TSTP Solution File: SYN357^7 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 : Mon Jun 24 20:02:34 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% 0.00/0.10 % Command : run_vampire %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sun Jun 23 18:31:38 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.13/0.30 This is a TH0_THM_EQU_NAR problem
% 0.15/0.30 Running higher-order theorem proving
% 0.15/0.30 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.15/0.32 % (2352)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)
% 0.15/0.32 % (2351)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.32 % (2353)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)
% 0.15/0.32 % (2354)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.32 % (2352)Instruction limit reached!
% 0.15/0.32 % (2352)------------------------------
% 0.15/0.32 % (2352)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (2352)Termination reason: Unknown
% 0.15/0.32 % (2352)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (2352)Memory used [KB]: 1023
% 0.15/0.32 % (2352)Time elapsed: 0.003 s
% 0.15/0.32 % (2352)Instructions burned: 6 (million)
% 0.15/0.32 % (2352)------------------------------
% 0.15/0.32 % (2352)------------------------------
% 0.15/0.32 % (2354)Instruction limit reached!
% 0.15/0.32 % (2354)------------------------------
% 0.15/0.32 % (2354)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (2354)Termination reason: Unknown
% 0.15/0.32 % (2354)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (2354)Memory used [KB]: 1023
% 0.15/0.32 % (2354)Time elapsed: 0.003 s
% 0.15/0.32 % (2354)Instructions burned: 4 (million)
% 0.15/0.32 % (2354)------------------------------
% 0.15/0.32 % (2354)------------------------------
% 0.15/0.32 % (2357)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.32 % (2355)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)
% 0.15/0.32 % (2356)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)
% 0.15/0.32 % (2355)Instruction limit reached!
% 0.15/0.32 % (2355)------------------------------
% 0.15/0.32 % (2355)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (2355)Termination reason: Unknown
% 0.15/0.32 % (2355)Termination phase: shuffling
% 0.15/0.32
% 0.15/0.32 % (2355)Memory used [KB]: 1023
% 0.15/0.32 % (2355)Time elapsed: 0.003 s
% 0.15/0.32 % (2355)Instructions burned: 4 (million)
% 0.15/0.32 % (2355)------------------------------
% 0.15/0.32 % (2355)------------------------------
% 0.15/0.33 % (2351)First to succeed.
% 0.15/0.33 % (2351)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% 0.15/0.33 thf(type_def_5, type, mu: $tType).
% 0.15/0.33 thf(func_def_0, type, mu: $tType).
% 0.15/0.33 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.15/0.33 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_8, type, mtrue: $i > $o).
% 0.15/0.33 thf(func_def_9, type, mfalse: $i > $o).
% 0.15/0.33 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.15/0.33 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.33 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.15/0.33 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.15/0.33 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.15/0.33 thf(func_def_37, type, big_p: mu > $i > $o).
% 0.15/0.33 thf(func_def_53, type, sK0: $i > mu).
% 0.15/0.33 thf(func_def_57, type, sK4: mu).
% 0.15/0.33 thf(func_def_58, type, sK5: mu > $i).
% 0.15/0.33 thf(func_def_59, type, sK6: mu > $i).
% 0.15/0.33 thf(f238,plain,(
% 0.15/0.33 $false),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f234])).
% 0.15/0.33 thf(f234,plain,(
% 0.15/0.33 ($true = $false)),
% 0.15/0.33 inference(superposition,[],[f233,f179])).
% 0.15/0.33 thf(f179,plain,(
% 0.15/0.33 ((exists_in_world @ sK4 @ sK3) = $true)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f177])).
% 0.15/0.33 thf(f177,plain,(
% 0.15/0.33 (((exists_in_world @ sK4 @ sK3) => (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((big_p @ sK4 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((big_p @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK3 @ Y1))))))))))) = $false)),
% 0.15/0.33 inference(beta_eta_normalization,[],[f176])).
% 0.15/0.33 thf(f176,plain,(
% 0.15/0.33 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((big_p @ Y0 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((big_p @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ sK3 @ Y2)))))))))))) @ sK4) = $false)),
% 0.15/0.33 inference(sigma_clausification,[],[f175])).
% 0.15/0.33 thf(f175,plain,(
% 0.15/0.33 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((big_p @ Y0 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((big_p @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ sK3 @ Y2))))))))))))) = $false)),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f173])).
% 0.15/0.33 thf(f173,plain,(
% 0.15/0.33 ($false = ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK3) => (~ (!! @ $i @ (^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((big_p @ Y0 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((big_p @ Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ sK3 @ Y2))))))))))))) | (~ (rel_s4 @ sK2 @ sK3))))),
% 0.15/0.33 inference(beta_eta_normalization,[],[f172])).
