TSTP Solution File: SYO423^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO423^1 : 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 : n025.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 09:04:23 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO423^1 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.14 % 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 : n025.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
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 08:51:08 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
% 0.15/0.38 % (25200)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (25198)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)
% 0.15/0.38 % (25199)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)
% 0.15/0.38 % (25201)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)
% 0.15/0.38 % (25202)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)
% 0.15/0.38 % (25203)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (25197)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (25204)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)
% 0.15/0.38 % (25201)Instruction limit reached!
% 0.15/0.38 % (25201)------------------------------
% 0.15/0.38 % (25201)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25201)Termination reason: Unknown
% 0.15/0.38 % (25201)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (25201)Memory used [KB]: 1023
% 0.15/0.38 % (25201)Time elapsed: 0.003 s
% 0.15/0.38 % (25201)Instructions burned: 2 (million)
% 0.15/0.38 % (25201)------------------------------
% 0.15/0.38 % (25201)------------------------------
% 0.15/0.38 % (25200)Instruction limit reached!
% 0.15/0.38 % (25200)------------------------------
% 0.15/0.38 % (25200)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25200)Termination reason: Unknown
% 0.15/0.38 % (25200)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (25200)Memory used [KB]: 1023
% 0.15/0.38 % (25200)Time elapsed: 0.004 s
% 0.15/0.38 % (25200)Instructions burned: 3 (million)
% 0.15/0.38 % (25200)------------------------------
% 0.15/0.38 % (25200)------------------------------
% 0.15/0.38 % (25204)Instruction limit reached!
% 0.15/0.38 % (25204)------------------------------
% 0.15/0.38 % (25204)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25204)Termination reason: Unknown
% 0.15/0.38 % (25204)Termination phase: shuffling
% 0.15/0.38
% 0.15/0.38 % (25204)Memory used [KB]: 1023
% 0.15/0.38 % (25204)Time elapsed: 0.004 s
% 0.15/0.38 % (25204)Instructions burned: 3 (million)
% 0.15/0.38 % (25204)------------------------------
% 0.15/0.38 % (25204)------------------------------
% 0.15/0.38 % (25198)Instruction limit reached!
% 0.15/0.38 % (25198)------------------------------
% 0.15/0.38 % (25198)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25198)Termination reason: Unknown
% 0.15/0.38 % (25198)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (25198)Memory used [KB]: 1023
% 0.15/0.38 % (25198)Time elapsed: 0.004 s
% 0.15/0.38 % (25198)Instructions burned: 5 (million)
% 0.15/0.38 % (25198)------------------------------
% 0.15/0.38 % (25198)------------------------------
% 0.15/0.38 % (25202)Refutation not found, incomplete strategy
% 0.15/0.38 % (25202)------------------------------
% 0.15/0.38 % (25202)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (25202)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (25202)Memory used [KB]: 5628
% 0.15/0.38 % (25202)Time elapsed: 0.007 s
% 0.15/0.38 % (25202)Instructions burned: 8 (million)
% 0.15/0.38 % (25202)------------------------------
% 0.15/0.38 % (25202)------------------------------
% 0.15/0.39 % (25203)First to succeed.
% 0.15/0.39 % (25197)Also succeeded, but the first one will report.
% 0.15/0.39 % (25203)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(type_def_5, type, mu: $tType).
% 0.15/0.39 thf(func_def_0, type, mu: $tType).
% 0.15/0.39 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.15/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_15, type, mtrue: $i > $o).
% 0.15/0.39 thf(func_def_16, type, mfalse: $i > $o).
% 0.15/0.39 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.15/0.39 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_33, type, rel_d: $i > $i > $o).
% 0.15/0.39 thf(func_def_34, type, mbox_d: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_35, type, mdia_d: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_36, type, p: $i > $o).
% 0.15/0.39 thf(func_def_37, type, q: $i > $o).
% 0.15/0.39 thf(func_def_55, type, sK2: $i > $i).
% 0.15/0.39 thf(f228,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f227])).
