TSTP Solution File: SYO468^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO468^6 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n029.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 09:05:06 EDT 2024
% Result : Theorem 0.18s 0.36s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYO468^6 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.12 % 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
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 10:24:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 This is a TH0_THM_EQU_NAR problem
% 0.12/0.34 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/benchmark/theBenchmark.p
% 0.18/0.35 % (22281)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.18/0.35 % (22283)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)
% 0.18/0.35 % (22285)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)
% 0.18/0.35 % (22284)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.35 % (22287)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.18/0.35 % (22284)Instruction limit reached!
% 0.18/0.35 % (22284)------------------------------
% 0.18/0.35 % (22284)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (22284)Termination reason: Unknown
% 0.18/0.35 % (22284)Termination phase: shuffling
% 0.18/0.35
% 0.18/0.35 % (22284)Memory used [KB]: 1023
% 0.18/0.35 % (22284)Time elapsed: 0.002 s
% 0.18/0.35 % (22284)Instructions burned: 2 (million)
% 0.18/0.35 % (22285)Instruction limit reached!
% 0.18/0.35 % (22285)------------------------------
% 0.18/0.35 % (22285)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.35 % (22285)Termination reason: Unknown
% 0.18/0.35 % (22285)Termination phase: shuffling
% 0.18/0.35
% 0.18/0.35 % (22285)Memory used [KB]: 1023
% 0.18/0.35 % (22285)Time elapsed: 0.003 s
% 0.18/0.35 % (22285)Instructions burned: 2 (million)
% 0.18/0.35 % (22285)------------------------------
% 0.18/0.35 % (22285)------------------------------
% 0.18/0.35 % (22284)------------------------------
% 0.18/0.35 % (22284)------------------------------
% 0.18/0.35 % (22288)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)
% 0.18/0.36 % (22288)Instruction limit reached!
% 0.18/0.36 % (22288)------------------------------
% 0.18/0.36 % (22288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (22288)Termination reason: Unknown
% 0.18/0.36 % (22288)Termination phase: shuffling
% 0.18/0.36
% 0.18/0.36 % (22288)Memory used [KB]: 1023
% 0.18/0.36 % (22288)Time elapsed: 0.003 s
% 0.18/0.36 % (22288)Instructions burned: 3 (million)
% 0.18/0.36 % (22288)------------------------------
% 0.18/0.36 % (22288)------------------------------
% 0.18/0.36 % (22283)First to succeed.
% 0.18/0.36 % (22286)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)
% 0.18/0.36 % (22281)Also succeeded, but the first one will report.
% 0.18/0.36 % (22289)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 theBenchmark for (2999ds/37Mi)
% 0.18/0.36 % (22283)Refutation found. Thanks to Tanya!
% 0.18/0.36 % SZS status Theorem for theBenchmark
% 0.18/0.36 % SZS output start Proof for theBenchmark
% 0.18/0.36 thf(type_def_5, type, mu: $tType).
% 0.18/0.36 thf(func_def_0, type, mu: $tType).
% 0.18/0.36 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.18/0.36 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_15, type, mtrue: $i > $o).
% 0.18/0.36 thf(func_def_16, type, mfalse: $i > $o).
% 0.18/0.36 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.18/0.36 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.18/0.36 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.18/0.36 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.18/0.36 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.18/0.36 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.18/0.36 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.18/0.36 thf(func_def_36, type, p: $i > $o).
% 0.18/0.36 thf(func_def_37, type, q: $i > $o).
% 0.18/0.36 thf(func_def_38, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.18/0.36 thf(f354,plain,(
% 0.18/0.36 $false),
% 0.18/0.36 inference(avatar_sat_refutation,[],[f342,f353])).
% 0.18/0.36 thf(f353,plain,(
% 0.18/0.36 ~spl0_2),
% 0.18/0.36 inference(avatar_contradiction_clause,[],[f352])).
% 0.18/0.36 thf(f352,plain,(
% 0.18/0.36 $false | ~spl0_2),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f348])).
% 0.18/0.36 thf(f348,plain,(
% 0.18/0.36 ($false = $true) | ~spl0_2),
% 0.18/0.36 inference(backward_demodulation,[],[f215,f306])).
% 0.18/0.36 thf(f306,plain,(
% 0.18/0.36 ($false = (rel_s5 @ sK2 @ sK1)) | ~spl0_2),
% 0.18/0.36 inference(avatar_component_clause,[],[f304])).
