22/0.39 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.22/0.39 thf(f113,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f103])).
% 0.22/0.39 thf(f103,plain,(
% 0.22/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.39 inference(fool_elimination,[],[f102])).
% 0.22/0.39 thf(f102,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.22/0.39 inference(rectify,[],[f3])).
% 0.22/0.39 thf(f3,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.22/0.39 thf(f112,plain,(
% 0.22/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f73])).
% 0.22/0.39 thf(f73,plain,(
% 0.22/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.22/0.39 inference(fool_elimination,[],[f72])).
% 0.22/0.39 thf(f72,plain,(
% 0.22/0.39 ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 0.22/0.39 inference(rectify,[],[f12])).
% 0.22/0.39 thf(f12,axiom,(
% 0.22/0.39 ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
% 0.22/0.39 thf(f120,plain,(
% 0.22/0.39 (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)))))),
% 0.22/0.39 inference(definition_unfolding,[],[f114,f116,f113])).
% 0.22/0.39 thf(f116,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.39 inference(cnf_transformation,[],[f45])).
% 0.22/0.39 thf(f45,plain,(
% 0.22/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.39 inference(fool_elimination,[],[f44])).
% 0.22/0.39 thf(f44,plain,(
% 0.22/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.22/0.39 inference(rectify,[],[f4])).
% 0.22/0.39 thf(f4,axiom,(
% 0.22/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.22/0.39 thf(f114,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f47])).
% 0.22/0.39 thf(f47,plain,(
% 0.22/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f46])).
% 0.22/0.39 thf(f46,plain,(
% 0.22/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.22/0.39 inference(rectify,[],[f6])).
% 0.22/0.39 thf(f6,axiom,(
% 0.22/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.39 thf(f111,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(cnf_transformation,[],[f101])).
% 0.22/0.39 thf(f101,plain,(
% 0.22/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.39 inference(fool_elimination,[],[f100])).
% 0.22/0.39 thf(f100,plain,(
% 0.22/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.22/0.39 inference(rectify,[],[f28])).
% 0.22/0.39 thf(f28,axiom,(
% 0.22/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.22/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.39 thf(f117,plain,(
% 0.22/0.39 ((mvalid @ (mimplies @ (mexists_ind @ (^[Y0 : mu]: (mbox_s5 @ (f @ Y0)))) @ (mbox_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0)))))) != $true)),
% 0.22/0.39 inference(cnf_transformation,[],[f110])).
% 0.22/0.39 thf(f110,plain,(
% 0.22/0.39 ((mvalid @ (mimplies @ (mexists_ind @ (^[Y0 : mu]: (mbox_s5 @ (f @ Y0)))) @ (mbox_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0)))))) != $true)),
% 0.22/0.39 inference(flattening,[],[f69])).
% 0.22/0.39 thf(f69,plain,(
% 0.22/0.39 ~((mvalid @ (mimplies @ (mexists_ind @ (^[Y0 : mu]: (mbox_s5 @ (f @ Y0)))) @ (mbox_s5 @ (mexists_ind @ (^[Y0 : mu]: (f @ Y0)))))) = $true)),
% 0.22/0.39 inference(fool_elimination,[],[f68])).
% 0.22/0.39 thf(f68,plain,(
% 0.22/0.39 ~(mvalid @ (mimplies @ (mexists_ind @ (^[X0 : mu] : (mbox_s5 @ (f @ X0)))) @ (mbox_s5 @ (mexists_ind @ (^[X1 : mu] : (f @ X1))))))),
% 0.22/0.39 inference(rectify,[],[f38])).
% 0.22/0.39 thf(f38,negated_conjecture,(
% 0.22/0.39 ~(mvalid @ (mimplies @ (mexists_ind @ (^[X0 : mu] : (mbox_s5 @ (f @ X0)))) @ (mbox_s5 @ (mexists_ind @ (^[X0 : mu] : (f @ X0))))))),
% 0.22/0.39 inference(negated_conjecture,[],[f37])).
