TSTP Solution File: SYO429^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO429^1 : 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 : n002.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 09:04:24 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO429^1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15 % 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
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 10:28:08 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a TH0_THM_EQU_NAR problem
% 0.14/0.37 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
% 0.14/0.39 % (29047)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.40 % (29048)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)
% 0.14/0.40 % (29050)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.40 % (29051)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)
% 0.14/0.40 % (29049)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)
% 0.14/0.40 % (29052)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)
% 0.14/0.40 % (29053)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.40 % (29047)First to succeed.
% 0.14/0.40 % (29054)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)
% 0.14/0.40 % (29050)Instruction limit reached!
% 0.14/0.40 % (29050)------------------------------
% 0.14/0.40 % (29050)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (29050)Termination reason: Unknown
% 0.14/0.40 % (29051)Instruction limit reached!
% 0.14/0.40 % (29051)------------------------------
% 0.14/0.40 % (29051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (29051)Termination reason: Unknown
% 0.14/0.40 % (29051)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (29051)Memory used [KB]: 1023
% 0.14/0.40 % (29051)Time elapsed: 0.004 s
% 0.14/0.40 % (29051)Instructions burned: 2 (million)
% 0.14/0.40 % (29051)------------------------------
% 0.14/0.40 % (29051)------------------------------
% 0.14/0.40 % (29050)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (29050)Memory used [KB]: 1023
% 0.14/0.40 % (29050)Time elapsed: 0.004 s
% 0.14/0.40 % (29050)Instructions burned: 2 (million)
% 0.14/0.40 % (29050)------------------------------
% 0.14/0.40 % (29050)------------------------------
% 0.14/0.40 % (29054)Instruction limit reached!
% 0.14/0.40 % (29054)------------------------------
% 0.14/0.40 % (29054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (29054)Termination reason: Unknown
% 0.14/0.40 % (29054)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (29054)Memory used [KB]: 1023
% 0.14/0.40 % (29054)Time elapsed: 0.005 s
% 0.14/0.40 % (29054)Instructions burned: 3 (million)
% 0.14/0.40 % (29054)------------------------------
% 0.14/0.40 % (29054)------------------------------
% 0.14/0.40 % (29048)Instruction limit reached!
% 0.14/0.40 % (29048)------------------------------
% 0.14/0.40 % (29048)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (29048)Termination reason: Unknown
% 0.14/0.40 % (29048)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (29048)Memory used [KB]: 1023
% 0.14/0.40 % (29048)Time elapsed: 0.006 s
% 0.14/0.40 % (29048)Instructions burned: 4 (million)
% 0.14/0.40 % (29048)------------------------------
% 0.14/0.40 % (29048)------------------------------
% 0.14/0.40 % (29047)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_33, type, rel_b: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_36, type, p: $i > $o).
% 0.14/0.40 thf(f236,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f235])).
% 0.14/0.40 thf(f235,plain,(
% 0.14/0.40 ($false = $true)),
% 0.14/0.40 inference(superposition,[],[f218,f230])).
% 0.14/0.40 thf(f230,plain,(
% 0.14/0.40 ((p @ sK1) = $true)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f224])).
% 0.14/0.40 thf(f224,plain,(
% 0.14/0.40 ((p @ sK1) = $true) | ($false = $true)),
% 0.14/0.40 inference(superposition,[],[f209,f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ((rel_b @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ((~ (rel_b @ sK1 @ sK2)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK2 @ Y0)))))) | (~ (rel_b @ sK1 @ sK2))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))) @ sK2))),
% 0.14/0.40 inference(sigma_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1))))))) @ sK1))),
% 0.14/0.40 inference(sigma_clausification,[],[f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))))) != $true)),
% 0.14/0.40 inference(boolean_simplification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))))) != $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 ($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 > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f139,f130,f145,f153,f138,f138,f153])).
% 0.14/0.40 thf(f138,plain,(
% 0.14/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f63])).
% 0.14/0.40 thf(f63,plain,(
% 0.14/0.40 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f62])).