% 0.18/0.36 thf(f304,plain,(
% 0.18/0.36 spl0_2 <=> ($false = (rel_s5 @ sK2 @ sK1))),
% 0.18/0.36 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.18/0.36 thf(f215,plain,(
% 0.18/0.36 ((rel_s5 @ sK2 @ sK1) = $true)),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f214])).
% 0.18/0.36 thf(f214,plain,(
% 0.18/0.36 ($false = $true) | ((rel_s5 @ sK2 @ sK1) = $true)),
% 0.18/0.36 inference(superposition,[],[f170,f189])).
% 0.18/0.36 thf(f189,plain,(
% 0.18/0.36 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.18/0.36 inference(not_proxy_clausification,[],[f188])).
% 0.18/0.36 thf(f188,plain,(
% 0.18/0.36 ((~ (rel_s5 @ sK1 @ sK2)) = $false)),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f186])).
% 0.18/0.36 thf(f186,plain,(
% 0.18/0.36 ($false = ((~ (rel_s5 @ sK1 @ sK2)) | ((p @ sK2) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))))))),
% 0.18/0.36 inference(beta_eta_normalization,[],[f185])).
% 0.18/0.36 thf(f185,plain,(
% 0.18/0.36 (((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((p @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1)))))))) @ sK2) = $false)),
% 0.18/0.36 inference(sigma_clausification,[],[f184])).
% 0.18/0.36 thf(f184,plain,(
% 0.18/0.36 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((p @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))))))))),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f182])).
% 0.18/0.36 thf(f182,plain,(
% 0.18/0.36 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((p @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (q @ Y1))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 0.18/0.36 inference(beta_eta_normalization,[],[f181])).
% 0.18/0.36 thf(f181,plain,(
% 0.18/0.36 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((p @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((q @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))) @ sK1))),
% 0.18/0.36 inference(sigma_clausification,[],[f180])).
% 0.18/0.36 thf(f180,plain,(
% 0.18/0.36 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((p @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (q @ Y2))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((q @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))))))))))) != $true)),
% 0.18/0.36 inference(beta_eta_normalization,[],[f158])).
% 0.18/0.36 thf(f158,plain,(
% 0.18/0.36 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ q) @ p)))))),
% 0.18/0.36 inference(definition_unfolding,[],[f115,f124,f121,f126,f149,f126,f126,f149,f126])).
% 0.18/0.36 thf(f149,plain,(
% 0.18/0.36 (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)))))),
% 0.18/0.36 inference(definition_unfolding,[],[f136,f121,f139])).
% 0.18/0.36 thf(f139,plain,(
% 0.18/0.36 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.18/0.36 inference(cnf_transformation,[],[f45])).
% 0.18/0.36 thf(f45,plain,(
% 0.18/0.36 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.18/0.36 inference(fool_elimination,[],[f44])).
% 0.18/0.36 thf(f44,plain,(
% 0.18/0.36 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.18/0.36 inference(rectify,[],[f3])).
% 0.18/0.36 thf(f3,axiom,(
% 0.18/0.36 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.18/0.36 thf(f136,plain,(
% 0.18/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.18/0.36 inference(cnf_transformation,[],[f103])).
% 0.18/0.36 thf(f103,plain,(
% 0.18/0.36 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.18/0.36 inference(fool_elimination,[],[f102])).
% 0.18/0.36 thf(f102,plain,(
% 0.18/0.36 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.18/0.36 inference(rectify,[],[f6])).
% 0.18/0.36 thf(f6,axiom,(
% 0.18/0.36 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.18/0.36 thf(f126,plain,(
% 0.18/0.36 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.18/0.36 inference(cnf_transformation,[],[f41])).
% 0.18/0.36 thf(f41,plain,(
% 0.18/0.36 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.18/0.36 inference(fool_elimination,[],[f40])).
% 0.18/0.36 thf(f40,plain,(
% 0.18/0.36 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.18/0.36 inference(rectify,[],[f32])).
% 0.18/0.36 thf(f32,axiom,(
% 0.18/0.36 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.18/0.36 thf(f121,plain,(
% 0.18/0.36 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.18/0.36 inference(cnf_transformation,[],[f82])).
% 0.18/0.36 thf(f82,plain,(
% 0.18/0.36 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.18/0.36 inference(fool_elimination,[],[f81])).
