TSTP Solution File: SYO455^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO455^6 : 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 : n019.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 09:04:42 EDT 2024
% Result : Theorem 0.25s 0.43s
% Output : Refutation 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.16 % Problem : SYO455^6 : TPTP v8.2.0. Released v4.0.0.
% 0.16/0.18 % 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
% 0.17/0.40 % Computer : n019.cluster.edu
% 0.17/0.40 % Model : x86_64 x86_64
% 0.17/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.40 % Memory : 8042.1875MB
% 0.17/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.40 % CPULimit : 300
% 0.17/0.40 % WCLimit : 300
% 0.17/0.40 % DateTime : Mon May 20 10:33:53 EDT 2024
% 0.17/0.40 % CPUTime :
% 0.17/0.40 This is a TH0_THM_EQU_NAR problem
% 0.17/0.40 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
% 0.25/0.42 % (25138)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.25/0.42 % (25134)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)
% 0.25/0.42 % (25133)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)
% 0.25/0.42 % (25136)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)
% 0.25/0.42 % (25136)Instruction limit reached!
% 0.25/0.42 % (25136)------------------------------
% 0.25/0.42 % (25136)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.42 % (25136)Termination reason: Unknown
% 0.25/0.42 % (25136)Termination phase: shuffling
% 0.25/0.42
% 0.25/0.42 % (25136)Memory used [KB]: 1023
% 0.25/0.42 % (25136)Time elapsed: 0.002 s
% 0.25/0.42 % (25136)Instructions burned: 2 (million)
% 0.25/0.42 % (25136)------------------------------
% 0.25/0.42 % (25136)------------------------------
% 0.25/0.43 % (25133)Instruction limit reached!
% 0.25/0.43 % (25133)------------------------------
% 0.25/0.43 % (25133)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.43 % (25133)Termination reason: Unknown
% 0.25/0.43 % (25133)Termination phase: Property scanning
% 0.25/0.43
% 0.25/0.43 % (25133)Memory used [KB]: 1023
% 0.25/0.43 % (25133)Time elapsed: 0.005 s
% 0.25/0.43 % (25133)Instructions burned: 6 (million)
% 0.25/0.43 % (25133)------------------------------
% 0.25/0.43 % (25133)------------------------------
% 0.25/0.43 % (25137)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)
% 0.25/0.43 % (25138)First to succeed.
% 0.25/0.43 % (25137)Refutation not found, incomplete strategy
% 0.25/0.43 % (25137)------------------------------
% 0.25/0.43 % (25137)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.43 % (25137)Termination reason: Refutation not found, incomplete strategy
% 0.25/0.43
% 0.25/0.43
% 0.25/0.43 % (25137)Memory used [KB]: 5628
% 0.25/0.43 % (25137)Time elapsed: 0.007 s
% 0.25/0.43 % (25137)Instructions burned: 10 (million)
% 0.25/0.43 % (25137)------------------------------
% 0.25/0.43 % (25137)------------------------------
% 0.25/0.43 % (25134)Also succeeded, but the first one will report.
% 0.25/0.43 % (25138)Refutation found. Thanks to Tanya!
% 0.25/0.43 % SZS status Theorem for theBenchmark
% 0.25/0.43 % SZS output start Proof for theBenchmark
% 0.25/0.43 thf(type_def_5, type, mu: $tType).
% 0.25/0.43 thf(func_def_0, type, mu: $tType).
% 0.25/0.43 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.25/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_15, type, mtrue: $i > $o).
% 0.25/0.43 thf(func_def_16, type, mfalse: $i > $o).
% 0.25/0.43 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.25/0.43 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.25/0.43 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.25/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.25/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.25/0.43 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.25/0.43 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.25/0.43 thf(func_def_36, type, p: $i > $o).
% 0.25/0.43 thf(func_def_37, type, q: $i > $o).
% 0.25/0.43 thf(f250,plain,(
% 0.25/0.43 $false),
% 0.25/0.43 inference(trivial_inequality_removal,[],[f249])).
% 0.25/0.43 thf(f249,plain,(
% 0.25/0.43 ($true = $false)),
% 0.25/0.43 inference(backward_demodulation,[],[f213,f248])).
% 0.25/0.43 thf(f248,plain,(
% 0.25/0.43 ((p @ sK1) = $false)),
% 0.25/0.43 inference(trivial_inequality_removal,[],[f247])).
% 0.25/0.43 thf(f247,plain,(
% 0.25/0.43 ((p @ sK1) = $false) | ($true = $false)),
% 0.25/0.43 inference(forward_demodulation,[],[f244,f209])).