% 0.15/0.39 thf(f227,plain,(
% 0.15/0.39 ($false = $true)),
% 0.15/0.39 inference(backward_demodulation,[],[f204,f226])).
% 0.15/0.39 thf(f226,plain,(
% 0.15/0.39 ($false = (q @ (sK2 @ (sK2 @ sK1))))),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f225])).
% 0.15/0.39 thf(f225,plain,(
% 0.15/0.39 ($false = $true) | ($false = (q @ (sK2 @ (sK2 @ sK1))))),
% 0.15/0.39 inference(forward_demodulation,[],[f224,f214])).
% 0.15/0.39 thf(f214,plain,(
% 0.15/0.39 ($true = (p @ (sK2 @ (sK2 @ sK1))))),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f211])).
% 0.15/0.39 thf(f211,plain,(
% 0.15/0.39 ($false = $true) | ($true = (p @ (sK2 @ (sK2 @ sK1))))),
% 0.15/0.39 inference(superposition,[],[f209,f185])).
% 0.15/0.39 thf(f185,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = (rel_d @ X1 @ (sK2 @ X1)))) )),
% 0.15/0.39 inference(sigma_clausification,[],[f184])).
% 0.15/0.39 thf(f184,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = (?? @ $i @ (rel_d @ X1)))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f183])).
% 0.15/0.39 thf(f183,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0))) @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f182])).
% 0.15/0.39 thf(f182,plain,(
% 0.15/0.39 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (rel_d @ Y0)))) = $true)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f150])).
% 0.15/0.39 thf(f150,plain,(
% 0.15/0.39 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ rel_d) = $true)),
% 0.15/0.39 inference(definition_unfolding,[],[f131,f116])).
% 0.15/0.39 thf(f116,plain,(
% 0.15/0.39 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f83])).
% 0.15/0.39 thf(f83,plain,(
% 0.15/0.39 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.15/0.39 inference(fool_elimination,[],[f82])).
% 0.15/0.39 thf(f82,plain,(
% 0.15/0.39 ((^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))) = mserial)),
% 0.15/0.39 inference(rectify,[],[f20])).
% 0.15/0.39 thf(f20,axiom,(
% 0.15/0.39 ((^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))) = mserial)),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial)).
% 0.15/0.39 thf(f131,plain,(
% 0.15/0.39 ((mserial @ rel_d) = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f73])).
% 0.15/0.39 thf(f73,plain,(
% 0.15/0.39 ((mserial @ rel_d) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f72])).
% 0.15/0.39 thf(f72,plain,(
% 0.15/0.39 (mserial @ rel_d)),
% 0.15/0.39 inference(rectify,[],[f34])).
% 0.15/0.39 thf(f34,axiom,(
% 0.15/0.39 (mserial @ rel_d)),
% 0.15/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.15/0.39 thf(f209,plain,(
% 0.15/0.39 ( ! [X0 : $i] : (($false = (rel_d @ (sK2 @ sK1) @ X0)) | ((p @ X0) = $true)) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f205])).
% 0.15/0.39 thf(f205,plain,(
% 0.15/0.39 ( ! [X0 : $i] : (((p @ X0) = $true) | ($false = $true) | ($false = (rel_d @ (sK2 @ sK1) @ X0))) )),
% 0.15/0.39 inference(superposition,[],[f181,f185])).
% 0.15/0.39 thf(f181,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (rel_d @ X1 @ X2)) | ((p @ X2) = $true)) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f180])).
% 0.15/0.39 thf(f180,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_d @ X1 @ X2))) | ((p @ X2) = $true) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f176])).
% 0.15/0.39 thf(f176,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (~ (p @ X2))) | ($true = (~ (rel_d @ X1 @ X2))) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f175])).
% 0.15/0.39 thf(f175,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = ((~ (q @ X2)) | (~ (p @ X2)))) | ($true = (~ (rel_d @ X1 @ X2)))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f174])).
% 0.15/0.39 thf(f174,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($true = (~ ((~ (q @ X2)) | (~ (p @ X2))))) | ($true = (~ (rel_d @ X1 @ X2))) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f173])).
