TSTP Solution File: LCL720^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL720^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 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 : n006.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 00:22:22 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL720^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.06/0.14 % 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
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 03:22:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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
% 0.15/0.39 % (12940)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (12939)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)
% 0.15/0.39 % (12934)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (12936)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)
% 0.15/0.39 % (12935)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)
% 0.15/0.39 % (12937)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (12938)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)
% 0.15/0.39 % (12941)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)
% 0.15/0.39 % (12937)Instruction limit reached!
% 0.15/0.39 % (12937)------------------------------
% 0.15/0.39 % (12937)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (12937)Termination reason: Unknown
% 0.15/0.39 % (12937)Termination phase: shuffling
% 0.15/0.39 % (12938)Instruction limit reached!
% 0.15/0.39 % (12938)------------------------------
% 0.15/0.39 % (12938)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (12938)Termination reason: Unknown
% 0.15/0.39 % (12938)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (12938)Memory used [KB]: 1023
% 0.15/0.39 % (12938)Time elapsed: 0.004 s
% 0.15/0.39 % (12938)Instructions burned: 2 (million)
% 0.15/0.39 % (12938)------------------------------
% 0.15/0.39 % (12938)------------------------------
% 0.15/0.39
% 0.15/0.39 % (12937)Memory used [KB]: 1023
% 0.15/0.39 % (12937)Time elapsed: 0.004 s
% 0.15/0.39 % (12937)Instructions burned: 2 (million)
% 0.15/0.39 % (12937)------------------------------
% 0.15/0.39 % (12937)------------------------------
% 0.15/0.40 % (12935)Instruction limit reached!
% 0.15/0.40 % (12935)------------------------------
% 0.15/0.40 % (12935)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (12935)Termination reason: Unknown
% 0.15/0.40 % (12935)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (12935)Memory used [KB]: 1023
% 0.15/0.40 % (12935)Time elapsed: 0.006 s
% 0.15/0.40 % (12935)Instructions burned: 4 (million)
% 0.15/0.40 % (12935)------------------------------
% 0.15/0.40 % (12935)------------------------------
% 0.22/0.40 % (12941)Instruction limit reached!
% 0.22/0.40 % (12941)------------------------------
% 0.22/0.40 % (12941)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (12941)Termination reason: Unknown
% 0.22/0.40 % (12941)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (12941)Memory used [KB]: 1023
% 0.22/0.40 % (12941)Time elapsed: 0.006 s
% 0.22/0.40 % (12941)Instructions burned: 4 (million)
% 0.22/0.40 % (12941)------------------------------
% 0.22/0.40 % (12941)------------------------------
% 0.22/0.40 % (12940)First to succeed.
% 0.22/0.40 % (12939)Refutation not found, incomplete strategy
% 0.22/0.40 % (12939)------------------------------
% 0.22/0.40 % (12939)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (12939)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.40
% 0.22/0.40
% 0.22/0.40 % (12939)Memory used [KB]: 5628
% 0.22/0.40 % (12939)Time elapsed: 0.010 s
% 0.22/0.40 % (12939)Instructions burned: 7 (million)
% 0.22/0.40 % (12939)------------------------------
% 0.22/0.40 % (12939)------------------------------
% 0.22/0.40 % (12940)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% 0.22/0.40 thf(type_def_5, type, mu: $tType).
% 0.22/0.40 thf(func_def_0, type, mu: $tType).
% 0.22/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.40 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.22/0.40 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.22/0.40 thf(func_def_36, type, phi: $i > $o).
% 0.22/0.40 thf(func_def_37, type, psi: $i > $o).
% 0.22/0.40 thf(f182,plain,(
% 0.22/0.40 $false),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f181])).
% 0.22/0.40 thf(f181,plain,(
% 0.22/0.40 ($false = $true)),
% 0.22/0.40 inference(forward_demodulation,[],[f180,f176])).
% 0.22/0.40 thf(f176,plain,(
% 0.22/0.40 ($false = (phi @ sK2))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f175])).
% 0.22/0.40 thf(f175,plain,(
% 0.22/0.40 ($false = (phi @ sK2)) | ($false = $true)),
% 0.22/0.40 inference(forward_demodulation,[],[f174,f168])).
% 0.22/0.40 thf(f168,plain,(
% 0.22/0.40 ((psi @ sK2) = $false)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f167])).
% 0.22/0.40 thf(f167,plain,(
% 0.22/0.40 (((~ (rel_k @ sK1 @ sK2)) | (psi @ sK2)) = $false)),
% 0.22/0.40 inference(beta_eta_normalization,[],[f166])).
% 0.22/0.40 thf(f166,plain,(
% 0.22/0.40 ($false = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (psi @ Y0))) @ sK2))),
% 0.22/0.40 inference(sigma_clausification,[],[f159])).
% 0.22/0.40 thf(f159,plain,(
% 0.22/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (psi @ Y0)))))),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f150])).
