TSTP Solution File: SYO458^6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO458^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n004.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 09:04:46 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO458^6 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % 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
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 09:49:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 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
% 0.13/0.37 % (31902)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)
% 0.13/0.37 % (31895)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (31896)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)
% 0.13/0.37 % (31902)Instruction limit reached!
% 0.13/0.37 % (31902)------------------------------
% 0.13/0.37 % (31902)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (31898)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (31902)Termination reason: Unknown
% 0.13/0.37 % (31902)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (31900)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)
% 0.13/0.37 % (31902)Memory used [KB]: 1023
% 0.13/0.37 % (31902)Time elapsed: 0.003 s
% 0.13/0.37 % (31902)Instructions burned: 4 (million)
% 0.13/0.37 % (31902)------------------------------
% 0.13/0.37 % (31902)------------------------------
% 0.13/0.37 % (31899)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)
% 0.13/0.37 % (31897)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)
% 0.13/0.37 % (31901)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (31898)Instruction limit reached!
% 0.13/0.37 % (31898)------------------------------
% 0.13/0.37 % (31898)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (31898)Termination reason: Unknown
% 0.13/0.37 % (31898)Termination phase: shuffling
% 0.13/0.37 % (31899)Instruction limit reached!
% 0.13/0.37 % (31899)------------------------------
% 0.13/0.37 % (31899)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (31899)Termination reason: Unknown
% 0.13/0.37 % (31899)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (31899)Memory used [KB]: 1023
% 0.13/0.37 % (31899)Time elapsed: 0.003 s
% 0.13/0.37 % (31899)Instructions burned: 2 (million)
% 0.13/0.37 % (31899)------------------------------
% 0.13/0.37 % (31899)------------------------------
% 0.13/0.37
% 0.13/0.37 % (31898)Memory used [KB]: 1023
% 0.13/0.37 % (31898)Time elapsed: 0.003 s
% 0.13/0.37 % (31898)Instructions burned: 2 (million)
% 0.13/0.37 % (31898)------------------------------
% 0.13/0.37 % (31898)------------------------------
% 0.13/0.37 % (31896)Instruction limit reached!
% 0.13/0.37 % (31896)------------------------------
% 0.13/0.37 % (31896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (31896)Termination reason: Unknown
% 0.13/0.37 % (31896)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (31896)Memory used [KB]: 1023
% 0.13/0.37 % (31896)Time elapsed: 0.004 s
% 0.13/0.37 % (31896)Instructions burned: 4 (million)
% 0.13/0.37 % (31896)------------------------------
% 0.13/0.37 % (31896)------------------------------
% 0.13/0.38 % (31900)First to succeed.
% 0.13/0.38 % (31901)Also succeeded, but the first one will report.
% 0.13/0.38 % (31895)Also succeeded, but the first one will report.
% 0.13/0.38 % (31900)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% 0.13/0.38 thf(type_def_5, type, mu: $tType).
% 0.13/0.38 thf(func_def_0, type, mu: $tType).
% 0.13/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.13/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.13/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.13/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.13/0.38 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_36, type, p: $i > $o).
% 0.13/0.38 thf(func_def_37, type, q: $i > $o).
% 0.13/0.38 thf(f210,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(avatar_sat_refutation,[],[f179,f189,f208])).
% 0.13/0.38 thf(f208,plain,(
% 0.13/0.38 ~spl0_4),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f207])).
% 0.13/0.38 thf(f207,plain,(
% 0.13/0.38 $false | ~spl0_4),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f206])).
% 0.13/0.38 thf(f206,plain,(
% 0.13/0.38 ($true = $false) | ~spl0_4),
% 0.13/0.38 inference(forward_demodulation,[],[f195,f177])).
% 0.13/0.38 thf(f177,plain,(
% 0.13/0.38 ((p @ sK2) = $false) | ~spl0_4),
% 0.13/0.38 inference(avatar_component_clause,[],[f175])).
% 0.13/0.38 thf(f175,plain,(
% 0.13/0.38 spl0_4 <=> ((p @ sK2) = $false)),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.13/0.38 thf(f195,plain,(
% 0.13/0.38 ((p @ sK2) = $true)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f193])).