% 0.14/0.40 thf(f62,plain,(
% 0.14/0.40 (mbox_b = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_b @ X1 @ X2) | (X0 @ X2)))))),
% 0.14/0.40 inference(rectify,[],[f32])).
% 0.14/0.40 thf(f32,axiom,(
% 0.14/0.40 (mbox_b = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_b @ X2 @ X7) | (X3 @ X7)))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_b)).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f113,f112,f138,f112])).
% 0.14/0.40 thf(f112,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f98])).
% 0.14/0.40 thf(f98,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f97])).
% 0.14/0.40 thf(f97,plain,(
% 0.14/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.41 thf(f113,plain,(
% 0.14/0.41 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.14/0.41 inference(cnf_transformation,[],[f40])).
% 0.14/0.41 thf(f40,plain,(
% 0.14/0.41 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.14/0.41 inference(fool_elimination,[],[f39])).
% 0.14/0.41 thf(f39,plain,(
% 0.14/0.41 ((^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))) = mdia_b)),
% 0.14/0.41 inference(rectify,[],[f33])).
% 0.14/0.41 thf(f33,axiom,(
% 0.14/0.41 ((^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))) = mdia_b)),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_b)).
% 0.14/0.41 thf(f145,plain,(
% 0.14/0.41 (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)))))),
% 0.14/0.41 inference(definition_unfolding,[],[f137,f127,f112])).
% 0.14/0.41 thf(f127,plain,(
% 0.14/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.41 inference(cnf_transformation,[],[f94])).
% 0.14/0.41 thf(f94,plain,(
% 0.14/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.41 inference(fool_elimination,[],[f93])).
% 0.14/0.41 thf(f93,plain,(
% 0.14/0.41 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.14/0.41 inference(rectify,[],[f4])).
% 0.14/0.41 thf(f4,axiom,(
% 0.14/0.41 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.41 thf(f137,plain,(
% 0.14/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.41 inference(cnf_transformation,[],[f69])).
% 0.14/0.41 thf(f69,plain,(
% 0.14/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.41 inference(fool_elimination,[],[f68])).
% 0.14/0.41 thf(f68,plain,(
% 0.14/0.41 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.41 inference(rectify,[],[f6])).
% 0.14/0.41 thf(f6,axiom,(
% 0.14/0.41 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.41 thf(f130,plain,(
% 0.14/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.41 inference(cnf_transformation,[],[f61])).
% 0.14/0.41 thf(f61,plain,(
% 0.14/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.41 inference(fool_elimination,[],[f60])).
% 0.14/0.41 thf(f60,plain,(
% 0.14/0.41 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.41 inference(rectify,[],[f28])).
% 0.14/0.41 thf(f28,axiom,(
% 0.14/0.41 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.41 thf(f139,plain,(
% 0.14/0.41 ((mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mbox_b @ (mdia_b @ p)))) != $true)),
% 0.14/0.41 inference(cnf_transformation,[],[f107])).
% 0.14/0.41 thf(f107,plain,(
% 0.14/0.41 ((mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mbox_b @ (mdia_b @ p)))) != $true)),
% 0.14/0.41 inference(flattening,[],[f79])).
% 0.14/0.41 thf(f79,plain,(
% 0.14/0.41 ~((mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mbox_b @ (mdia_b @ p)))) = $true)),
% 0.14/0.41 inference(fool_elimination,[],[f78])).
% 0.14/0.41 thf(f78,plain,(
% 0.14/0.41 ~(mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mbox_b @ (mdia_b @ p))))),
% 0.14/0.41 inference(rectify,[],[f37])).
% 0.14/0.41 thf(f37,negated_conjecture,(
% 0.14/0.41 ~(mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mbox_b @ (mdia_b @ p))))),
% 0.14/0.41 inference(negated_conjecture,[],[f36])).
% 0.14/0.41 thf(f36,conjecture,(
% 0.14/0.41 (mvalid @ (mimplies @ (mdia_b @ (mbox_b @ p)) @ (mbox_b @ (mdia_b @ p))))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.14/0.41 thf(f209,plain,(
% 0.14/0.41 ( ! [X0 : $i] : (($false = (rel_b @ X0 @ sK2)) | ((p @ X0) = $true)) )),
% 0.14/0.41 inference(trivial_inequality_removal,[],[f203])).
