TSTP Solution File: SYO495^6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO495^6 : 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 : n022.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 09:05:27 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO495^6 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:29:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (20066)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (20067)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)
% 0.13/0.37 % (20069)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (20068)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)
% 0.13/0.37 % (20073)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)
% 0.13/0.37 % (20070)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)
% 0.13/0.37 % (20069)Instruction limit reached!
% 0.13/0.37 % (20069)------------------------------
% 0.13/0.37 % (20069)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (20070)Instruction limit reached!
% 0.13/0.37 % (20070)------------------------------
% 0.13/0.37 % (20070)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (20069)Termination reason: Unknown
% 0.13/0.37 % (20069)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (20069)Memory used [KB]: 1023
% 0.13/0.37 % (20069)Time elapsed: 0.003 s
% 0.13/0.37 % (20069)Instructions burned: 3 (million)
% 0.13/0.37 % (20069)------------------------------
% 0.13/0.37 % (20069)------------------------------
% 0.13/0.37 % (20070)Termination reason: Unknown
% 0.13/0.37 % (20070)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (20070)Memory used [KB]: 1023
% 0.13/0.37 % (20070)Time elapsed: 0.003 s
% 0.13/0.37 % (20070)Instructions burned: 2 (million)
% 0.13/0.37 % (20070)------------------------------
% 0.13/0.37 % (20070)------------------------------
% 0.13/0.37 % (20073)Instruction limit reached!
% 0.13/0.37 % (20073)------------------------------
% 0.13/0.37 % (20073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (20073)Termination reason: Unknown
% 0.13/0.37 % (20073)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (20073)Memory used [KB]: 1023
% 0.13/0.37 % (20073)Time elapsed: 0.003 s
% 0.13/0.37 % (20073)Instructions burned: 3 (million)
% 0.13/0.37 % (20073)------------------------------
% 0.13/0.37 % (20073)------------------------------
% 0.13/0.37 % (20067)Instruction limit reached!
% 0.13/0.37 % (20067)------------------------------
% 0.13/0.37 % (20067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (20067)Termination reason: Unknown
% 0.13/0.37 % (20067)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (20067)Memory used [KB]: 1023
% 0.13/0.37 % (20067)Time elapsed: 0.004 s
% 0.13/0.37 % (20067)Instructions burned: 5 (million)
% 0.13/0.37 % (20067)------------------------------
% 0.13/0.37 % (20067)------------------------------
% 0.13/0.37 % (20071)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)
% 0.13/0.38 % (20071)First to succeed.
% 0.13/0.38 % (20072)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (20068)Also succeeded, but the first one will report.
% 0.13/0.38 % (20071)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% 0.13/0.38 thf(type_def_5, type, mu: $tType).
% 0.13/0.38 thf(func_def_0, type, mu: $tType).
% 0.13/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.13/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.13/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.13/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.13/0.38 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_36, type, f: mu > $i > $o).
% 0.13/0.38 thf(func_def_37, type, g: mu > $i > $o).
% 0.13/0.38 thf(func_def_56, type, sK3: mu).
% 0.13/0.38 thf(f157,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f156])).
% 0.13/0.38 thf(f156,plain,(
% 0.13/0.38 ($false = $true)),
% 0.13/0.38 inference(forward_demodulation,[],[f155,f132])).
% 0.13/0.38 thf(f132,plain,(
% 0.13/0.38 ($false = (g @ sK3 @ sK2))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f130])).
% 0.13/0.38 thf(f130,plain,(
% 0.13/0.38 (((g @ sK3 @ sK2) | (f @ sK3 @ sK2)) = $false)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f129])).
% 0.13/0.38 thf(f129,plain,(
% 0.13/0.38 (((^[Y0 : mu]: ((g @ Y0 @ sK2) | (f @ Y0 @ sK2))) @ sK3) = $false)),
% 0.13/0.38 inference(sigma_clausification,[],[f128])).
% 0.13/0.38 thf(f128,plain,(
% 0.13/0.38 ($false = (!! @ mu @ (^[Y0 : mu]: ((g @ Y0 @ sK2) | (f @ Y0 @ sK2)))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f126])).