% 0.15/0.33 thf(f172,plain,(
% 0.15/0.33 (((^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ $i @ (^[Y4 : $i]: ((big_p @ Y1 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (!! @ $i @ (^[Y4 : $i]: ((big_p @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y0 @ Y3))))))))))))) | (~ (rel_s4 @ sK2 @ Y0)))) @ sK3) = $false)),
% 0.15/0.33 inference(sigma_clausification,[],[f171])).
% 0.15/0.33 thf(f171,plain,(
% 0.15/0.33 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (~ (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ (!! @ $i @ (^[Y3 : $i]: (((~ (!! @ $i @ (^[Y4 : $i]: ((big_p @ Y1 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (!! @ $i @ (^[Y4 : $i]: ((big_p @ Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y0 @ Y3))))))))))))) | (~ (rel_s4 @ sK2 @ Y0))))))),
% 0.15/0.33 inference(beta_eta_normalization,[],[f170])).
% 0.15/0.33 thf(f170,plain,(
% 0.15/0.33 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: ((big_p @ Y2 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (!! @ $i @ (^[Y5 : $i]: ((big_p @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y1 @ Y4))))))))))))) | (~ (rel_s4 @ Y0 @ Y1)))))) @ sK2))),
% 0.15/0.33 inference(sigma_clausification,[],[f169])).
% 0.15/0.33 thf(f169,plain,(
% 0.15/0.33 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (~ (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y1) => (~ (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: ((big_p @ Y2 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (!! @ $i @ (^[Y5 : $i]: ((big_p @ Y3 @ Y5) | (~ (rel_s4 @ Y4 @ Y5)))))) | (~ (rel_s4 @ Y1 @ Y4))))))))))))) | (~ (rel_s4 @ Y0 @ Y1))))))))),
% 0.15/0.33 inference(beta_eta_normalization,[],[f164])).
% 0.15/0.33 thf(f164,plain,(
% 0.15/0.33 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ 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]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ 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]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ (big_p @ Y0)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (rel_s4 @ Y3 @ Y4)))))))) @ (big_p @ Y1)))))))))))),
% 0.15/0.33 inference(definition_unfolding,[],[f122,f148,f136,f133,f160,f136,f155,f136,f136])).
% 0.15/0.33 thf(f155,plain,(
% 0.15/0.33 (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)))))),
% 0.15/0.33 inference(definition_unfolding,[],[f146,f116,f134])).
% 0.15/0.33 thf(f134,plain,(
% 0.15/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f63])).
% 0.15/0.33 thf(f63,plain,(
% 0.15/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.33 inference(fool_elimination,[],[f62])).
% 0.15/0.33 thf(f62,plain,(
% 0.15/0.33 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.33 inference(rectify,[],[f2])).
% 0.15/0.33 thf(f2,axiom,(
% 0.15/0.33 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.15/0.33 thf(f116,plain,(
% 0.15/0.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f53])).
% 0.15/0.33 thf(f53,plain,(
% 0.15/0.33 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f52])).
% 0.15/0.33 thf(f52,plain,(
% 0.15/0.33 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.15/0.33 inference(rectify,[],[f3])).
% 0.15/0.33 thf(f3,axiom,(
% 0.15/0.33 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.15/0.33 thf(f146,plain,(
% 0.15/0.33 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.33 inference(cnf_transformation,[],[f55])).
% 0.15/0.33 thf(f55,plain,(
% 0.15/0.33 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.33 inference(fool_elimination,[],[f54])).
% 0.15/0.33 thf(f54,plain,(
% 0.15/0.33 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.33 inference(rectify,[],[f9])).
% 0.15/0.33 thf(f9,axiom,(
% 0.15/0.33 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.33 thf(f160,plain,(
% 0.15/0.33 (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)))))))),
% 0.15/0.33 inference(definition_unfolding,[],[f139,f134,f133,f134])).
% 0.15/0.33 thf(f139,plain,(
% 0.15/0.33 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f102])).
% 0.15/0.33 thf(f102,plain,(
% 0.15/0.33 (mexists_ind = (^[Y0 : mu > $i > $o]: (mnot @ (mforall_ind @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))))))),
% 0.15/0.33 inference(fool_elimination,[],[f101])).
% 0.15/0.33 thf(f101,plain,(
% 0.15/0.33 (mexists_ind = (^[X0 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X1 : mu] : (mnot @ (X0 @ X1)))))))),
% 0.15/0.33 inference(rectify,[],[f16])).
% 0.15/0.33 thf(f16,axiom,(
% 0.15/0.33 (mexists_ind = (^[X3 : mu > $i > $o] : (mnot @ (mforall_ind @ (^[X0 : mu] : (mnot @ (X3 @ X0)))))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_ind)).
% 0.15/0.33 thf(f133,plain,(
% 0.15/0.33 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f104])).
% 0.15/0.33 thf(f104,plain,(
% 0.15/0.33 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f103])).
