TSTP Solution File: SYO407^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO407^1 : 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 : n023.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 09:04:19 EDT 2024
% Result : Theorem 0.19s 0.38s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO407^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.13 % 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
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 09:23:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37 % (27683)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)
% 0.19/0.37 % (27682)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.37 % (27684)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)
% 0.19/0.37 % (27687)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)
% 0.19/0.37 % (27683)Instruction limit reached!
% 0.19/0.37 % (27683)------------------------------
% 0.19/0.37 % (27683)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (27683)Termination reason: Unknown
% 0.19/0.37 % (27683)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (27683)Memory used [KB]: 1023
% 0.19/0.37 % (27683)Time elapsed: 0.004 s
% 0.19/0.37 % (27683)Instructions burned: 4 (million)
% 0.19/0.37 % (27683)------------------------------
% 0.19/0.37 % (27683)------------------------------
% 0.19/0.37 % (27687)Refutation not found, incomplete strategy
% 0.19/0.37 % (27687)------------------------------
% 0.19/0.37 % (27687)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (27687)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.37
% 0.19/0.37
% 0.19/0.37 % (27687)Memory used [KB]: 5628
% 0.19/0.37 % (27687)Time elapsed: 0.007 s
% 0.19/0.37 % (27687)Instructions burned: 8 (million)
% 0.19/0.37 % (27687)------------------------------
% 0.19/0.37 % (27687)------------------------------
% 0.19/0.37 % (27689)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)
% 0.19/0.37 % (27684)First to succeed.
% 0.19/0.37 % (27686)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)
% 0.19/0.37 % (27689)Instruction limit reached!
% 0.19/0.37 % (27689)------------------------------
% 0.19/0.37 % (27689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.37 % (27689)Termination reason: Unknown
% 0.19/0.37 % (27689)Termination phase: shuffling
% 0.19/0.37
% 0.19/0.37 % (27689)Memory used [KB]: 1023
% 0.19/0.37 % (27689)Time elapsed: 0.003 s
% 0.19/0.37 % (27689)Instructions burned: 3 (million)
% 0.19/0.37 % (27689)------------------------------
% 0.19/0.37 % (27689)------------------------------
% 0.19/0.38 % (27686)Instruction limit reached!
% 0.19/0.38 % (27686)------------------------------
% 0.19/0.38 % (27686)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (27686)Termination reason: Unknown
% 0.19/0.38 % (27686)Termination phase: shuffling
% 0.19/0.38
% 0.19/0.38 % (27686)Memory used [KB]: 1023
% 0.19/0.38 % (27686)Time elapsed: 0.004 s
% 0.19/0.38 % (27686)Instructions burned: 2 (million)
% 0.19/0.38 % (27686)------------------------------
% 0.19/0.38 % (27686)------------------------------
% 0.19/0.38 % (27685)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.38 % (27685)Instruction limit reached!
% 0.19/0.38 % (27685)------------------------------
% 0.19/0.38 % (27685)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (27685)Termination reason: Unknown
% 0.19/0.38 % (27685)Termination phase: shuffling
% 0.19/0.38
% 0.19/0.38 % (27685)Memory used [KB]: 1023
% 0.19/0.38 % (27685)Time elapsed: 0.003 s
% 0.19/0.38 % (27685)Instructions burned: 2 (million)
% 0.19/0.38 % (27685)------------------------------
% 0.19/0.38 % (27685)------------------------------
% 0.19/0.38 % (27682)Also succeeded, but the first one will report.
% 0.19/0.38 % (27684)Refutation found. Thanks to Tanya!
% 0.19/0.38 % SZS status Theorem for theBenchmark
% 0.19/0.38 % SZS output start Proof for theBenchmark
% 0.19/0.38 thf(type_def_5, type, mu: $tType).
% 0.19/0.38 thf(func_def_0, type, mu: $tType).
% 0.19/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.19/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.19/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.19/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.19/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.19/0.38 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.19/0.38 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.19/0.38 thf(func_def_36, type, p: $i > $o).
% 0.19/0.38 thf(func_def_37, type, q: $i > $o).
% 0.19/0.38 thf(func_def_38, type, r: $i > $o).