% 0.15/0.39 thf(f173,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | (((~ (rel_d @ X1 @ X2)) | (~ ((~ (q @ X2)) | (~ (p @ X2))))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f172])).
% 0.15/0.39 thf(f172,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0)))))) @ X2) = $true) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.39 inference(pi_clausification,[],[f171])).
% 0.15/0.39 thf(f171,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0))))))))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f161])).
% 0.15/0.39 thf(f161,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0))))))))) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f160])).
% 0.15/0.39 thf(f160,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0))))))))))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f159])).
% 0.15/0.39 thf(f159,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((~ (rel_d @ sK1 @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0))))))))))) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f158])).
% 0.15/0.39 thf(f158,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0))))))))))) | ((~ (rel_d @ sK1 @ X1)) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f157])).
% 0.15/0.39 thf(f157,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((~ (rel_d @ sK1 @ X1)) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | (~ ((~ (q @ Y0)) | (~ (p @ Y0))))))))))))) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f156])).
% 0.15/0.39 thf(f156,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ ((~ (q @ Y1)) | (~ (p @ Y1)))))))))))) @ X1))) )),
% 0.15/0.40 inference(pi_clausification,[],[f155])).
% 0.15/0.40 thf(f155,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ ((~ (q @ Y1)) | (~ (p @ Y1))))))))))))) = $true)),
% 0.15/0.40 inference(not_proxy_clausification,[],[f154])).
% 0.15/0.40 thf(f154,plain,(
% 0.15/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ sK1 @ Y0)) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | ((~ (q @ Y1)) | (~ (p @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ ((~ (q @ Y1)) | (~ (p @ Y1)))))))))))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f153])).
% 0.15/0.40 thf(f153,plain,(
% 0.15/0.40 ($false = ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | ((~ (q @ Y2)) | (~ (p @ Y2))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (~ ((~ (q @ Y2)) | (~ (p @ Y2))))))))))))))) @ sK1))),
% 0.15/0.40 inference(sigma_clausification,[],[f152])).
% 0.15/0.40 thf(f152,plain,(
% 0.15/0.40 ((!! @ $i @ (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_d @ Y0 @ Y1)) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | ((~ (q @ Y2)) | (~ (p @ Y2))))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (~ ((~ (q @ Y2)) | (~ (p @ Y2)))))))))))))))) != $true)),
% 0.15/0.40 inference(beta_eta_normalization,[],[f151])).
% 0.15/0.40 thf(f151,plain,(
% 0.15/0.40 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ 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_d @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ q))))))))),
% 0.15/0.40 inference(definition_unfolding,[],[f139,f108,f107,f106,f140,f106,f140,f106,f141,f107])).
% 0.15/0.40 thf(f141,plain,(
% 0.15/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.15/0.40 inference(definition_unfolding,[],[f105,f112,f107])).
% 0.15/0.40 thf(f112,plain,(
% 0.15/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f91])).
% 0.15/0.40 thf(f91,plain,(
% 0.15/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f90])).
% 0.15/0.40 thf(f90,plain,(
% 0.15/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.15/0.40 inference(rectify,[],[f4])).
% 0.15/0.40 thf(f4,axiom,(
% 0.15/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.15/0.40 thf(f105,plain,(
% 0.15/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.40 inference(cnf_transformation,[],[f93])).
% 0.15/0.40 thf(f93,plain,(
% 0.15/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.40 inference(fool_elimination,[],[f92])).
% 0.15/0.40 thf(f92,plain,(
% 0.15/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.15/0.40 inference(rectify,[],[f6])).
% 0.15/0.40 thf(f6,axiom,(
% 0.15/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.40 thf(f140,plain,(
% 0.15/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.15/0.40 inference(definition_unfolding,[],[f128,f107,f112,f107,f107])).
% 0.15/0.40 thf(f128,plain,(
% 0.15/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f101])).
% 0.15/0.40 thf(f101,plain,(
% 0.15/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.15/0.40 inference(fool_elimination,[],[f100])).
