TSTP Solution File: SYN357^7 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% 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 : n024.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 08:22:01 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
% 0.07/0.12 % Problem : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% 0.07/0.14 % 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 : n024.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 : Mon May 20 13:42:38 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/benchmark/theBenchmark.p
% 0.14/0.37 % (11225)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (11228)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (11226)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (11227)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.37 % (11229)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (11231)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (11230)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.37 % (11232)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)
% 0.14/0.37 % (11228)Instruction limit reached!
% 0.14/0.37 % (11228)------------------------------
% 0.14/0.37 % (11228)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11228)Termination reason: Unknown
% 0.14/0.37 % (11228)Termination phase: shuffling
% 0.14/0.37 % (11229)Instruction limit reached!
% 0.14/0.37 % (11229)------------------------------
% 0.14/0.37 % (11229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11229)Termination reason: Unknown
% 0.14/0.37 % (11229)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (11229)Memory used [KB]: 1023
% 0.14/0.37 % (11229)Time elapsed: 0.004 s
% 0.14/0.37 % (11229)Instructions burned: 3 (million)
% 0.14/0.37 % (11229)------------------------------
% 0.14/0.37 % (11229)------------------------------
% 0.14/0.37
% 0.14/0.37 % (11228)Memory used [KB]: 1023
% 0.14/0.37 % (11228)Time elapsed: 0.004 s
% 0.14/0.37 % (11228)Instructions burned: 3 (million)
% 0.14/0.37 % (11228)------------------------------
% 0.14/0.37 % (11228)------------------------------
% 0.14/0.37 % (11232)Instruction limit reached!
% 0.14/0.37 % (11232)------------------------------
% 0.14/0.37 % (11232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (11232)Termination reason: Unknown
% 0.14/0.37 % (11232)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (11232)Memory used [KB]: 1023
% 0.14/0.37 % (11232)Time elapsed: 0.004 s
% 0.14/0.37 % (11232)Instructions burned: 3 (million)
% 0.14/0.37 % (11232)------------------------------
% 0.14/0.37 % (11232)------------------------------
% 0.14/0.38 % (11226)Instruction limit reached!
% 0.14/0.38 % (11226)------------------------------
% 0.14/0.38 % (11226)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (11226)Termination reason: Unknown
% 0.14/0.38 % (11226)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (11226)Memory used [KB]: 1023
% 0.14/0.38 % (11226)Time elapsed: 0.005 s
% 0.14/0.38 % (11226)Instructions burned: 5 (million)
% 0.14/0.38 % (11226)------------------------------
% 0.14/0.38 % (11226)------------------------------
% 0.14/0.38 % (11230)First to succeed.
% 0.14/0.38 % (11231)Instruction limit reached!
% 0.14/0.38 % (11231)------------------------------
% 0.14/0.38 % (11231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (11231)Termination reason: Unknown
% 0.14/0.38 % (11231)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (11231)Memory used [KB]: 5756
% 0.14/0.38 % (11231)Time elapsed: 0.013 s
% 0.14/0.38 % (11231)Instructions burned: 18 (million)
% 0.14/0.38 % (11231)------------------------------
% 0.14/0.38 % (11231)------------------------------
% 0.21/0.39 % (11225)Also succeeded, but the first one will report.
% 0.21/0.39 % (11230)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% 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, qmltpeq: 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 > $o).
% 0.21/0.39 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_8, type, mtrue: $i > $o).
% 0.21/0.39 thf(func_def_9, type, mfalse: $i > $o).
% 0.21/0.39 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.21/0.39 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.39 thf(func_def_30, type, mvalid: ($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) > $o).
% 0.21/0.39 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.21/0.39 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.21/0.39 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.21/0.39 thf(func_def_37, type, big_p: mu > $i > $o).
% 0.21/0.39 thf(func_def_53, type, sK0: $i > mu).
% 0.21/0.39 thf(func_def_57, type, sK4: mu).
% 0.21/0.39 thf(func_def_58, type, sK5: mu > $i).
% 0.21/0.39 thf(func_def_59, type, sK6: mu > $i).
% 0.21/0.39 thf(f179,plain,(
% 0.21/0.39 $false),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f175])).