% 0.19/0.38 thf(func_def_39, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.19/0.38 thf(f194,plain,(
% 0.19/0.38 $false),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f193])).
% 0.19/0.38 thf(f193,plain,(
% 0.19/0.38 ($false = $true)),
% 0.19/0.38 inference(forward_demodulation,[],[f192,f173])).
% 0.19/0.38 thf(f173,plain,(
% 0.19/0.38 ((r @ sK2) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f172])).
% 0.19/0.38 thf(f172,plain,(
% 0.19/0.38 (((~ (p @ sK2)) | (r @ sK2)) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f170])).
% 0.19/0.38 thf(f170,plain,(
% 0.19/0.38 ((((~ (p @ sK2)) | (r @ sK2)) | (~ (rel_k @ sK1 @ sK2))) = $false)),
% 0.19/0.38 inference(beta_eta_normalization,[],[f169])).
% 0.19/0.38 thf(f169,plain,(
% 0.19/0.38 (((^[Y0 : $i]: (((~ (p @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.19/0.38 inference(sigma_clausification,[],[f151])).
% 0.19/0.38 thf(f151,plain,(
% 0.19/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f150])).
% 0.19/0.38 thf(f150,plain,(
% 0.19/0.38 ((((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (q @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.19/0.38 inference(beta_eta_normalization,[],[f149])).
% 0.19/0.38 thf(f149,plain,(
% 0.19/0.38 (((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (q @ Y1)) | (r @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (r @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) @ sK1) = $false)),
% 0.19/0.38 inference(sigma_clausification,[],[f148])).
% 0.19/0.38 thf(f148,plain,(
% 0.19/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (q @ Y1)) | (r @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (r @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))) != $true)),
% 0.19/0.38 inference(boolean_simplification,[],[f147])).
% 0.19/0.38 thf(f147,plain,(
% 0.19/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (q @ Y1)) | (r @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))))) | (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (r @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))),
% 0.19/0.38 inference(beta_eta_normalization,[],[f146])).
% 0.19/0.38 thf(f146,plain,(
% 0.19/0.38 (((^[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]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ 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)))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ 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)))) @ q @ r))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ 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)))) @ p @ r)))) != $true)),
% 0.19/0.38 inference(definition_unfolding,[],[f119,f111,f137,f136,f110,f137,f110,f137,f110,f137])).
% 0.19/0.38 thf(f110,plain,(
% 0.19/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f71])).
% 0.19/0.38 thf(f71,plain,(
% 0.19/0.38 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.19/0.38 inference(fool_elimination,[],[f70])).
% 0.19/0.38 thf(f70,plain,(
% 0.19/0.38 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))) = mbox_k)),
% 0.19/0.38 inference(rectify,[],[f32])).
% 0.19/0.38 thf(f32,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))) = mbox_k)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_k)).
% 0.19/0.38 thf(f136,plain,(
% 0.19/0.38 (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)))))))),
% 0.19/0.38 inference(definition_unfolding,[],[f133,f120,f115,f120,f120])).
% 0.19/0.38 thf(f115,plain,(
% 0.19/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f73])).
% 0.19/0.38 thf(f73,plain,(
% 0.19/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.19/0.38 inference(fool_elimination,[],[f72])).
% 0.19/0.38 thf(f72,plain,(
% 0.19/0.38 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.19/0.38 inference(rectify,[],[f4])).
% 0.19/0.38 thf(f4,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.19/0.38 thf(f120,plain,(
% 0.19/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f100])).
% 0.19/0.38 thf(f100,plain,(
% 0.19/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.38 inference(fool_elimination,[],[f99])).
% 0.19/0.38 thf(f99,plain,(
% 0.19/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.19/0.38 inference(rectify,[],[f3])).
% 0.19/0.38 thf(f3,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.19/0.38 thf(f133,plain,(
% 0.19/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.19/0.38 inference(cnf_transformation,[],[f86])).
% 0.19/0.38 thf(f86,plain,(
% 0.19/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.19/0.38 inference(fool_elimination,[],[f85])).
% 0.19/0.38 thf(f85,plain,(
% 0.19/0.38 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.19/0.38 inference(rectify,[],[f5])).