% 0.13/0.38 thf(f193,plain,(
% 0.13/0.38 ($true = $false) | ((p @ sK2) = $true)),
% 0.13/0.38 inference(superposition,[],[f147,f159])).
% 0.13/0.38 thf(f159,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($true = (p @ X1))) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f158])).
% 0.13/0.38 thf(f158,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (~ (rel_s5 @ sK1 @ X1))) | ($true = (p @ X1))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f157])).
% 0.13/0.38 thf(f157,plain,(
% 0.13/0.38 ( ! [X1 : $i] : ((((p @ X1) | (~ (rel_s5 @ sK1 @ X1))) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f156])).
% 0.13/0.38 thf(f156,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f155])).
% 0.13/0.38 thf(f155,plain,(
% 0.13/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))))),
% 0.13/0.38 inference(not_proxy_clausification,[],[f148])).
% 0.13/0.38 thf(f148,plain,(
% 0.13/0.38 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f127])).
% 0.13/0.38 thf(f127,plain,(
% 0.13/0.38 (((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))))) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f126])).
% 0.13/0.38 thf(f126,plain,(
% 0.13/0.38 (((!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ ((q @ Y0) | (~ (p @ Y0)))))) | (~ (rel_s5 @ sK1 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))))) = $false)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f125])).
% 0.13/0.38 thf(f125,plain,(
% 0.13/0.38 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ ((q @ Y1) | (~ (p @ Y1)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1))))))))) @ sK1) = $false)),
% 0.13/0.38 inference(sigma_clausification,[],[f124])).
% 0.13/0.38 thf(f124,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ ((q @ Y1) | (~ (p @ Y1)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))))))))),
% 0.13/0.38 inference(boolean_simplification,[],[f123])).
% 0.13/0.38 thf(f123,plain,(
% 0.13/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ ((~ ((p @ Y1) | (~ (q @ Y1)))) | (~ ((q @ Y1) | (~ (p @ Y1)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))))))))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f122])).
% 0.13/0.38 thf(f122,plain,(
% 0.13/0.38 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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)))) @ ((^[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]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ p @ q)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f118,f112,f120,f119,f111,f111,f111,f121])).
% 0.13/0.38 thf(f121,plain,(
% 0.13/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f115,f119,f120,f120])).
% 0.13/0.38 thf(f115,plain,(
% 0.13/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f60])).
% 0.13/0.38 thf(f60,plain,(
% 0.13/0.38 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.13/0.38 inference(fool_elimination,[],[f59])).
% 0.13/0.38 thf(f59,plain,(
% 0.13/0.38 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.13/0.38 inference(rectify,[],[f8])).
% 0.13/0.38 thf(f8,axiom,(
% 0.13/0.38 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.13/0.38 thf(f111,plain,(
% 0.13/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f68])).
% 0.13/0.38 thf(f68,plain,(
% 0.13/0.38 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f67])).
% 0.13/0.38 thf(f67,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))) = mbox_s5)),
% 0.13/0.38 inference(rectify,[],[f32])).
% 0.13/0.38 thf(f32,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))) = mbox_s5)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.13/0.38 thf(f119,plain,(
% 0.13/0.38 (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)))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f113,f117,f116,f117,f117])).
% 0.13/0.38 thf(f116,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f72])).
% 0.13/0.38 thf(f72,plain,(
% 0.13/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f71])).
% 0.13/0.38 thf(f71,plain,(
% 0.13/0.38 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.13/0.38 inference(rectify,[],[f4])).
% 0.13/0.38 thf(f4,axiom,(
% 0.13/0.38 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.13/0.38 thf(f117,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f91])).
% 0.13/0.38 thf(f91,plain,(
% 0.13/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.38 inference(fool_elimination,[],[f90])).
% 0.13/0.38 thf(f90,plain,(
% 0.13/0.38 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.13/0.38 inference(rectify,[],[f3])).
% 0.13/0.38 thf(f3,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.13/0.38 thf(f113,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f95])).