% 0.13/0.38 thf(f126,plain,(
% 0.13/0.38 ($false = ((!! @ mu @ (^[Y0 : mu]: ((g @ Y0 @ sK2) | (f @ Y0 @ sK2)))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f125])).
% 0.13/0.38 thf(f125,plain,(
% 0.13/0.38 (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((g @ Y1 @ Y0) | (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.13/0.38 inference(sigma_clausification,[],[f124])).
% 0.13/0.38 thf(f124,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((g @ Y1 @ Y0) | (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f122])).
% 0.13/0.38 thf(f122,plain,(
% 0.13/0.38 ($false = ((!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((g @ Y1 @ Y0) | (f @ Y1 @ Y0)))) | (~ (rel_s5 @ sK1 @ Y0))))) | (~ (!! @ mu @ (^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((g @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1)))))))))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f121])).
% 0.13/0.38 thf(f121,plain,(
% 0.13/0.38 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((g @ Y2 @ Y1) | (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((g @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))))))))) @ sK1))),
% 0.13/0.38 inference(sigma_clausification,[],[f120])).
% 0.13/0.38 thf(f120,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((g @ Y2 @ Y1) | (f @ Y2 @ Y1)))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (!! @ mu @ (^[Y1 : mu]: ((!! @ $i @ (^[Y2 : $i]: ((g @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((f @ Y1 @ Y2) | (~ (rel_s5 @ Y0 @ Y2)))))))))))) != $true)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f119])).
% 0.13/0.38 thf(f119,plain,(
% 0.13/0.38 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y2 @ Y3) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ (f @ Y0)) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ (g @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y2 @ Y3) | (Y1 @ Y3))))))) @ (f @ Y0) @ (g @ Y0))))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f116,f115,f118,f113,f114,f111,f111,f111,f113,f114])).
% 0.13/0.38 thf(f111,plain,(
% 0.13/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f43])).
% 0.13/0.38 thf(f43,plain,(
% 0.13/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f42])).
% 0.13/0.38 thf(f42,plain,(
% 0.13/0.38 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))))),
% 0.13/0.38 inference(rectify,[],[f32])).
% 0.13/0.38 thf(f32,axiom,(
% 0.13/0.38 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.13/0.38 thf(f114,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f63])).
% 0.13/0.38 thf(f63,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f62])).
% 0.13/0.38 thf(f62,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.13/0.38 inference(rectify,[],[f4])).
% 0.13/0.38 thf(f4,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.13/0.38 thf(f113,plain,(
% 0.13/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f53])).
% 0.13/0.38 thf(f53,plain,(
% 0.13/0.38 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.13/0.38 inference(fool_elimination,[],[f52])).
% 0.13/0.38 thf(f52,plain,(
% 0.13/0.38 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)),
% 0.13/0.38 inference(rectify,[],[f10])).
% 0.13/0.38 thf(f10,axiom,(
% 0.13/0.38 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.13/0.38 thf(f118,plain,(
% 0.13/0.38 (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)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f117,f114,f112])).
% 0.13/0.38 thf(f112,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f96])).
% 0.13/0.38 thf(f96,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(fool_elimination,[],[f95])).
% 0.13/0.38 thf(f95,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.13/0.38 inference(rectify,[],[f3])).
% 0.13/0.38 thf(f3,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.13/0.38 thf(f117,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f98])).
% 0.13/0.38 thf(f98,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f97])).
% 0.13/0.38 thf(f97,plain,(
% 0.13/0.38 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.13/0.38 inference(rectify,[],[f6])).
% 0.13/0.38 thf(f6,axiom,(
% 0.13/0.38 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.13/0.38 thf(f115,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f94])).
% 0.13/0.38 thf(f94,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f93])).
% 0.13/0.38 thf(f93,plain,(
% 0.13/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.13/0.38 inference(rectify,[],[f28])).
% 0.13/0.38 thf(f28,axiom,(
% 0.13/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.38 thf(f116,plain,(
% 0.13/0.38 ((mvalid @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mbox_s5 @ (f @ Y0)) @ (mbox_s5 @ (g @ Y0))))) @ (mbox_s5 @ (mforall_ind @ (^[Y0 : mu]: (mor @ (f @ Y0) @ (g @ Y0))))))) != $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f110])).