% 0.22/0.40 thf(f150,plain,(
% 0.22/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (phi @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (psi @ Y0))))) = $false)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f149])).
% 0.22/0.40 thf(f149,plain,(
% 0.22/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (phi @ Y0)) | (psi @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (phi @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (psi @ Y0)))))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f148])).
% 0.22/0.40 thf(f148,plain,(
% 0.22/0.40 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (phi @ Y1)) | (psi @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (phi @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (psi @ Y1))))))) @ sK1))),
% 0.22/0.40 inference(sigma_clausification,[],[f147])).
% 0.22/0.40 thf(f147,plain,(
% 0.22/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((~ (phi @ Y1)) | (psi @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (phi @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (psi @ Y1)))))))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f146])).
% 0.22/0.40 thf(f146,plain,(
% 0.22/0.40 ($true != ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ phi @ psi)) @ ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ phi) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ psi)))))),
% 0.22/0.40 inference(definition_unfolding,[],[f123,f122,f137,f128,f137,f137,f128,f128])).
% 0.22/0.40 thf(f128,plain,(
% 0.22/0.40 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f100])).
% 0.22/0.40 thf(f100,plain,(
% 0.22/0.40 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.40 inference(fool_elimination,[],[f99])).
% 0.22/0.40 thf(f99,plain,(
% 0.22/0.40 (mbox_k = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_k @ X1 @ X2)))))),
% 0.22/0.40 inference(rectify,[],[f32])).
% 0.22/0.40 thf(f32,axiom,(
% 0.22/0.40 (mbox_k = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_k @ X2 @ X7)))))),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_k)).
% 0.22/0.40 thf(f137,plain,(
% 0.22/0.40 (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)))))),
% 0.22/0.40 inference(definition_unfolding,[],[f118,f103,f114])).
% 0.22/0.40 thf(f114,plain,(
% 0.22/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f50])).
% 0.22/0.40 thf(f50,plain,(
% 0.22/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.40 inference(fool_elimination,[],[f49])).
% 0.22/0.40 thf(f49,plain,(
% 0.22/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.22/0.40 inference(rectify,[],[f3])).
% 0.22/0.40 thf(f3,axiom,(
% 0.22/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.22/0.40 thf(f103,plain,(
% 0.22/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f63])).
% 0.22/0.40 thf(f63,plain,(
% 0.22/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.22/0.40 inference(fool_elimination,[],[f62])).
% 0.22/0.40 thf(f62,plain,(
% 0.22/0.40 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.22/0.40 inference(rectify,[],[f4])).
% 0.22/0.40 thf(f4,axiom,(
% 0.22/0.40 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.22/0.40 thf(f118,plain,(
% 0.22/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.40 inference(cnf_transformation,[],[f53])).
% 0.22/0.40 thf(f53,plain,(
% 0.22/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.40 inference(fool_elimination,[],[f52])).
% 0.22/0.40 thf(f52,plain,(
% 0.22/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.22/0.40 inference(rectify,[],[f6])).
% 0.22/0.40 thf(f6,axiom,(
% 0.22/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.40 thf(f122,plain,(
% 0.22/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.40 inference(cnf_transformation,[],[f94])).
% 0.22/0.40 thf(f94,plain,(
% 0.22/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.40 inference(fool_elimination,[],[f93])).
% 0.22/0.40 thf(f93,plain,(
% 0.22/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.22/0.40 inference(rectify,[],[f28])).
% 0.22/0.40 thf(f28,axiom,(
% 0.22/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.22/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.40 thf(f123,plain,(
% 0.22/0.40 ((mvalid @ (mimplies @ (mbox_k @ (mimplies @ phi @ psi)) @ (mimplies @ (mbox_k @ phi) @ (mbox_k @ psi)))) != $true)),
% 0.22/0.40 inference(cnf_transformation,[],[f101])).
% 0.22/0.40 thf(f101,plain,(
% 0.22/0.40 ((mvalid @ (mimplies @ (mbox_k @ (mimplies @ phi @ psi)) @ (mimplies @ (mbox_k @ phi) @ (mbox_k @ psi)))) != $true)),
% 0.22/0.40 inference(flattening,[],[f38])).
% 0.22/0.40 thf(f38,plain,(
% 0.22/0.40 ~((mvalid @ (mimplies @ (mbox_k @ (mimplies @ phi @ psi)) @ (mimplies @ (mbox_k @ phi) @ (mbox_k @ psi)))) = $true)),
% 0.22/0.40 inference(fool_elimination,[],[f37])).
% 0.22/0.40 thf(f37,plain,(
% 0.22/0.40 ~(mvalid @ (mimplies @ (mbox_k @ (mimplies @ phi @ psi)) @ (mimplies @ (mbox_k @ phi) @ (mbox_k @ psi))))),
% 0.22/0.40 inference(rectify,[],[f35])).