% 0.19/0.38 thf(f5,axiom,(
% 0.19/0.38 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.19/0.38 thf(f137,plain,(
% 0.19/0.38 (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)))))),
% 0.19/0.38 inference(definition_unfolding,[],[f105,f115,f120])).
% 0.19/0.38 thf(f105,plain,(
% 0.19/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.38 inference(cnf_transformation,[],[f65])).
% 0.19/0.38 thf(f65,plain,(
% 0.19/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.38 inference(fool_elimination,[],[f64])).
% 0.19/0.38 thf(f64,plain,(
% 0.19/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.19/0.38 inference(rectify,[],[f6])).
% 0.19/0.38 thf(f6,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.19/0.38 thf(f111,plain,(
% 0.19/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.38 inference(cnf_transformation,[],[f63])).
% 0.19/0.38 thf(f63,plain,(
% 0.19/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.38 inference(fool_elimination,[],[f62])).
% 0.19/0.38 thf(f62,plain,(
% 0.19/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.19/0.38 inference(rectify,[],[f28])).
% 0.19/0.38 thf(f28,axiom,(
% 0.19/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.19/0.38 thf(f119,plain,(
% 0.19/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ q @ r))) @ (mbox_k @ (mimplies @ p @ r)))) != $true)),
% 0.19/0.38 inference(cnf_transformation,[],[f101])).
% 0.19/0.38 thf(f101,plain,(
% 0.19/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ q @ r))) @ (mbox_k @ (mimplies @ p @ r)))) != $true)),
% 0.19/0.38 inference(flattening,[],[f69])).
% 0.19/0.38 thf(f69,plain,(
% 0.19/0.38 ~((mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ q @ r))) @ (mbox_k @ (mimplies @ p @ r)))) = $true)),
% 0.19/0.38 inference(fool_elimination,[],[f68])).
% 0.19/0.38 thf(f68,plain,(
% 0.19/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ q @ r))) @ (mbox_k @ (mimplies @ p @ r))))),
% 0.19/0.38 inference(rectify,[],[f35])).
% 0.19/0.38 thf(f35,negated_conjecture,(
% 0.19/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ q @ r))) @ (mbox_k @ (mimplies @ p @ r))))),
% 0.19/0.38 inference(negated_conjecture,[],[f34])).
% 0.19/0.38 thf(f34,conjecture,(
% 0.19/0.38 (mvalid @ (mimplies @ (mand @ (mbox_k @ (mimplies @ p @ q)) @ (mbox_k @ (mimplies @ q @ r))) @ (mbox_k @ (mimplies @ p @ r))))),
% 0.19/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.19/0.38 thf(f192,plain,(
% 0.19/0.38 ((r @ sK2) = $true)),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f191])).
% 0.19/0.38 thf(f191,plain,(
% 0.19/0.38 ($false = $true) | ((r @ sK2) = $true)),
% 0.19/0.38 inference(forward_demodulation,[],[f187,f182])).
% 0.19/0.38 thf(f182,plain,(
% 0.19/0.38 ((q @ sK2) = $true)),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f181])).
% 0.19/0.38 thf(f181,plain,(
% 0.19/0.38 ((q @ sK2) = $true) | ($false = $true)),
% 0.19/0.38 inference(forward_demodulation,[],[f180,f175])).
% 0.19/0.38 thf(f175,plain,(
% 0.19/0.38 ((p @ sK2) = $true)),
% 0.19/0.38 inference(not_proxy_clausification,[],[f174])).
% 0.19/0.38 thf(f174,plain,(
% 0.19/0.38 ((~ (p @ sK2)) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f172])).
% 0.19/0.38 thf(f180,plain,(
% 0.19/0.38 ((p @ sK2) = $false) | ((q @ sK2) = $true)),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f178])).
% 0.19/0.38 thf(f178,plain,(
% 0.19/0.38 ((p @ sK2) = $false) | ((q @ sK2) = $true) | ($false = $true)),
% 0.19/0.38 inference(superposition,[],[f176,f161])).
% 0.19/0.38 thf(f161,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($false = (p @ X1)) | ((q @ X1) = $true)) )),
% 0.19/0.38 inference(not_proxy_clausification,[],[f160])).
% 0.19/0.38 thf(f160,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((q @ X1) = $true) | ((rel_k @ sK1 @ X1) = $false) | ((~ (p @ X1)) = $true)) )),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f159])).