% 0.14/0.41 thf(f203,plain,(
% 0.14/0.41 ( ! [X0 : $i] : (((p @ X0) = $true) | ($false = $true) | ($false = (rel_b @ X0 @ sK2))) )),
% 0.14/0.41 inference(superposition,[],[f171,f192])).
% 0.14/0.41 thf(f192,plain,(
% 0.14/0.41 ( ! [X2 : $i,X1 : $i] : (((rel_b @ X2 @ X1) = $true) | ((rel_b @ X1 @ X2) = $false)) )),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f191])).
% 0.14/0.41 thf(f191,plain,(
% 0.14/0.41 ( ! [X2 : $i,X1 : $i] : ((((rel_b @ X1 @ X2) => (rel_b @ X2 @ X1)) = $true)) )),
% 0.14/0.41 inference(beta_eta_normalization,[],[f190])).
% 0.14/0.41 thf(f190,plain,(
% 0.14/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_b @ X1 @ Y0) => (rel_b @ Y0 @ X1))) @ X2))) )),
% 0.14/0.41 inference(pi_clausification,[],[f189])).
% 0.14/0.41 thf(f189,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_b @ X1 @ Y0) => (rel_b @ Y0 @ X1)))) = $true)) )),
% 0.14/0.41 inference(beta_eta_normalization,[],[f188])).
% 0.14/0.41 thf(f188,plain,(
% 0.14/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y0 @ Y1) => (rel_b @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.14/0.41 inference(pi_clausification,[],[f187])).
% 0.14/0.41 thf(f187,plain,(
% 0.14/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y0 @ Y1) => (rel_b @ Y1 @ Y0)))))))),
% 0.14/0.41 inference(beta_eta_normalization,[],[f154])).
% 0.14/0.41 thf(f154,plain,(
% 0.14/0.41 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_b))),
% 0.14/0.41 inference(definition_unfolding,[],[f121,f134])).
% 0.14/0.41 thf(f134,plain,(
% 0.14/0.41 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.14/0.41 inference(cnf_transformation,[],[f46])).
% 0.14/0.41 thf(f46,plain,(
% 0.14/0.41 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.14/0.41 inference(fool_elimination,[],[f45])).
% 0.14/0.41 thf(f45,plain,(
% 0.14/0.41 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.14/0.41 inference(rectify,[],[f19])).
% 0.14/0.41 thf(f19,axiom,(
% 0.14/0.41 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.14/0.41 thf(f121,plain,(
% 0.14/0.41 ((msymmetric @ rel_b) = $true)),
% 0.14/0.41 inference(cnf_transformation,[],[f100])).
% 0.14/0.41 thf(f100,plain,(
% 0.14/0.41 ((msymmetric @ rel_b) = $true)),
% 0.14/0.41 inference(fool_elimination,[],[f99])).
% 0.14/0.41 thf(f99,plain,(
% 0.14/0.41 (msymmetric @ rel_b)),
% 0.14/0.41 inference(rectify,[],[f35])).
% 0.14/0.41 thf(f35,axiom,(
% 0.14/0.41 (msymmetric @ rel_b)),
% 0.14/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.14/0.41 thf(f171,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (((rel_b @ sK2 @ X1) = $false) | ($true = (p @ X1))) )),
% 0.14/0.41 inference(not_proxy_clausification,[],[f170])).
% 0.14/0.41 thf(f170,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (((~ (rel_b @ sK2 @ X1)) = $true) | ($true = (p @ X1))) )),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.41 thf(f169,plain,(
% 0.14/0.41 ( ! [X1 : $i] : ((((p @ X1) | (~ (rel_b @ sK2 @ X1))) = $true)) )),
% 0.14/0.41 inference(beta_eta_normalization,[],[f168])).
% 0.14/0.41 thf(f168,plain,(
% 0.14/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK2 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.41 inference(pi_clausification,[],[f167])).