% 0.13/0.38 thf(f110,plain,(
% 0.13/0.38 ((mvalid @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mbox_s5 @ (f @ Y0)) @ (mbox_s5 @ (g @ Y0))))) @ (mbox_s5 @ (mforall_ind @ (^[Y0 : mu]: (mor @ (f @ Y0) @ (g @ Y0))))))) != $true)),
% 0.13/0.38 inference(flattening,[],[f86])).
% 0.13/0.38 thf(f86,plain,(
% 0.13/0.38 ~((mvalid @ (mimplies @ (mforall_ind @ (^[Y0 : mu]: (mor @ (mbox_s5 @ (f @ Y0)) @ (mbox_s5 @ (g @ Y0))))) @ (mbox_s5 @ (mforall_ind @ (^[Y0 : mu]: (mor @ (f @ Y0) @ (g @ Y0))))))) = $true)),
% 0.13/0.38 inference(fool_elimination,[],[f85])).
% 0.13/0.38 thf(f85,plain,(
% 0.13/0.38 ~(mvalid @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (mor @ (mbox_s5 @ (f @ X0)) @ (mbox_s5 @ (g @ X0))))) @ (mbox_s5 @ (mforall_ind @ (^[X1 : mu] : (mor @ (f @ X1) @ (g @ X1)))))))),
% 0.13/0.38 inference(rectify,[],[f38])).
% 0.13/0.38 thf(f38,negated_conjecture,(
% 0.13/0.38 ~(mvalid @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (mor @ (mbox_s5 @ (f @ X0)) @ (mbox_s5 @ (g @ X0))))) @ (mbox_s5 @ (mforall_ind @ (^[X0 : mu] : (mor @ (f @ X0) @ (g @ X0)))))))),
% 0.13/0.38 inference(negated_conjecture,[],[f37])).
% 0.13/0.38 thf(f37,conjecture,(
% 0.13/0.38 (mvalid @ (mimplies @ (mforall_ind @ (^[X0 : mu] : (mor @ (mbox_s5 @ (f @ X0)) @ (mbox_s5 @ (g @ X0))))) @ (mbox_s5 @ (mforall_ind @ (^[X0 : mu] : (mor @ (f @ X0) @ (g @ X0)))))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.13/0.38 thf(f155,plain,(
% 0.13/0.38 ($true = (g @ sK3 @ sK2))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f153])).
% 0.13/0.38 thf(f153,plain,(
% 0.13/0.38 ($true = (g @ sK3 @ sK2)) | ($false = $true)),
% 0.13/0.38 inference(superposition,[],[f133,f151])).
% 0.13/0.38 thf(f151,plain,(
% 0.13/0.38 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ((g @ sK3 @ X0) = $true)) )),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f150])).
% 0.13/0.38 thf(f150,plain,(
% 0.13/0.38 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ((g @ sK3 @ X0) = $true) | ($false = $true)) )),
% 0.13/0.38 inference(forward_demodulation,[],[f149,f133])).
% 0.13/0.38 thf(f149,plain,(
% 0.13/0.38 ( ! [X0 : $i] : (((rel_s5 @ sK1 @ sK2) = $false) | ((g @ sK3 @ X0) = $true) | ($false = (rel_s5 @ sK1 @ X0))) )),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f146])).
% 0.13/0.38 thf(f146,plain,(
% 0.13/0.38 ( ! [X0 : $i] : (((g @ sK3 @ X0) = $true) | ($false = $true) | ($false = (rel_s5 @ sK1 @ X0)) | ((rel_s5 @ sK1 @ sK2) = $false)) )),
% 0.13/0.38 inference(superposition,[],[f131,f145])).
% 0.13/0.38 thf(f145,plain,(
% 0.13/0.38 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($true = (f @ X1 @ X2)) | ((rel_s5 @ sK1 @ X3) = $false) | ((g @ X1 @ X3) = $true) | ($false = (rel_s5 @ sK1 @ X2))) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f144])).