% 0.13/0.38 thf(f95,plain,(
% 0.13/0.38 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.13/0.38 inference(fool_elimination,[],[f94])).
% 0.13/0.38 thf(f94,plain,(
% 0.13/0.38 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.13/0.38 inference(rectify,[],[f5])).
% 0.13/0.38 thf(f5,axiom,(
% 0.13/0.38 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.13/0.38 thf(f120,plain,(
% 0.13/0.38 (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)))))),
% 0.13/0.38 inference(definition_unfolding,[],[f114,f116,f117])).
% 0.13/0.38 thf(f114,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f51])).
% 0.13/0.38 thf(f51,plain,(
% 0.13/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f50])).
% 0.13/0.38 thf(f50,plain,(
% 0.13/0.38 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.13/0.38 inference(rectify,[],[f6])).
% 0.13/0.38 thf(f6,axiom,(
% 0.13/0.38 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.13/0.38 thf(f112,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(cnf_transformation,[],[f85])).
% 0.13/0.38 thf(f85,plain,(
% 0.13/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.38 inference(fool_elimination,[],[f84])).
% 0.13/0.38 thf(f84,plain,(
% 0.13/0.38 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.13/0.38 inference(rectify,[],[f28])).
% 0.13/0.38 thf(f28,axiom,(
% 0.13/0.38 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.38 thf(f118,plain,(
% 0.13/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ q)) @ (mbox_s5 @ (mequiv @ p @ q)))) != $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f110])).
% 0.13/0.38 thf(f110,plain,(
% 0.13/0.38 ((mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ q)) @ (mbox_s5 @ (mequiv @ p @ q)))) != $true)),
% 0.13/0.38 inference(flattening,[],[f57])).
% 0.13/0.38 thf(f57,plain,(
% 0.13/0.38 ~((mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ q)) @ (mbox_s5 @ (mequiv @ p @ q)))) = $true)),
% 0.13/0.38 inference(fool_elimination,[],[f56])).
% 0.13/0.38 thf(f56,plain,(
% 0.13/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ q)) @ (mbox_s5 @ (mequiv @ p @ q))))),
% 0.13/0.38 inference(rectify,[],[f38])).
% 0.13/0.38 thf(f38,negated_conjecture,(
% 0.13/0.38 ~(mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ q)) @ (mbox_s5 @ (mequiv @ p @ q))))),
% 0.13/0.38 inference(negated_conjecture,[],[f37])).
% 0.13/0.38 thf(f37,conjecture,(
% 0.13/0.38 (mvalid @ (mimplies @ (mand @ (mbox_s5 @ p) @ (mbox_s5 @ q)) @ (mbox_s5 @ (mequiv @ p @ q))))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.13/0.38 thf(f147,plain,(
% 0.13/0.38 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.13/0.38 inference(not_proxy_clausification,[],[f131])).
% 0.13/0.38 thf(f131,plain,(
% 0.13/0.38 ((~ (rel_s5 @ sK1 @ sK2)) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f130])).
% 0.13/0.38 thf(f130,plain,(
% 0.13/0.38 ($false = ((~ ((~ ((p @ sK2) | (~ (q @ sK2)))) | (~ ((q @ sK2) | (~ (p @ sK2)))))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f129])).
% 0.13/0.38 thf(f129,plain,(
% 0.13/0.38 (((^[Y0 : $i]: ((~ ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ ((q @ Y0) | (~ (p @ Y0)))))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2) = $false)),
% 0.13/0.38 inference(sigma_clausification,[],[f128])).
% 0.13/0.38 thf(f128,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((~ ((~ ((p @ Y0) | (~ (q @ Y0)))) | (~ ((q @ Y0) | (~ (p @ Y0)))))) | (~ (rel_s5 @ sK1 @ Y0))))) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f126])).
% 0.13/0.38 thf(f189,plain,(
% 0.13/0.38 ~spl0_3),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f188])).
% 0.13/0.38 thf(f188,plain,(
% 0.13/0.38 $false | ~spl0_3),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f187])).