% 0.14/0.41 thf(f167,plain,(
% 0.14/0.41 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK2 @ Y0))))) = $true)),
% 0.14/0.41 inference(not_proxy_clausification,[],[f166])).
% 0.14/0.41 thf(f166,plain,(
% 0.14/0.41 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK2 @ Y0)))))))),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.41 thf(f218,plain,(
% 0.14/0.41 ((p @ sK1) = $false)),
% 0.14/0.41 inference(trivial_inequality_removal,[],[f212])).
% 0.14/0.41 thf(f212,plain,(
% 0.14/0.41 ($false = $true) | ((p @ sK1) = $false)),
% 0.14/0.41 inference(superposition,[],[f208,f183])).
% 0.14/0.41 thf(f183,plain,(
% 0.14/0.41 ($true = (rel_b @ sK1 @ sK3))),
% 0.14/0.41 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.41 thf(f175,plain,(
% 0.14/0.41 ($false = (~ (rel_b @ sK1 @ sK3)))),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.41 thf(f174,plain,(
% 0.14/0.41 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_b @ sK3 @ Y0)))))) | (~ (rel_b @ sK1 @ sK3))) = $false)),
% 0.14/0.41 inference(beta_eta_normalization,[],[f173])).
% 0.14/0.41 thf(f173,plain,(
% 0.14/0.41 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))) @ sK3) = $false)),
% 0.14/0.41 inference(sigma_clausification,[],[f161])).
% 0.14/0.41 thf(f161,plain,(
% 0.14/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f160])).
% 0.14/0.41 thf(f208,plain,(
% 0.14/0.41 ( ! [X0 : $i] : (((rel_b @ X0 @ sK3) = $false) | ((p @ X0) = $false)) )),
% 0.14/0.41 inference(trivial_inequality_removal,[],[f204])).
% 0.14/0.41 thf(f204,plain,(
% 0.14/0.41 ( ! [X0 : $i] : (($false = $true) | ((rel_b @ X0 @ sK3) = $false) | ((p @ X0) = $false)) )),
% 0.14/0.41 inference(superposition,[],[f182,f192])).
% 0.14/0.41 thf(f182,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (($false = (rel_b @ sK3 @ X1)) | ($false = (p @ X1))) )),
% 0.14/0.41 inference(not_proxy_clausification,[],[f181])).
% 0.14/0.41 thf(f181,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (((~ (p @ X1)) = $true) | ($false = (rel_b @ sK3 @ X1))) )),
% 0.14/0.41 inference(not_proxy_clausification,[],[f180])).
% 0.14/0.41 thf(f180,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (((~ (rel_b @ sK3 @ X1)) = $true) | ((~ (p @ X1)) = $true)) )),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f179])).
% 0.14/0.41 thf(f179,plain,(
% 0.14/0.41 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (~ (rel_b @ sK3 @ X1))))) )),
% 0.14/0.41 inference(beta_eta_normalization,[],[f178])).
% 0.14/0.41 thf(f178,plain,(
% 0.14/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_b @ sK3 @ Y0)))) @ X1) = $true)) )),
% 0.14/0.41 inference(pi_clausification,[],[f177])).
% 0.14/0.41 thf(f177,plain,(
% 0.14/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_b @ sK3 @ Y0))))))),
% 0.14/0.41 inference(not_proxy_clausification,[],[f176])).
% 0.14/0.41 thf(f176,plain,(
% 0.14/0.41 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_b @ sK3 @ Y0)))))) = $false)),
% 0.14/0.41 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.41 % SZS output end Proof for theBenchmark
% 0.14/0.41 % (29047)------------------------------
% 0.14/0.41 % (29047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (29047)Termination reason: Refutation
% 0.14/0.41
% 0.14/0.41 % (29047)Memory used [KB]: 5628
% 0.14/0.41 % (29047)Time elapsed: 0.014 s
% 0.14/0.41 % (29047)Instructions burned: 14 (million)
% 0.14/0.41 % (29047)------------------------------
% 0.14/0.41 % (29047)------------------------------
% 0.14/0.41 % (29046)Success in time 0.029 s
% 0.14/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------