% 0.22/0.40 thf(f35,negated_conjecture,(
% 0.22/0.40 ~(mvalid @ (mimplies @ (mbox_k @ (mimplies @ phi @ psi)) @ (mimplies @ (mbox_k @ phi) @ (mbox_k @ psi))))),
% 0.22/0.41 inference(negated_conjecture,[],[f34])).
% 0.22/0.41 thf(f34,conjecture,(
% 0.22/0.41 (mvalid @ (mimplies @ (mbox_k @ (mimplies @ phi @ psi)) @ (mimplies @ (mbox_k @ phi) @ (mbox_k @ psi))))),
% 0.22/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.22/0.41 thf(f174,plain,(
% 0.22/0.41 ($false = (phi @ sK2)) | ((psi @ sK2) = $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f171])).
% 0.22/0.41 thf(f171,plain,(
% 0.22/0.41 ($false = (phi @ sK2)) | ((psi @ sK2) = $true) | ($false = $true)),
% 0.22/0.41 inference(superposition,[],[f170,f158])).
% 0.22/0.41 thf(f158,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ((psi @ X1) = $true) | ((phi @ X1) = $false)) )),
% 0.22/0.41 inference(not_proxy_clausification,[],[f157])).
% 0.22/0.41 thf(f157,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (((psi @ X1) = $true) | ((phi @ X1) = $false) | ((~ (rel_k @ sK1 @ X1)) = $true)) )),
% 0.22/0.41 inference(not_proxy_clausification,[],[f156])).
% 0.22/0.41 thf(f156,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = (~ (phi @ X1))) | ((~ (rel_k @ sK1 @ X1)) = $true) | ((psi @ X1) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f155])).
% 0.22/0.41 thf(f155,plain,(
% 0.22/0.41 ( ! [X1 : $i] : ((((~ (phi @ X1)) | (psi @ X1)) = $true) | ((~ (rel_k @ sK1 @ X1)) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f154])).
% 0.22/0.41 thf(f154,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | ((~ (phi @ X1)) | (psi @ X1))))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f153])).
% 0.22/0.41 thf(f153,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (phi @ Y0)) | (psi @ Y0)))) @ X1))) )),
% 0.22/0.41 inference(pi_clausification,[],[f152])).
% 0.22/0.41 thf(f152,plain,(
% 0.22/0.41 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (phi @ Y0)) | (psi @ Y0))))) = $true)),
% 0.22/0.41 inference(not_proxy_clausification,[],[f151])).
% 0.22/0.41 thf(f151,plain,(
% 0.22/0.41 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | ((~ (phi @ Y0)) | (psi @ Y0)))))))),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f149])).
% 0.22/0.41 thf(f170,plain,(
% 0.22/0.41 ((rel_k @ sK1 @ sK2) = $true)),
% 0.22/0.41 inference(not_proxy_clausification,[],[f169])).
% 0.22/0.41 thf(f169,plain,(
% 0.22/0.41 ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f167])).
% 0.22/0.41 thf(f180,plain,(
% 0.22/0.41 ((phi @ sK2) = $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f178])).
% 0.22/0.41 thf(f178,plain,(
% 0.22/0.41 ($false = $true) | ((phi @ sK2) = $true)),
% 0.22/0.41 inference(superposition,[],[f170,f165])).
% 0.22/0.41 thf(f165,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($false = (rel_k @ sK1 @ X1)) | ((phi @ X1) = $true)) )),
% 0.22/0.41 inference(not_proxy_clausification,[],[f164])).
% 0.22/0.41 thf(f164,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | ((phi @ X1) = $true)) )),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f163])).
% 0.22/0.41 thf(f163,plain,(
% 0.22/0.41 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | (phi @ X1)))) )),
% 0.22/0.41 inference(beta_eta_normalization,[],[f162])).
% 0.22/0.41 thf(f162,plain,(
% 0.22/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (phi @ Y0))) @ X1) = $true)) )),
% 0.22/0.41 inference(pi_clausification,[],[f161])).
% 0.22/0.41 thf(f161,plain,(
% 0.22/0.41 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (phi @ Y0)))) = $true)),
% 0.22/0.41 inference(not_proxy_clausification,[],[f160])).
% 0.22/0.41 thf(f160,plain,(
% 0.22/0.41 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (phi @ Y0))))) = $false)),
% 0.22/0.41 inference(binary_proxy_clausification,[],[f150])).
% 0.22/0.41 % SZS output end Proof for theBenchmark
% 0.22/0.41 % (12940)------------------------------
% 0.22/0.41 % (12940)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (12940)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (12940)Memory used [KB]: 5628
% 0.22/0.41 % (12940)Time elapsed: 0.014 s
% 0.22/0.41 % (12940)Instructions burned: 11 (million)
% 0.22/0.41 % (12940)------------------------------
% 0.22/0.41 % (12940)------------------------------
% 0.22/0.41 % (12933)Success in time 0.026 s
% 0.22/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------