% 0.13/0.38 thf(f187,plain,(
% 0.13/0.38 ($true = $false) | ~spl0_3),
% 0.13/0.38 inference(forward_demodulation,[],[f182,f172])).
% 0.13/0.38 thf(f172,plain,(
% 0.13/0.38 ((q @ sK2) = $false) | ~spl0_3),
% 0.13/0.38 inference(avatar_component_clause,[],[f170])).
% 0.13/0.38 thf(f170,plain,(
% 0.13/0.38 spl0_3 <=> ((q @ sK2) = $false)),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.13/0.38 thf(f182,plain,(
% 0.13/0.38 ($true = (q @ sK2))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f181])).
% 0.13/0.38 thf(f181,plain,(
% 0.13/0.38 ($true = (q @ sK2)) | ($true = $false)),
% 0.13/0.38 inference(superposition,[],[f147,f154])).
% 0.13/0.38 thf(f154,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((rel_s5 @ sK1 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.13/0.38 inference(not_proxy_clausification,[],[f153])).
% 0.13/0.38 thf(f153,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (q @ X1)) | ($true = (~ (rel_s5 @ sK1 @ X1)))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f152])).
% 0.13/0.38 thf(f152,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((q @ X1) | (~ (rel_s5 @ sK1 @ X1))))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f151])).
% 0.13/0.38 thf(f151,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f150])).
% 0.13/0.38 thf(f150,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0))))) = $true)),
% 0.13/0.38 inference(not_proxy_clausification,[],[f149])).
% 0.13/0.38 thf(f149,plain,(
% 0.13/0.38 ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK1 @ Y0)))))) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f127])).
% 0.13/0.38 thf(f179,plain,(
% 0.13/0.38 spl0_3 | spl0_4),
% 0.13/0.38 inference(avatar_split_clause,[],[f140,f175,f170])).
% 0.13/0.38 thf(f140,plain,(
% 0.13/0.38 ((p @ sK2) = $false) | ((q @ sK2) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f138])).
% 0.13/0.38 thf(f138,plain,(
% 0.13/0.38 ($false = ((q @ sK2) | (~ (p @ sK2)))) | ((p @ sK2) = $false)),
% 0.13/0.38 inference(not_proxy_clausification,[],[f137])).
% 0.13/0.38 thf(f137,plain,(
% 0.13/0.38 ((p @ sK2) = $false) | ($true = (~ ((q @ sK2) | (~ (p @ sK2)))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f135])).
% 0.13/0.38 thf(f135,plain,(
% 0.13/0.38 (((p @ sK2) | (~ (q @ sK2))) = $false) | ($true = (~ ((q @ sK2) | (~ (p @ sK2)))))),
% 0.13/0.38 inference(not_proxy_clausification,[],[f134])).
% 0.13/0.38 thf(f134,plain,(
% 0.13/0.38 ((~ ((p @ sK2) | (~ (q @ sK2)))) = $true) | ($true = (~ ((q @ sK2) | (~ (p @ sK2)))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f133])).
% 0.13/0.38 thf(f133,plain,(
% 0.13/0.38 (((~ ((p @ sK2) | (~ (q @ sK2)))) | (~ ((q @ sK2) | (~ (p @ sK2))))) = $true)),
% 0.13/0.38 inference(not_proxy_clausification,[],[f132])).
% 0.13/0.38 thf(f132,plain,(
% 0.13/0.38 ($false = (~ ((~ ((p @ sK2) | (~ (q @ sK2)))) | (~ ((q @ sK2) | (~ (p @ sK2)))))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f130])).
% 0.13/0.38 % SZS output end Proof for theBenchmark
% 0.13/0.38 % (31900)------------------------------
% 0.13/0.38 % (31900)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (31900)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (31900)Memory used [KB]: 5628
% 0.13/0.38 % (31900)Time elapsed: 0.012 s
% 0.13/0.38 % (31900)Instructions burned: 12 (million)
% 0.13/0.38 % (31900)------------------------------
% 0.13/0.38 % (31900)------------------------------
% 0.13/0.38 % (31894)Success in time 0.014 s
% 0.13/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------