% 0.15/0.40 thf(f100,plain,(
% 0.15/0.40 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.15/0.40 inference(rectify,[],[f5])).
% 0.15/0.40 thf(f5,axiom,(
% 0.15/0.40 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.15/0.40 thf(f106,plain,(
% 0.15/0.40 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f71])).
% 0.15/0.40 thf(f71,plain,(
% 0.15/0.40 (mbox_d = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_d @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f70])).
% 0.15/0.40 thf(f70,plain,(
% 0.15/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_d @ X1 @ X2)))) = mbox_d)),
% 0.15/0.40 inference(rectify,[],[f32])).
% 0.15/0.40 thf(f32,axiom,(
% 0.15/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_d @ X2 @ X7)))) = mbox_d)),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_d)).
% 0.15/0.40 thf(f107,plain,(
% 0.15/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f65])).
% 0.15/0.40 thf(f65,plain,(
% 0.15/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.40 inference(fool_elimination,[],[f64])).
% 0.15/0.40 thf(f64,plain,(
% 0.15/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.40 inference(rectify,[],[f3])).
% 0.15/0.40 thf(f3,axiom,(
% 0.15/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.15/0.40 thf(f108,plain,(
% 0.15/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.40 inference(cnf_transformation,[],[f57])).
% 0.15/0.40 thf(f57,plain,(
% 0.15/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.40 inference(fool_elimination,[],[f56])).
% 0.15/0.40 thf(f56,plain,(
% 0.15/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.15/0.40 inference(rectify,[],[f28])).
% 0.15/0.40 thf(f28,axiom,(
% 0.15/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.40 thf(f139,plain,(
% 0.15/0.40 ((mvalid @ (mnot @ (mbox_d @ (mand @ (mbox_d @ (mand @ p @ q)) @ (mbox_d @ (mimplies @ p @ (mnot @ q))))))) != $true)),
% 0.15/0.40 inference(cnf_transformation,[],[f104])).
% 0.15/0.40 thf(f104,plain,(
% 0.15/0.40 ((mvalid @ (mnot @ (mbox_d @ (mand @ (mbox_d @ (mand @ p @ q)) @ (mbox_d @ (mimplies @ p @ (mnot @ q))))))) != $true)),
% 0.15/0.40 inference(flattening,[],[f45])).
% 0.15/0.40 thf(f45,plain,(
% 0.15/0.40 ~((mvalid @ (mnot @ (mbox_d @ (mand @ (mbox_d @ (mand @ p @ q)) @ (mbox_d @ (mimplies @ p @ (mnot @ q))))))) = $true)),
% 0.15/0.40 inference(fool_elimination,[],[f44])).
% 0.15/0.40 thf(f44,plain,(
% 0.15/0.40 ~(mvalid @ (mnot @ (mbox_d @ (mand @ (mbox_d @ (mand @ p @ q)) @ (mbox_d @ (mimplies @ p @ (mnot @ q)))))))),
% 0.15/0.40 inference(rectify,[],[f36])).
% 0.15/0.40 thf(f36,negated_conjecture,(
% 0.15/0.40 ~(mvalid @ (mnot @ (mbox_d @ (mand @ (mbox_d @ (mand @ p @ q)) @ (mbox_d @ (mimplies @ p @ (mnot @ q)))))))),
% 0.15/0.40 inference(negated_conjecture,[],[f35])).
% 0.15/0.40 thf(f35,conjecture,(
% 0.15/0.40 (mvalid @ (mnot @ (mbox_d @ (mand @ (mbox_d @ (mand @ p @ q)) @ (mbox_d @ (mimplies @ p @ (mnot @ q)))))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.15/0.40 thf(f224,plain,(
% 0.15/0.40 ($false = (p @ (sK2 @ (sK2 @ sK1)))) | ($false = (q @ (sK2 @ (sK2 @ sK1))))),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f221])).
% 0.15/0.40 thf(f221,plain,(
% 0.15/0.40 ($false = (q @ (sK2 @ (sK2 @ sK1)))) | ($false = (p @ (sK2 @ (sK2 @ sK1)))) | ($false = $true)),
% 0.15/0.40 inference(superposition,[],[f220,f185])).