% 0.19/0.38 thf(f159,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | (((~ (p @ X1)) | (q @ X1)) = $true)) )),
% 0.19/0.38 inference(not_proxy_clausification,[],[f158])).
% 0.19/0.38 thf(f158,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | (((~ (p @ X1)) | (q @ X1)) = $true)) )),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f157])).
% 0.19/0.38 thf(f157,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((((~ (p @ X1)) | (q @ X1)) | (~ (rel_k @ sK1 @ X1))) = $true)) )),
% 0.19/0.38 inference(beta_eta_normalization,[],[f156])).
% 0.19/0.38 thf(f156,plain,(
% 0.19/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.19/0.38 inference(pi_clausification,[],[f155])).
% 0.19/0.38 thf(f155,plain,(
% 0.19/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $true)),
% 0.19/0.38 inference(not_proxy_clausification,[],[f154])).
% 0.19/0.38 thf(f154,plain,(
% 0.19/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f152])).
% 0.19/0.38 thf(f152,plain,(
% 0.19/0.38 (((~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (q @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f150])).
% 0.19/0.38 thf(f176,plain,(
% 0.19/0.38 ((rel_k @ sK1 @ sK2) = $true)),
% 0.19/0.38 inference(not_proxy_clausification,[],[f171])).
% 0.19/0.38 thf(f171,plain,(
% 0.19/0.38 ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f170])).
% 0.19/0.38 thf(f187,plain,(
% 0.19/0.38 ((q @ sK2) = $false) | ((r @ sK2) = $true)),
% 0.19/0.38 inference(trivial_inequality_removal,[],[f185])).
% 0.19/0.38 thf(f185,plain,(
% 0.19/0.38 ((r @ sK2) = $true) | ($false = $true) | ((q @ sK2) = $false)),
% 0.19/0.38 inference(superposition,[],[f168,f176])).
% 0.19/0.38 thf(f168,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false) | ((r @ X1) = $true)) )),
% 0.19/0.38 inference(not_proxy_clausification,[],[f167])).
% 0.19/0.38 thf(f167,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((~ (q @ X1)) = $true) | ((rel_k @ sK1 @ X1) = $false) | ((r @ X1) = $true)) )),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f166])).
% 0.19/0.38 thf(f166,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | (((~ (q @ X1)) | (r @ X1)) = $true)) )),
% 0.19/0.38 inference(not_proxy_clausification,[],[f165])).
% 0.19/0.38 thf(f165,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((~ (rel_k @ sK1 @ X1)) = $true) | (((~ (q @ X1)) | (r @ X1)) = $true)) )),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f164])).
% 0.19/0.38 thf(f164,plain,(
% 0.19/0.38 ( ! [X1 : $i] : (((((~ (q @ X1)) | (r @ X1)) | (~ (rel_k @ sK1 @ X1))) = $true)) )),
% 0.19/0.38 inference(beta_eta_normalization,[],[f163])).
% 0.19/0.38 thf(f163,plain,(
% 0.19/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((~ (q @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.19/0.38 inference(pi_clausification,[],[f162])).
% 0.19/0.38 thf(f162,plain,(
% 0.19/0.38 ((!! @ $i @ (^[Y0 : $i]: (((~ (q @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $true)),
% 0.19/0.38 inference(not_proxy_clausification,[],[f153])).
% 0.19/0.38 thf(f153,plain,(
% 0.19/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (q @ Y0)) | (r @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.19/0.38 inference(binary_proxy_clausification,[],[f152])).
% 0.19/0.38 % SZS output end Proof for theBenchmark
% 0.19/0.38 % (27684)------------------------------
% 0.19/0.38 % (27684)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (27684)Termination reason: Refutation
% 0.19/0.38
% 0.19/0.38 % (27684)Memory used [KB]: 5628
% 0.19/0.38 % (27684)Time elapsed: 0.012 s
% 0.19/0.38 % (27684)Instructions burned: 13 (million)
% 0.19/0.38 % (27684)------------------------------
% 0.19/0.38 % (27684)------------------------------
% 0.19/0.38 % (27681)Success in time 0.012 s
% 0.19/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------