% 0.25/0.43 thf(f209,plain,(
% 0.25/0.43 ((q @ sK1) = $false)),
% 0.25/0.43 inference(trivial_inequality_removal,[],[f207])).
% 0.25/0.43 thf(f207,plain,(
% 0.25/0.43 ((q @ sK1) = $false) | ($true = $false)),
% 0.25/0.43 inference(superposition,[],[f205,f196])).
% 0.25/0.43 thf(f196,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((q @ X1) = $false)) )),
% 0.25/0.43 inference(not_proxy_clausification,[],[f195])).
% 0.25/0.43 thf(f195,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((~ (q @ X1)) = $true)) )),
% 0.25/0.43 inference(not_proxy_clausification,[],[f194])).
% 0.25/0.43 thf(f194,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (((~ (rel_s5 @ sK1 @ X1)) = $true) | ((~ (q @ X1)) = $true)) )),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f193])).
% 0.25/0.43 thf(f193,plain,(
% 0.25/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK1 @ X1)) | (~ (q @ X1))) = $true)) )),
% 0.25/0.43 inference(beta_eta_normalization,[],[f192])).
% 0.25/0.43 thf(f192,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (q @ Y0)))) @ X1))) )),
% 0.25/0.43 inference(pi_clausification,[],[f191])).
% 0.25/0.43 thf(f191,plain,(
% 0.25/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (q @ Y0))))))),
% 0.25/0.43 inference(not_proxy_clausification,[],[f175])).
% 0.25/0.43 thf(f175,plain,(
% 0.25/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (q @ Y0)))))))),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f174])).
% 0.25/0.43 thf(f174,plain,(
% 0.25/0.43 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (q @ Y0))))))) = $false)),
% 0.25/0.43 inference(beta_eta_normalization,[],[f173])).
% 0.25/0.43 thf(f173,plain,(
% 0.25/0.43 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (q @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))))) @ sK1) = $false)),
% 0.25/0.43 inference(sigma_clausification,[],[f172])).
% 0.25/0.43 thf(f172,plain,(
% 0.25/0.43 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (q @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1))))))))) != $true)),
% 0.25/0.43 inference(boolean_simplification,[],[f171])).
% 0.25/0.43 thf(f171,plain,(
% 0.25/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (p @ Y1)) | (q @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1))))))))) != $true)),
% 0.25/0.43 inference(beta_eta_normalization,[],[f161])).
% 0.25/0.43 thf(f161,plain,(
% 0.25/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))) != $true)),
% 0.25/0.43 inference(definition_unfolding,[],[f146,f147,f149,f148,f119,f119,f139,f115,f157])).
% 0.25/0.43 thf(f157,plain,(
% 0.25/0.43 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.25/0.43 inference(definition_unfolding,[],[f120,f115,f119,f115])).
% 0.25/0.43 thf(f120,plain,(
% 0.25/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.25/0.43 inference(cnf_transformation,[],[f65])).
% 0.25/0.43 thf(f65,plain,(
% 0.25/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.25/0.43 inference(fool_elimination,[],[f64])).
% 0.25/0.43 thf(f64,plain,(
% 0.25/0.43 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.25/0.43 inference(rectify,[],[f33])).
% 0.25/0.43 thf(f33,axiom,(
% 0.25/0.43 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.25/0.43 thf(f115,plain,(
% 0.25/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.25/0.43 inference(cnf_transformation,[],[f47])).
% 0.25/0.43 thf(f47,plain,(
% 0.25/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.25/0.43 inference(fool_elimination,[],[f46])).
% 0.25/0.43 thf(f46,plain,(
% 0.25/0.43 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.25/0.43 inference(rectify,[],[f3])).
% 0.25/0.43 thf(f3,axiom,(
% 0.25/0.43 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.25/0.43 thf(f139,plain,(
% 0.25/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.25/0.43 inference(cnf_transformation,[],[f72])).
% 0.25/0.43 thf(f72,plain,(
% 0.25/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.25/0.43 inference(fool_elimination,[],[f71])).
% 0.25/0.43 thf(f71,plain,(
% 0.25/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.25/0.43 inference(rectify,[],[f4])).
% 0.25/0.43 thf(f4,axiom,(
% 0.25/0.43 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.25/0.43 thf(f119,plain,(
% 0.25/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.25/0.43 inference(cnf_transformation,[],[f41])).
% 0.25/0.43 thf(f41,plain,(
% 0.25/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.25/0.43 inference(fool_elimination,[],[f40])).
% 0.25/0.43 thf(f40,plain,(
% 0.25/0.43 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.25/0.43 inference(rectify,[],[f32])).
% 0.25/0.43 thf(f32,axiom,(
% 0.25/0.43 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.25/0.43 thf(f148,plain,(
% 0.25/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.25/0.43 inference(definition_unfolding,[],[f121,f115,f139,f115,f115])).