% 0.15/0.40 thf(f220,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = (rel_d @ (sK2 @ sK1) @ X0)) | ($false = (q @ X0)) | ($false = (p @ X0))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f215])).
% 0.15/0.40 thf(f215,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = $true) | ($false = (p @ X0)) | ($false = (rel_d @ (sK2 @ sK1) @ X0)) | ($false = (q @ X0))) )),
% 0.15/0.40 inference(superposition,[],[f170,f185])).
% 0.15/0.40 thf(f170,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (rel_d @ X1 @ X2)) | ($false = (p @ X2)) | ($false = (q @ X2))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.15/0.40 thf(f169,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (p @ X2))) | ($false = (q @ X2)) | ($false = (rel_d @ X1 @ X2)) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f168])).
% 0.15/0.40 thf(f168,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (q @ X2)) | ($true = (~ (rel_d @ X1 @ X2))) | ($true = (~ (p @ X2)))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f167])).
% 0.15/0.40 thf(f167,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (q @ X2))) | ($false = (rel_d @ sK1 @ X1)) | ($true = (~ (rel_d @ X1 @ X2))) | ($true = (~ (p @ X2)))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f166])).
% 0.15/0.40 thf(f166,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (q @ X2)) | (~ (p @ X2)))) | ($false = (rel_d @ sK1 @ X1)) | ($true = (~ (rel_d @ X1 @ X2)))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f165])).
% 0.15/0.40 thf(f165,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (rel_d @ X1 @ X2)) | ((~ (q @ X2)) | (~ (p @ X2))))) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f164])).
% 0.15/0.40 thf(f164,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))) @ X2)) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.40 inference(pi_clausification,[],[f163])).
% 0.15/0.40 thf(f163,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))) | ($false = (rel_d @ sK1 @ X1))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f162])).
% 0.15/0.40 thf(f162,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_d @ X1 @ Y0)) | ((~ (q @ Y0)) | (~ (p @ Y0))))))))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f160])).
% 0.15/0.40 thf(f204,plain,(
% 0.15/0.40 ((q @ (sK2 @ (sK2 @ sK1))) = $true)),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f201])).
% 0.15/0.40 thf(f201,plain,(
% 0.15/0.40 ($false = $true) | ((q @ (sK2 @ (sK2 @ sK1))) = $true)),
% 0.15/0.40 inference(superposition,[],[f191,f185])).
% 0.15/0.40 thf(f191,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = (rel_d @ (sK2 @ sK1) @ X0)) | ($true = (q @ X0))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f186])).
% 0.15/0.40 thf(f186,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($true = (q @ X0)) | ($false = (rel_d @ (sK2 @ sK1) @ X0)) | ($false = $true)) )),
% 0.15/0.40 inference(superposition,[],[f179,f185])).
% 0.15/0.40 thf(f179,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($true = (q @ X2)) | ($false = (rel_d @ X1 @ X2))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.15/0.40 thf(f178,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (q @ X2)) | ($false = (rel_d @ sK1 @ X1)) | ($true = (~ (rel_d @ X1 @ X2)))) )),
% 0.15/0.40 inference(not_proxy_clausification,[],[f177])).
% 0.15/0.40 thf(f177,plain,(
% 0.15/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_d @ sK1 @ X1)) | ($false = (~ (q @ X2))) | ($true = (~ (rel_d @ X1 @ X2)))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f175])).
% 0.15/0.40 % SZS output end Proof for theBenchmark
% 0.15/0.40 % (25203)------------------------------
% 0.15/0.40 % (25203)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (25203)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (25203)Memory used [KB]: 5756
% 0.15/0.40 % (25203)Time elapsed: 0.016 s
% 0.15/0.40 % (25203)Instructions burned: 16 (million)
% 0.15/0.40 % (25203)------------------------------
% 0.15/0.40 % (25203)------------------------------
% 0.15/0.40 % (25193)Success in time 0.018 s
% 0.15/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------