% 0.21/0.39 thf(f175,plain,(
% 0.21/0.39 ($false = $true)),
% 0.21/0.39 inference(superposition,[],[f174,f140])).
% 0.21/0.39 thf(f140,plain,(
% 0.21/0.39 ((exists_in_world @ sK4 @ sK3) = $true)),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f138])).
% 0.21/0.39 thf(f138,plain,(
% 0.21/0.39 ($false = ((exists_in_world @ sK4 @ sK3) => (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK3 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ sK4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ Y0 @ Y2)))))))))))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f137])).
% 0.21/0.39 thf(f137,plain,(
% 0.21/0.39 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK3 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_p @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_p @ Y1 @ Y3))))))))))))))) @ sK4))),
% 0.21/0.39 inference(sigma_clausification,[],[f134])).
% 0.21/0.39 thf(f134,plain,(
% 0.21/0.39 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK3 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_p @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_p @ Y1 @ Y3)))))))))))))))))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f133])).
% 0.21/0.39 thf(f133,plain,(
% 0.21/0.39 ($false = ((~ (rel_s4 @ sK2 @ sK3)) | (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ sK3 @ Y2)) | ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_p @ Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (big_p @ Y1 @ Y3))))))))))))))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f132])).
% 0.21/0.39 thf(f132,plain,(
% 0.21/0.39 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y0 @ Y3)) | ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_p @ Y1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_p @ Y2 @ Y4)))))))))))))))))) @ sK3))),
% 0.21/0.39 inference(sigma_clausification,[],[f131])).
% 0.21/0.39 thf(f131,plain,(
% 0.21/0.39 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y0 @ Y3)) | ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_p @ Y1 @ Y4))))) | (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (big_p @ Y2 @ Y4))))))))))))))))))))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f130])).
% 0.21/0.39 thf(f130,plain,(
% 0.21/0.39 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y1 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_p @ Y2 @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_p @ Y3 @ Y5)))))))))))))))))))) @ sK2))),
% 0.21/0.39 inference(sigma_clausification,[],[f129])).
% 0.21/0.39 thf(f129,plain,(
% 0.21/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y1 @ Y4)) | ((~ (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_p @ Y2 @ Y5))))) | (!! @ $i @ (^[Y5 : $i]: ((~ (rel_s4 @ Y4 @ Y5)) | (big_p @ Y3 @ Y5))))))))))))))))))))) != $true)),
% 0.21/0.39 inference(beta_eta_normalization,[],[f128])).
% 0.21/0.39 thf(f128,plain,(
% 0.21/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((exists_in_world @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ (Y1 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ (big_p @ Y0)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ (big_p @ Y1)))))))))) != $true)),
% 0.21/0.39 inference(definition_unfolding,[],[f116,f118,f117,f120,f126,f117,f127,f117,f117])).
% 0.21/0.39 thf(f127,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.39 inference(definition_unfolding,[],[f123,f122,f125])).
% 0.21/0.39 thf(f125,plain,(
% 0.21/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f84])).
% 0.21/0.39 thf(f84,plain,(
% 0.21/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.39 inference(fool_elimination,[],[f83])).
% 0.21/0.39 thf(f83,plain,(
% 0.21/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.21/0.39 inference(rectify,[],[f2])).
% 0.21/0.39 thf(f2,axiom,(
% 0.21/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.39 thf(f122,plain,(
% 0.21/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f92])).
% 0.21/0.39 thf(f92,plain,(
% 0.21/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f91])).
% 0.21/0.39 thf(f91,plain,(
% 0.21/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.21/0.39 inference(rectify,[],[f3])).
% 0.21/0.39 thf(f3,axiom,(
% 0.21/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.39 thf(f123,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.39 inference(cnf_transformation,[],[f86])).
% 0.21/0.39 thf(f86,plain,(
% 0.21/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f85])).
% 0.21/0.39 thf(f85,plain,(
% 0.21/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.39 inference(rectify,[],[f9])).
% 0.21/0.39 thf(f9,axiom,(
% 0.21/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.39 thf(f126,plain,(
% 0.21/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))))))),
% 0.21/0.39 inference(definition_unfolding,[],[f124,f125,f120,f125])).
% 0.21/0.39 thf(f124,plain,(
% 0.21/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f73])).