% 0.22/0.39 thf(f37,conjecture,(
% 0.22/0.39 (mvalid @ (mimplies @ (mexists_ind @ (^[X0 : mu] : (mbox_s5 @ (f @ X0)))) @ (mbox_s5 @ (mexists_ind @ (^[X0 : mu] : (f @ X0))))))),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.22/0.40 thf(f147,plain,(
% 0.22/0.40 ((rel_s5 @ sK1 @ sK2) = $false)),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f144])).
% 0.22/0.40 thf(f144,plain,(
% 0.22/0.40 ((rel_s5 @ sK1 @ sK2) = $false) | ($true = $false)),
% 0.22/0.40 inference(superposition,[],[f143,f135])).
% 0.22/0.40 thf(f135,plain,(
% 0.22/0.40 ( ! [X1 : mu] : (($false = (f @ X1 @ sK2))) )),
% 0.22/0.40 inference(not_proxy_clausification,[],[f134])).
% 0.22/0.40 thf(f134,plain,(
% 0.22/0.40 ( ! [X1 : mu] : (((~ (f @ X1 @ sK2)) = $true)) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f133])).
% 0.22/0.40 thf(f133,plain,(
% 0.22/0.40 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: (~ (f @ Y0 @ sK2))) @ X1))) )),
% 0.22/0.40 inference(pi_clausification,[],[f132])).
% 0.22/0.40 thf(f132,plain,(
% 0.22/0.40 ((!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK2)))) = $true)),
% 0.22/0.40 inference(not_proxy_clausification,[],[f131])).
% 0.22/0.40 thf(f131,plain,(
% 0.22/0.40 ((~ (!! @ mu @ (^[Y0 : mu]: (~ (f @ Y0 @ sK2))))) = $false)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f129])).
% 0.22/0.40 thf(f143,plain,(
% 0.22/0.40 ( ! [X1 : $i] : (($true = (f @ sK3 @ X1)) | ($false = (rel_s5 @ sK1 @ X1))) )),
% 0.22/0.40 inference(not_proxy_clausification,[],[f142])).
% 0.22/0.40 thf(f142,plain,(
% 0.22/0.40 ( ! [X1 : $i] : (((~ (rel_s5 @ sK1 @ X1)) = $true) | ($true = (f @ sK3 @ X1))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f141])).
% 0.22/0.40 thf(f141,plain,(
% 0.22/0.40 ( ! [X1 : $i] : (($true = ((f @ sK3 @ X1) | (~ (rel_s5 @ sK1 @ X1))))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f140])).
% 0.22/0.40 thf(f140,plain,(
% 0.22/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((f @ sK3 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.22/0.40 inference(pi_clausification,[],[f139])).
% 0.22/0.40 thf(f139,plain,(
% 0.22/0.40 ((!! @ $i @ (^[Y0 : $i]: ((f @ sK3 @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true)),
% 0.22/0.40 inference(not_proxy_clausification,[],[f138])).
% 0.22/0.40 thf(f138,plain,(
% 0.22/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((f @ sK3 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false)),
% 0.22/0.40 inference(beta_eta_normalization,[],[f137])).
% 0.22/0.40 thf(f137,plain,(
% 0.22/0.40 (((^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))))) @ sK3) = $false)),
% 0.22/0.40 inference(sigma_clausification,[],[f126])).
% 0.22/0.40 thf(f126,plain,(
% 0.22/0.40 ((!! @ mu @ (^[Y0 : mu]: (~ (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1)))))))) = $false)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f125])).
% 0.22/0.40 % SZS output end Proof for theBenchmark
% 0.22/0.40 % (9951)------------------------------
% 0.22/0.40 % (9951)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (9951)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (9951)Memory used [KB]: 5628
% 0.22/0.40 % (9951)Time elapsed: 0.008 s
% 0.22/0.40 % (9951)Instructions burned: 10 (million)
% 0.22/0.40 % (9951)------------------------------
% 0.22/0.40 % (9951)------------------------------
% 0.22/0.40 % (9945)Success in time 0.02 s
% 0.22/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------