% 0.18/0.36 thf(f81,plain,(
% 0.18/0.36 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.18/0.36 inference(rectify,[],[f4])).
% 0.18/0.36 thf(f4,axiom,(
% 0.18/0.36 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.18/0.36 thf(f124,plain,(
% 0.18/0.36 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.18/0.36 inference(cnf_transformation,[],[f57])).
% 0.18/0.36 thf(f57,plain,(
% 0.18/0.36 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.18/0.36 inference(fool_elimination,[],[f56])).
% 0.18/0.36 thf(f56,plain,(
% 0.18/0.36 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.18/0.36 inference(rectify,[],[f28])).
% 0.18/0.36 thf(f28,axiom,(
% 0.18/0.36 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.18/0.36 thf(f115,plain,(
% 0.18/0.36 ((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ q)) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ p)))) != $true)),
% 0.18/0.36 inference(cnf_transformation,[],[f110])).
% 0.18/0.36 thf(f110,plain,(
% 0.18/0.36 ((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ q)) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ p)))) != $true)),
% 0.18/0.36 inference(flattening,[],[f43])).
% 0.18/0.36 thf(f43,plain,(
% 0.18/0.36 ~((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ q)) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ p)))) = $true)),
% 0.18/0.36 inference(fool_elimination,[],[f42])).
% 0.18/0.36 thf(f42,plain,(
% 0.18/0.36 ~(mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ q)) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ p))))),
% 0.18/0.36 inference(rectify,[],[f38])).
% 0.18/0.36 thf(f38,negated_conjecture,(
% 0.18/0.36 ~(mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ q)) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ p))))),
% 0.18/0.36 inference(negated_conjecture,[],[f37])).
% 0.18/0.36 thf(f37,conjecture,(
% 0.18/0.36 (mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ q)) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ p))))),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.18/0.36 thf(f170,plain,(
% 0.18/0.36 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ X2 @ X1) = $false) | ((rel_s5 @ X1 @ X2) = $true)) )),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f169])).
% 0.18/0.36 thf(f169,plain,(
% 0.18/0.36 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)) = $true)) )),
% 0.18/0.36 inference(beta_eta_normalization,[],[f168])).
% 0.18/0.36 thf(f168,plain,(
% 0.18/0.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2) = $true)) )),
% 0.18/0.36 inference(pi_clausification,[],[f167])).
% 0.18/0.36 thf(f167,plain,(
% 0.18/0.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))) = $true)) )),
% 0.18/0.36 inference(beta_eta_normalization,[],[f166])).
% 0.18/0.36 thf(f166,plain,(
% 0.18/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 0.18/0.36 inference(pi_clausification,[],[f165])).
% 0.18/0.36 thf(f165,plain,(
% 0.18/0.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))) = $true)),
% 0.18/0.36 inference(beta_eta_normalization,[],[f160])).
% 0.18/0.36 thf(f160,plain,(
% 0.18/0.36 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5) = $true)),
% 0.18/0.36 inference(definition_unfolding,[],[f141,f120])).
% 0.18/0.36 thf(f120,plain,(
% 0.18/0.36 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.18/0.36 inference(cnf_transformation,[],[f107])).
% 0.18/0.36 thf(f107,plain,(
% 0.18/0.36 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.18/0.36 inference(fool_elimination,[],[f106])).
% 0.18/0.36 thf(f106,plain,(
% 0.18/0.36 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))))),
% 0.18/0.36 inference(rectify,[],[f19])).
% 0.18/0.36 thf(f19,axiom,(
% 0.18/0.36 (msymmetric = (^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.18/0.36 thf(f141,plain,(
% 0.18/0.36 ((msymmetric @ rel_s5) = $true)),
% 0.18/0.36 inference(cnf_transformation,[],[f101])).
% 0.18/0.36 thf(f101,plain,(
% 0.18/0.36 ((msymmetric @ rel_s5) = $true)),
% 0.18/0.36 inference(fool_elimination,[],[f100])).
% 0.18/0.36 thf(f100,plain,(
% 0.18/0.36 (msymmetric @ rel_s5)),
% 0.18/0.36 inference(rectify,[],[f36])).
% 0.18/0.36 thf(f36,axiom,(
% 0.18/0.36 (msymmetric @ rel_s5)),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.18/0.36 thf(f342,plain,(
% 0.18/0.36 spl0_2),
% 0.18/0.36 inference(avatar_split_clause,[],[f341,f304])).