% 0.13/0.38 thf(f144,plain,(
% 0.13/0.38 ( ! [X2 : $i,X3 : $i,X1 : mu] : (($true = (~ (rel_s5 @ sK1 @ X2))) | ($true = (f @ X1 @ X2)) | ((rel_s5 @ sK1 @ X3) = $false) | ((g @ X1 @ X3) = $true)) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f143])).
% 0.13/0.38 thf(f143,plain,(
% 0.13/0.38 ( ! [X2 : $i,X3 : $i,X1 : mu] : (((g @ X1 @ X3) = $true) | ((~ (rel_s5 @ sK1 @ X3)) = $true) | ($true = (~ (rel_s5 @ sK1 @ X2))) | ($true = (f @ X1 @ X2))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f142])).
% 0.13/0.38 thf(f142,plain,(
% 0.13/0.38 ( ! [X2 : $i,X3 : $i,X1 : mu] : ((((f @ X1 @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | ((g @ X1 @ X3) = $true) | ((~ (rel_s5 @ sK1 @ X3)) = $true)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f141])).
% 0.13/0.38 thf(f141,plain,(
% 0.13/0.38 ( ! [X2 : $i,X3 : $i,X1 : mu] : ((((g @ X1 @ X3) | (~ (rel_s5 @ sK1 @ X3))) = $true) | (((f @ X1 @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f140])).
% 0.13/0.38 thf(f140,plain,(
% 0.13/0.38 ( ! [X2 : $i,X3 : $i,X1 : mu] : ((((f @ X1 @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true) | ($true = ((^[Y0 : $i]: ((g @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ X3))) )),
% 0.13/0.38 inference(pi_clausification,[],[f139])).
% 0.13/0.38 thf(f139,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((g @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) | (((f @ X1 @ X2) | (~ (rel_s5 @ sK1 @ X2))) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f138])).
% 0.13/0.38 thf(f138,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : mu] : (($true = (!! @ $i @ (^[Y0 : $i]: ((g @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) | ($true = ((^[Y0 : $i]: ((f @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ X2))) )),
% 0.13/0.38 inference(pi_clausification,[],[f137])).
% 0.13/0.38 thf(f137,plain,(
% 0.13/0.38 ( ! [X1 : mu] : (((!! @ $i @ (^[Y0 : $i]: ((f @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((g @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f136])).
% 0.13/0.38 thf(f136,plain,(
% 0.13/0.38 ( ! [X1 : mu] : ((((!! @ $i @ (^[Y0 : $i]: ((g @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((f @ X1 @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f135])).
% 0.13/0.38 thf(f135,plain,(
% 0.13/0.38 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((g @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))))) @ X1) = $true)) )),
% 0.13/0.38 inference(pi_clausification,[],[f134])).
% 0.13/0.38 thf(f134,plain,(
% 0.13/0.38 ((!! @ mu @ (^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((g @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1)))))))) = $true)),
% 0.13/0.38 inference(not_proxy_clausification,[],[f123])).
% 0.13/0.38 thf(f123,plain,(
% 0.13/0.38 ($false = (~ (!! @ mu @ (^[Y0 : mu]: ((!! @ $i @ (^[Y1 : $i]: ((g @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((f @ Y0 @ Y1) | (~ (rel_s5 @ sK1 @ Y1))))))))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f122])).
% 0.13/0.38 thf(f131,plain,(
% 0.13/0.38 ((f @ sK3 @ sK2) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f130])).
% 0.13/0.38 thf(f133,plain,(
% 0.13/0.38 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.13/0.38 inference(not_proxy_clausification,[],[f127])).
% 0.13/0.38 thf(f127,plain,(
% 0.13/0.38 ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f126])).
% 0.13/0.38 % SZS output end Proof for theBenchmark
% 0.13/0.38 % (20071)------------------------------
% 0.13/0.38 % (20071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (20071)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (20071)Memory used [KB]: 5628
% 0.13/0.38 % (20071)Time elapsed: 0.010 s
% 0.13/0.38 % (20071)Instructions burned: 10 (million)
% 0.13/0.38 % (20071)------------------------------
% 0.13/0.38 % (20071)------------------------------
% 0.13/0.38 % (20065)Success in time 0.018 s
% 0.13/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------