% 0.21/0.39 thf(f73,plain,(
% 0.21/0.39 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.21/0.39 inference(fool_elimination,[],[f72])).
% 0.21/0.39 thf(f72,plain,(
% 0.21/0.39 ((^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))) = mexists_ind)),
% 0.21/0.39 inference(rectify,[],[f16])).
% 0.21/0.39 thf(f16,axiom,(
% 0.21/0.39 ((^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))) = mexists_ind)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind)).
% 0.21/0.39 thf(f120,plain,(
% 0.21/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f80])).
% 0.21/0.39 thf(f80,plain,(
% 0.21/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f79])).
% 0.21/0.39 thf(f79,plain,(
% 0.21/0.39 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.21/0.39 inference(rectify,[],[f15])).
% 0.21/0.39 thf(f15,axiom,(
% 0.21/0.39 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.21/0.39 thf(f117,plain,(
% 0.21/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f98])).
% 0.21/0.39 thf(f98,plain,(
% 0.21/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f97])).
% 0.21/0.39 thf(f97,plain,(
% 0.21/0.39 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))))),
% 0.21/0.39 inference(rectify,[],[f32])).
% 0.21/0.39 thf(f32,axiom,(
% 0.21/0.39 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 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,[],[f51])).
% 0.21/0.39 thf(f51,plain,(
% 0.21/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.39 inference(fool_elimination,[],[f50])).
% 0.21/0.39 thf(f50,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/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.39 thf(f116,plain,(
% 0.21/0.39 ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ (mbox_s4 @ (big_p @ Y1)))))))))) != $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f111])).
% 0.21/0.39 thf(f111,plain,(
% 0.21/0.39 ((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ (mbox_s4 @ (big_p @ Y1)))))))))) != $true)),
% 0.21/0.39 inference(flattening,[],[f43])).
% 0.21/0.39 thf(f43,plain,(
% 0.21/0.39 ~((mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ (mbox_s4 @ (big_p @ Y1)))))))))) = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f42])).
% 0.21/0.39 thf(f42,plain,(
% 0.21/0.39 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ X0)) @ (mbox_s4 @ (big_p @ X1))))))))))),
% 0.21/0.39 inference(rectify,[],[f38])).
% 0.21/0.39 thf(f38,negated_conjecture,(
% 0.21/0.39 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ X0)) @ (mbox_s4 @ (big_p @ X1))))))))))),
% 0.21/0.39 inference(negated_conjecture,[],[f37])).
% 0.21/0.39 thf(f37,conjecture,(
% 0.21/0.39 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ X0)) @ (mbox_s4 @ (big_p @ X1))))))))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2108)).
% 0.21/0.39 thf(f174,plain,(
% 0.21/0.39 ($false = (exists_in_world @ sK4 @ sK3))),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f173])).
% 0.21/0.39 thf(f173,plain,(
% 0.21/0.39 ($false = $true) | ($false = (exists_in_world @ sK4 @ sK3))),
% 0.21/0.39 inference(duplicate_literal_removal,[],[f170])).
% 0.21/0.39 thf(f170,plain,(
% 0.21/0.39 ($false = $true) | ($false = (exists_in_world @ sK4 @ sK3)) | ($false = (exists_in_world @ sK4 @ sK3))),
% 0.21/0.39 inference(superposition,[],[f160,f168])).
% 0.21/0.39 thf(f168,plain,(
% 0.21/0.39 ( ! [X0 : mu] : (($true = (big_p @ sK4 @ (sK6 @ X0))) | ((exists_in_world @ X0 @ sK3) = $false)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f167])).
% 0.21/0.39 thf(f167,plain,(
% 0.21/0.39 ( ! [X0 : mu] : (($false = $true) | ($true = (big_p @ sK4 @ (sK6 @ X0))) | ((exists_in_world @ X0 @ sK3) = $false)) )),
% 0.21/0.39 inference(duplicate_literal_removal,[],[f164])).
% 0.21/0.39 thf(f164,plain,(
% 0.21/0.39 ( ! [X0 : mu] : (($true = (big_p @ sK4 @ (sK6 @ X0))) | ((exists_in_world @ X0 @ sK3) = $false) | ((exists_in_world @ X0 @ sK3) = $false) | ($false = $true)) )),
% 0.21/0.39 inference(superposition,[],[f157,f162])).