% 0.25/0.43 thf(f121,plain,(
% 0.25/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.25/0.43 inference(cnf_transformation,[],[f105])).
% 0.25/0.43 thf(f105,plain,(
% 0.25/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.25/0.43 inference(fool_elimination,[],[f104])).
% 0.25/0.43 thf(f104,plain,(
% 0.25/0.43 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.25/0.43 inference(rectify,[],[f5])).
% 0.25/0.43 thf(f5,axiom,(
% 0.25/0.43 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.25/0.43 thf(f149,plain,(
% 0.25/0.43 (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)))))),
% 0.25/0.43 inference(definition_unfolding,[],[f130,f139,f115])).
% 0.25/0.43 thf(f130,plain,(
% 0.25/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.25/0.43 inference(cnf_transformation,[],[f109])).
% 0.25/0.43 thf(f109,plain,(
% 0.25/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.25/0.43 inference(fool_elimination,[],[f108])).
% 0.25/0.43 thf(f108,plain,(
% 0.25/0.43 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.25/0.43 inference(rectify,[],[f6])).
% 0.25/0.43 thf(f6,axiom,(
% 0.25/0.43 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.25/0.43 thf(f147,plain,(
% 0.25/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.25/0.43 inference(cnf_transformation,[],[f59])).
% 0.25/0.43 thf(f59,plain,(
% 0.25/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.25/0.43 inference(fool_elimination,[],[f58])).
% 0.25/0.43 thf(f58,plain,(
% 0.25/0.43 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.25/0.43 inference(rectify,[],[f28])).
% 0.25/0.43 thf(f28,axiom,(
% 0.25/0.43 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.25/0.43 thf(f146,plain,(
% 0.25/0.43 ((mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ (mor @ (mnot @ p) @ q))) @ (mdia_s5 @ q))) != $true)),
% 0.25/0.43 inference(cnf_transformation,[],[f110])).
% 0.25/0.43 thf(f110,plain,(
% 0.25/0.43 ((mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ (mor @ (mnot @ p) @ q))) @ (mdia_s5 @ q))) != $true)),
% 0.25/0.43 inference(flattening,[],[f74])).
% 0.25/0.43 thf(f74,plain,(
% 0.25/0.43 ~((mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ (mor @ (mnot @ p) @ q))) @ (mdia_s5 @ q))) = $true)),
% 0.25/0.43 inference(fool_elimination,[],[f73])).
% 0.25/0.43 thf(f73,plain,(
% 0.25/0.43 ~(mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ (mor @ (mnot @ p) @ q))) @ (mdia_s5 @ q)))),
% 0.25/0.43 inference(rectify,[],[f38])).
% 0.25/0.43 thf(f38,negated_conjecture,(
% 0.25/0.43 ~(mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ (mor @ (mnot @ p) @ q))) @ (mdia_s5 @ q)))),
% 0.25/0.43 inference(negated_conjecture,[],[f37])).
% 0.25/0.43 thf(f37,conjecture,(
% 0.25/0.43 (mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ (mor @ (mnot @ p) @ q))) @ (mdia_s5 @ q)))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.25/0.43 thf(f205,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (((rel_s5 @ X1 @ X1) = $true)) )),
% 0.25/0.43 inference(beta_eta_normalization,[],[f204])).
% 0.25/0.43 thf(f204,plain,(
% 0.25/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s5 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.25/0.43 inference(pi_clausification,[],[f203])).
% 0.25/0.43 thf(f203,plain,(
% 0.25/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s5 @ Y0 @ Y0))))),
% 0.25/0.43 inference(beta_eta_normalization,[],[f158])).
% 0.25/0.43 thf(f158,plain,(
% 0.25/0.43 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s5))),
% 0.25/0.43 inference(definition_unfolding,[],[f127,f136])).
% 0.25/0.43 thf(f136,plain,(
% 0.25/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.25/0.43 inference(cnf_transformation,[],[f43])).
% 0.25/0.43 thf(f43,plain,(
% 0.25/0.43 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.25/0.43 inference(fool_elimination,[],[f42])).
% 0.25/0.43 thf(f42,plain,(
% 0.25/0.43 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.25/0.43 inference(rectify,[],[f18])).
% 0.25/0.43 thf(f18,axiom,(
% 0.25/0.43 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.25/0.43 thf(f127,plain,(
% 0.25/0.43 ((mreflexive @ rel_s5) = $true)),
% 0.25/0.43 inference(cnf_transformation,[],[f55])).