% 0.18/0.36 thf(f341,plain,(
% 0.18/0.36 ($false = (rel_s5 @ sK2 @ sK1))),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f340])).
% 0.18/0.36 thf(f340,plain,(
% 0.18/0.36 ($false = (rel_s5 @ sK2 @ sK1)) | ($false = $true)),
% 0.18/0.36 inference(forward_demodulation,[],[f322,f203])).
% 0.18/0.36 thf(f203,plain,(
% 0.18/0.36 ((q @ sK3) = $false)),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f199])).
% 0.18/0.36 thf(f199,plain,(
% 0.18/0.36 ($false = ((q @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0)))))))),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f198])).
% 0.18/0.36 thf(f198,plain,(
% 0.18/0.36 (((~ (rel_s5 @ sK1 @ sK3)) | ((q @ sK3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0))))))) = $false)),
% 0.18/0.36 inference(beta_eta_normalization,[],[f197])).
% 0.18/0.36 thf(f197,plain,(
% 0.18/0.36 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))) @ sK3))),
% 0.18/0.36 inference(sigma_clausification,[],[f183])).
% 0.18/0.36 thf(f183,plain,(
% 0.18/0.36 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((q @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $false)),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f182])).
% 0.18/0.36 thf(f322,plain,(
% 0.18/0.36 ($false = (rel_s5 @ sK2 @ sK1)) | ((q @ sK3) = $true)),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f314])).
% 0.18/0.36 thf(f314,plain,(
% 0.18/0.36 ($false = (rel_s5 @ sK2 @ sK1)) | ($false = $true) | ((q @ sK3) = $true)),
% 0.18/0.36 inference(superposition,[],[f232,f196])).
% 0.18/0.36 thf(f196,plain,(
% 0.18/0.36 ( ! [X1 : $i] : (((rel_s5 @ sK2 @ X1) = $false) | ((q @ X1) = $true)) )),
% 0.18/0.36 inference(not_proxy_clausification,[],[f195])).
% 0.18/0.36 thf(f195,plain,(
% 0.18/0.36 ( ! [X1 : $i] : (((q @ X1) = $true) | ((~ (rel_s5 @ sK2 @ X1)) = $true)) )),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f194])).
% 0.18/0.36 thf(f194,plain,(
% 0.18/0.36 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK2 @ X1)) | (q @ X1)) = $true)) )),
% 0.18/0.36 inference(beta_eta_normalization,[],[f193])).
% 0.18/0.36 thf(f193,plain,(
% 0.18/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))) @ X1) = $true)) )),
% 0.18/0.36 inference(pi_clausification,[],[f192])).
% 0.18/0.36 thf(f192,plain,(
% 0.18/0.36 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))) = $true)),
% 0.18/0.36 inference(not_proxy_clausification,[],[f190])).
% 0.18/0.36 thf(f190,plain,(
% 0.18/0.36 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0))))))),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f187])).
% 0.18/0.36 thf(f187,plain,(
% 0.18/0.36 (((p @ sK2) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (q @ Y0)))))) = $false)),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f186])).
% 0.18/0.36 thf(f232,plain,(
% 0.18/0.36 ( ! [X0 : $i] : (((rel_s5 @ X0 @ sK3) = $true) | ((rel_s5 @ X0 @ sK1) = $false)) )),
% 0.18/0.36 inference(trivial_inequality_removal,[],[f226])).
% 0.18/0.36 thf(f226,plain,(
% 0.18/0.36 ( ! [X0 : $i] : (((rel_s5 @ X0 @ sK1) = $false) | ((rel_s5 @ X0 @ sK3) = $true) | ($false = $true)) )),
% 0.18/0.36 inference(superposition,[],[f201,f179])).
% 0.18/0.36 thf(f179,plain,(
% 0.18/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X3)) | ((rel_s5 @ X1 @ X3) = $true) | ($false = (rel_s5 @ X1 @ X2))) )),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f178])).
% 0.18/0.36 thf(f178,plain,(
% 0.18/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((rel_s5 @ X1 @ X2) & (rel_s5 @ X2 @ X3))) | ((rel_s5 @ X1 @ X3) = $true)) )),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f177])).
% 0.18/0.36 thf(f177,plain,(
% 0.18/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X1 @ X2) & (rel_s5 @ X2 @ X3)) => (rel_s5 @ X1 @ X3)) = $true)) )),
% 0.18/0.36 inference(beta_eta_normalization,[],[f176])).