% 0.21/0.39 thf(f162,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($true = (rel_s4 @ (sK5 @ X1) @ (sK6 @ X1))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f161])).
% 0.21/0.39 thf(f161,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = (~ (rel_s4 @ (sK5 @ X1) @ (sK6 @ X1)))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.39 thf(f159,plain,(
% 0.21/0.39 ( ! [X1 : mu] : ((((~ (rel_s4 @ (sK5 @ X1) @ (sK6 @ X1))) | (big_p @ X1 @ (sK6 @ X1))) = $false) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f158])).
% 0.21/0.39 thf(f158,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = ((^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ X1 @ Y0))) @ (sK6 @ X1))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(sigma_clausification,[],[f151])).
% 0.21/0.39 thf(f151,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ X1 @ Y0))))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f148])).
% 0.21/0.39 thf(f148,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ sK4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ X1 @ Y0)))))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f147])).
% 0.21/0.39 thf(f147,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = ((~ (rel_s4 @ sK3 @ (sK5 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ sK4 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ X1 @ Y0))))))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f146])).
% 0.21/0.39 thf(f146,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ sK4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ X1 @ Y1))))))) @ (sK5 @ X1)))) )),
% 0.21/0.39 inference(sigma_clausification,[],[f145])).
% 0.21/0.39 thf(f145,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ sK4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ X1 @ Y1)))))))))) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f144])).
% 0.21/0.39 thf(f144,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ sK4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ X1 @ Y1)))))))))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f143])).
% 0.21/0.39 thf(f143,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($true = ((exists_in_world @ X1 @ sK3) => (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ sK4 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (big_p @ X1 @ Y1)))))))))))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f142])).
% 0.21/0.39 thf(f142,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK3 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ sK4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ Y0 @ Y2))))))))))) @ X1))) )),
% 0.21/0.39 inference(pi_clausification,[],[f141])).
% 0.21/0.39 thf(f141,plain,(
% 0.21/0.39 ($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK3 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ sK4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ Y0 @ Y2)))))))))))))),
% 0.21/0.39 inference(not_proxy_clausification,[],[f139])).
% 0.21/0.39 thf(f139,plain,(
% 0.21/0.39 ($false = (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ sK3 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ sK4 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (big_p @ Y0 @ Y2))))))))))))))),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f138])).
% 0.21/0.39 thf(f157,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : mu] : (($false = (rel_s4 @ (sK5 @ X1) @ X2)) | ($false = (exists_in_world @ X1 @ sK3)) | ($true = (big_p @ sK4 @ X2))) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f156])).
% 0.21/0.39 thf(f156,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : mu] : (($true = (~ (rel_s4 @ (sK5 @ X1) @ X2))) | ($false = (exists_in_world @ X1 @ sK3)) | ($true = (big_p @ sK4 @ X2))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f155])).
% 0.21/0.39 thf(f155,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : mu] : (($true = ((~ (rel_s4 @ (sK5 @ X1) @ X2)) | (big_p @ sK4 @ X2))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(beta_eta_normalization,[],[f154])).
% 0.21/0.39 thf(f154,plain,(
% 0.21/0.39 ( ! [X2 : $i,X1 : mu] : ((((^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ sK4 @ Y0))) @ X2) = $true) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(pi_clausification,[],[f153])).
% 0.21/0.39 thf(f153,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ sK4 @ Y0)))) = $true) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(not_proxy_clausification,[],[f152])).
% 0.21/0.39 thf(f152,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ (sK5 @ X1) @ Y0)) | (big_p @ sK4 @ Y0))))))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f148])).
% 0.21/0.39 thf(f160,plain,(
% 0.21/0.39 ( ! [X1 : mu] : (($false = (big_p @ X1 @ (sK6 @ X1))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.21/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (11230)------------------------------
% 0.21/0.39 % (11230)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (11230)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (11230)Memory used [KB]: 5756
% 0.21/0.39 % (11230)Time elapsed: 0.014 s
% 0.21/0.39 % (11230)Instructions burned: 14 (million)
% 0.21/0.39 % (11230)------------------------------
% 0.21/0.39 % (11230)------------------------------
% 0.21/0.39 % (11224)Success in time 0.018 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------