% 0.15/0.33 thf(f103,plain,(
% 0.15/0.33 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.15/0.33 inference(rectify,[],[f15])).
% 0.15/0.33 thf(f15,axiom,(
% 0.15/0.33 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_ind)).
% 0.15/0.33 thf(f136,plain,(
% 0.15/0.33 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f75])).
% 0.15/0.33 thf(f75,plain,(
% 0.15/0.33 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f74])).
% 0.15/0.33 thf(f74,plain,(
% 0.15/0.33 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))))),
% 0.15/0.33 inference(rectify,[],[f32])).
% 0.15/0.33 thf(f32,axiom,(
% 0.15/0.33 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X6] : (~(rel_s4 @ X2 @ X6) | (X3 @ X6)))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.15/0.33 thf(f148,plain,(
% 0.15/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.33 inference(cnf_transformation,[],[f100])).
% 0.15/0.33 thf(f100,plain,(
% 0.15/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.33 inference(fool_elimination,[],[f99])).
% 0.15/0.33 thf(f99,plain,(
% 0.15/0.33 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.15/0.33 inference(rectify,[],[f28])).
% 0.15/0.33 thf(f28,axiom,(
% 0.15/0.33 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.33 thf(f122,plain,(
% 0.15/0.33 ($true != (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ (mbox_s4 @ (big_p @ Y1)))))))))))),
% 0.15/0.33 inference(cnf_transformation,[],[f111])).
% 0.15/0.33 thf(f111,plain,(
% 0.15/0.33 ($true != (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ (mbox_s4 @ (big_p @ Y1)))))))))))),
% 0.15/0.33 inference(flattening,[],[f51])).
% 0.15/0.33 thf(f51,plain,(
% 0.15/0.33 ~($true = (mvalid @ (mbox_s4 @ (mforall_ind @ (^[Y0 : mu]: (mexists_ind @ (^[Y1 : mu]: (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ Y0)) @ (mbox_s4 @ (big_p @ Y1)))))))))))),
% 0.15/0.33 inference(fool_elimination,[],[f50])).
% 0.15/0.33 thf(f50,plain,(
% 0.15/0.33 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ X0)) @ (mbox_s4 @ (big_p @ X1))))))))))),
% 0.15/0.33 inference(rectify,[],[f38])).
% 0.15/0.33 thf(f38,negated_conjecture,(
% 0.15/0.33 ~(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ X0)) @ (mbox_s4 @ (big_p @ X1))))))))))),
% 0.15/0.33 inference(negated_conjecture,[],[f37])).
% 0.15/0.33 thf(f37,conjecture,(
% 0.15/0.33 (mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : (mexists_ind @ (^[X1 : mu] : (mbox_s4 @ (mimplies @ (mbox_s4 @ (big_p @ X0)) @ (mbox_s4 @ (big_p @ X1))))))))))),
% 0.15/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2108)).
% 0.15/0.33 thf(f233,plain,(
% 0.15/0.33 ((exists_in_world @ sK4 @ sK3) = $false)),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f232])).
% 0.15/0.33 thf(f232,plain,(
% 0.15/0.33 ((exists_in_world @ sK4 @ sK3) = $false) | ($true = $false)),
% 0.15/0.33 inference(duplicate_literal_removal,[],[f229])).
% 0.15/0.33 thf(f229,plain,(
% 0.15/0.33 ($true = $false) | ((exists_in_world @ sK4 @ sK3) = $false) | ((exists_in_world @ sK4 @ sK3) = $false)),
% 0.15/0.33 inference(superposition,[],[f199,f227])).
% 0.15/0.33 thf(f227,plain,(
% 0.15/0.33 ( ! [X0 : mu] : (($true = (big_p @ sK4 @ (sK6 @ X0))) | ((exists_in_world @ X0 @ sK3) = $false)) )),
% 0.15/0.33 inference(trivial_inequality_removal,[],[f226])).
% 0.15/0.33 thf(f226,plain,(
% 0.15/0.33 ( ! [X0 : mu] : (($true = $false) | ((exists_in_world @ X0 @ sK3) = $false) | ($true = (big_p @ sK4 @ (sK6 @ X0)))) )),
% 0.15/0.33 inference(duplicate_literal_removal,[],[f214])).
% 0.15/0.33 thf(f214,plain,(
% 0.15/0.33 ( ! [X0 : mu] : (((exists_in_world @ X0 @ sK3) = $false) | ((exists_in_world @ X0 @ sK3) = $false) | ($true = $false) | ($true = (big_p @ sK4 @ (sK6 @ X0)))) )),
% 0.15/0.33 inference(superposition,[],[f195,f200])).
% 0.15/0.33 thf(f200,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($true = (rel_s4 @ (sK5 @ X1) @ (sK6 @ X1))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(not_proxy_clausification,[],[f198])).