% 0.25/0.43 thf(f55,plain,(
% 0.25/0.43 ((mreflexive @ rel_s5) = $true)),
% 0.25/0.43 inference(fool_elimination,[],[f54])).
% 0.25/0.43 thf(f54,plain,(
% 0.25/0.43 (mreflexive @ rel_s5)),
% 0.25/0.43 inference(rectify,[],[f34])).
% 0.25/0.43 thf(f34,axiom,(
% 0.25/0.43 (mreflexive @ rel_s5)),
% 0.25/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.25/0.43 thf(f244,plain,(
% 0.25/0.43 ((q @ sK1) = $true) | ((p @ sK1) = $false)),
% 0.25/0.43 inference(trivial_inequality_removal,[],[f241])).
% 0.25/0.43 thf(f241,plain,(
% 0.25/0.43 ((q @ sK1) = $true) | ((p @ sK1) = $false) | ($true = $false)),
% 0.25/0.43 inference(superposition,[],[f205,f190])).
% 0.25/0.43 thf(f190,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((p @ X1) = $false) | ((q @ X1) = $true)) )),
% 0.25/0.43 inference(not_proxy_clausification,[],[f189])).
% 0.25/0.43 thf(f189,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (((~ (rel_s5 @ sK1 @ X1)) = $true) | ((q @ X1) = $true) | ((p @ X1) = $false)) )),
% 0.25/0.43 inference(not_proxy_clausification,[],[f188])).
% 0.25/0.43 thf(f188,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ((q @ X1) = $true) | ((~ (rel_s5 @ sK1 @ X1)) = $true)) )),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f187])).
% 0.25/0.43 thf(f187,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (q @ X1))) | ((~ (rel_s5 @ sK1 @ X1)) = $true)) )),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f186])).
% 0.25/0.43 thf(f186,plain,(
% 0.25/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK1 @ X1)) | ((~ (p @ X1)) | (q @ X1))) = $true)) )),
% 0.25/0.43 inference(beta_eta_normalization,[],[f185])).
% 0.25/0.43 thf(f185,plain,(
% 0.25/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0)))) @ X1) = $true)) )),
% 0.25/0.43 inference(pi_clausification,[],[f184])).
% 0.25/0.43 thf(f184,plain,(
% 0.25/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0))))) = $true)),
% 0.25/0.43 inference(not_proxy_clausification,[],[f177])).
% 0.25/0.43 thf(f177,plain,(
% 0.25/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0)))))) = $false)),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f176])).
% 0.25/0.43 thf(f176,plain,(
% 0.25/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((~ (p @ Y0)) | (q @ Y0))))))) = $false)),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f174])).
% 0.25/0.43 thf(f213,plain,(
% 0.25/0.43 ((p @ sK1) = $true)),
% 0.25/0.43 inference(trivial_inequality_removal,[],[f210])).
% 0.25/0.43 thf(f210,plain,(
% 0.25/0.43 ((p @ sK1) = $true) | ($true = $false)),
% 0.25/0.43 inference(superposition,[],[f183,f205])).
% 0.25/0.43 thf(f183,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($false = (rel_s5 @ sK1 @ X1)) | ((p @ X1) = $true)) )),
% 0.25/0.43 inference(not_proxy_clausification,[],[f182])).
% 0.25/0.43 thf(f182,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (((p @ X1) = $true) | ((~ (rel_s5 @ sK1 @ X1)) = $true)) )),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f181])).
% 0.25/0.43 thf(f181,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK1 @ X1)) | (p @ X1)))) )),
% 0.25/0.43 inference(beta_eta_normalization,[],[f180])).
% 0.25/0.43 thf(f180,plain,(
% 0.25/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0))) @ X1))) )),
% 0.25/0.43 inference(pi_clausification,[],[f179])).
% 0.25/0.43 thf(f179,plain,(
% 0.25/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0)))))),
% 0.25/0.43 inference(not_proxy_clausification,[],[f178])).
% 0.25/0.43 thf(f178,plain,(
% 0.25/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0))))) = $false)),
% 0.25/0.43 inference(binary_proxy_clausification,[],[f176])).
% 0.25/0.43 % SZS output end Proof for theBenchmark
% 0.25/0.43 % (25138)------------------------------
% 0.25/0.43 % (25138)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.25/0.43 % (25138)Termination reason: Refutation
% 0.25/0.43
% 0.25/0.43 % (25138)Memory used [KB]: 5756
% 0.25/0.43 % (25138)Time elapsed: 0.013 s
% 0.25/0.43 % (25138)Instructions burned: 16 (million)
% 0.25/0.43 % (25138)------------------------------
% 0.25/0.43 % (25138)------------------------------
% 0.25/0.43 % (25131)Success in time 0.025 s
% 0.25/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------