% 0.18/0.36 thf(f176,plain,(
% 0.18/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s5 @ X1 @ X2) & (rel_s5 @ X2 @ Y0)) => (rel_s5 @ X1 @ Y0))) @ X3) = $true)) )),
% 0.18/0.36 inference(pi_clausification,[],[f175])).
% 0.18/0.36 thf(f175,plain,(
% 0.18/0.36 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X1 @ X2) & (rel_s5 @ X2 @ Y0)) => (rel_s5 @ X1 @ Y0)))) = $true)) )),
% 0.18/0.36 inference(beta_eta_normalization,[],[f174])).
% 0.18/0.36 thf(f174,plain,(
% 0.18/0.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y0 @ Y1)) => (rel_s5 @ X1 @ Y1))))) @ X2) = $true)) )),
% 0.18/0.36 inference(pi_clausification,[],[f173])).
% 0.18/0.36 thf(f173,plain,(
% 0.18/0.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y0 @ Y1)) => (rel_s5 @ X1 @ Y1)))))) = $true)) )),
% 0.18/0.36 inference(beta_eta_normalization,[],[f172])).
% 0.18/0.36 thf(f172,plain,(
% 0.18/0.36 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ Y2)) => (rel_s5 @ Y0 @ Y2))))))) @ X1) = $true)) )),
% 0.18/0.36 inference(pi_clausification,[],[f171])).
% 0.18/0.36 thf(f171,plain,(
% 0.18/0.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ Y2)) => (rel_s5 @ Y0 @ Y2)))))))) = $true)),
% 0.18/0.36 inference(beta_eta_normalization,[],[f161])).
% 0.18/0.36 thf(f161,plain,(
% 0.18/0.36 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))) @ rel_s5) = $true)),
% 0.18/0.36 inference(definition_unfolding,[],[f146,f127])).
% 0.18/0.36 thf(f127,plain,(
% 0.18/0.36 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.18/0.36 inference(cnf_transformation,[],[f105])).
% 0.18/0.36 thf(f105,plain,(
% 0.18/0.36 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.18/0.36 inference(fool_elimination,[],[f104])).
% 0.18/0.36 thf(f104,plain,(
% 0.18/0.36 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X1) & (X0 @ X3 @ X2)) => (X0 @ X3 @ X1)))))),
% 0.18/0.36 inference(rectify,[],[f21])).
% 0.18/0.36 thf(f21,axiom,(
% 0.18/0.36 (mtransitive = (^[X6 : $i > $i > $o] : (! [X10,X9,X8] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))))),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.18/0.36 thf(f146,plain,(
% 0.18/0.36 ((mtransitive @ rel_s5) = $true)),
% 0.18/0.36 inference(cnf_transformation,[],[f99])).
% 0.18/0.36 thf(f99,plain,(
% 0.18/0.36 ((mtransitive @ rel_s5) = $true)),
% 0.18/0.36 inference(fool_elimination,[],[f98])).
% 0.18/0.36 thf(f98,plain,(
% 0.18/0.36 (mtransitive @ rel_s5)),
% 0.18/0.36 inference(rectify,[],[f35])).
% 0.18/0.36 thf(f35,axiom,(
% 0.18/0.36 (mtransitive @ rel_s5)),
% 0.18/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.18/0.36 thf(f201,plain,(
% 0.18/0.36 ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.18/0.36 inference(not_proxy_clausification,[],[f200])).
% 0.18/0.36 thf(f200,plain,(
% 0.18/0.36 ($false = (~ (rel_s5 @ sK1 @ sK3)))),
% 0.18/0.36 inference(binary_proxy_clausification,[],[f198])).
% 0.18/0.36 % SZS output end Proof for theBenchmark
% 0.18/0.36 % (22283)------------------------------
% 0.18/0.36 % (22283)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.18/0.36 % (22283)Termination reason: Refutation
% 0.18/0.36
% 0.18/0.36 % (22283)Memory used [KB]: 5756
% 0.18/0.36 % (22283)Time elapsed: 0.012 s
% 0.18/0.36 % (22283)Instructions burned: 24 (million)
% 0.18/0.36 % (22283)------------------------------
% 0.18/0.36 % (22283)------------------------------
% 0.18/0.36 % (22280)Success in time 0.021 s
% 0.18/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------