% 0.15/0.33 thf(f198,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ((~ (rel_s4 @ (sK5 @ X1) @ (sK6 @ X1))) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f197])).
% 0.15/0.33 thf(f197,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($false = ((big_p @ X1 @ (sK6 @ X1)) | (~ (rel_s4 @ (sK5 @ X1) @ (sK6 @ X1)))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f196])).
% 0.15/0.33 thf(f196,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | (((^[Y0 : $i]: ((big_p @ X1 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))) @ (sK6 @ X1)) = $false)) )),
% 0.15/0.33 inference(sigma_clausification,[],[f189])).
% 0.15/0.33 thf(f189,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (((!! @ $i @ (^[Y0 : $i]: ((big_p @ X1 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0))))) = $false) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f188])).
% 0.15/0.33 thf(f188,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((big_p @ sK4 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((big_p @ X1 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))))) = $false)) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f186])).
% 0.15/0.33 thf(f186,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((big_p @ sK4 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((big_p @ X1 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))))) | (~ (rel_s4 @ sK3 @ (sK5 @ X1)))) = $false) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f185])).
% 0.15/0.33 thf(f185,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((big_p @ sK4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((big_p @ X1 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK3 @ Y0)))) @ (sK5 @ X1))) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(sigma_clausification,[],[f184])).
% 0.15/0.33 thf(f184,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((big_p @ sK4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((big_p @ X1 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK3 @ Y0))))) = $false) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(not_proxy_clausification,[],[f183])).
% 0.15/0.33 thf(f183,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((big_p @ sK4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((big_p @ X1 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK3 @ Y0)))))))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f182])).
% 0.15/0.33 thf(f182,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($true = ((exists_in_world @ X1 @ sK3) => (~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((big_p @ sK4 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((big_p @ X1 @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK3 @ Y0))))))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f181])).
% 0.15/0.33 thf(f181,plain,(
% 0.15/0.33 ( ! [X1 : mu] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((big_p @ sK4 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((big_p @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK3 @ Y1)))))))) @ X1) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f180])).
% 0.15/0.33 thf(f180,plain,(
% 0.15/0.33 ((!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((big_p @ sK4 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((big_p @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK3 @ Y1))))))))) = $true)),
% 0.15/0.33 inference(not_proxy_clausification,[],[f178])).
% 0.15/0.33 thf(f178,plain,(
% 0.15/0.33 ($false = (~ (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK3) => (~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((big_p @ sK4 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((big_p @ Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ sK3 @ Y1)))))))))))),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f177])).
% 0.15/0.33 thf(f195,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : mu] : (((rel_s4 @ (sK5 @ X1) @ X2) = $false) | ($true = (big_p @ sK4 @ X2)) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(not_proxy_clausification,[],[f194])).
% 0.15/0.33 thf(f194,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($true = (big_p @ sK4 @ X2)) | ($true = (~ (rel_s4 @ (sK5 @ X1) @ X2)))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f193])).
% 0.15/0.33 thf(f193,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($true = ((big_p @ sK4 @ X2) | (~ (rel_s4 @ (sK5 @ X1) @ X2))))) )),
% 0.15/0.33 inference(beta_eta_normalization,[],[f192])).
% 0.15/0.33 thf(f192,plain,(
% 0.15/0.33 ( ! [X2 : $i,X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | (((^[Y0 : $i]: ((big_p @ sK4 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))) @ X2) = $true)) )),
% 0.15/0.33 inference(pi_clausification,[],[f191])).
% 0.15/0.33 thf(f191,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (($false = (exists_in_world @ X1 @ sK3)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((big_p @ sK4 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0))))))) )),
% 0.15/0.33 inference(not_proxy_clausification,[],[f190])).
% 0.15/0.33 thf(f190,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (((~ (!! @ $i @ (^[Y0 : $i]: ((big_p @ sK4 @ Y0) | (~ (rel_s4 @ (sK5 @ X1) @ Y0)))))) = $false) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f188])).
% 0.15/0.33 thf(f199,plain,(
% 0.15/0.33 ( ! [X1 : mu] : (((big_p @ X1 @ (sK6 @ X1)) = $false) | ($false = (exists_in_world @ X1 @ sK3))) )),
% 0.15/0.33 inference(binary_proxy_clausification,[],[f197])).
% 0.15/0.33 % SZS output end Proof for theBenchmark
% 0.15/0.33 % (2351)------------------------------
% 0.15/0.33 % (2351)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.33 % (2351)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (2351)Memory used [KB]: 5756
% 0.15/0.33 % (2351)Time elapsed: 0.010 s
% 0.15/0.33 % (2351)Instructions burned: 17 (million)
% 0.15/0.33 % (2351)------------------------------
% 0.15/0.33 % (2351)------------------------------
% 0.15/0.33 % (2350)Success in time 0.009 s
%------------------------------------------------------------------------------