TSTP Solution File: SYO433^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO433^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n017.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 09:04:25 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
% 0.00/0.12 % Problem : SYO433^1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 09:58:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (20019)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (20021)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)
% 0.14/0.38 % (20023)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)
% 0.14/0.38 % (20024)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)
% 0.14/0.38 % (20023)Instruction limit reached!
% 0.14/0.38 % (20023)------------------------------
% 0.14/0.38 % (20023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20023)Termination reason: Unknown
% 0.14/0.38 % (20023)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (20023)Memory used [KB]: 1023
% 0.14/0.38 % (20023)Time elapsed: 0.002 s
% 0.14/0.38 % (20023)Instructions burned: 2 (million)
% 0.14/0.38 % (20023)------------------------------
% 0.14/0.38 % (20023)------------------------------
% 0.14/0.38 % (20020)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)
% 0.14/0.38 % (20022)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (20025)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (20020)Instruction limit reached!
% 0.14/0.38 % (20020)------------------------------
% 0.14/0.38 % (20020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20020)Termination reason: Unknown
% 0.14/0.38 % (20020)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (20020)Memory used [KB]: 1023
% 0.14/0.38 % (20020)Time elapsed: 0.004 s
% 0.14/0.38 % (20020)Instructions burned: 5 (million)
% 0.14/0.38 % (20020)------------------------------
% 0.14/0.38 % (20020)------------------------------
% 0.14/0.38 % (20026)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)
% 0.14/0.38 % (20022)Instruction limit reached!
% 0.14/0.38 % (20022)------------------------------
% 0.14/0.38 % (20022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20022)Termination reason: Unknown
% 0.14/0.38 % (20022)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (20022)Memory used [KB]: 1023
% 0.14/0.38 % (20022)Time elapsed: 0.003 s
% 0.14/0.38 % (20022)Instructions burned: 3 (million)
% 0.14/0.38 % (20022)------------------------------
% 0.14/0.38 % (20022)------------------------------
% 0.14/0.38 % (20026)Instruction limit reached!
% 0.14/0.38 % (20026)------------------------------
% 0.14/0.38 % (20026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (20026)Termination reason: Unknown
% 0.14/0.38 % (20026)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (20026)Memory used [KB]: 1023
% 0.14/0.38 % (20026)Time elapsed: 0.003 s
% 0.14/0.39 % (20026)Instructions burned: 3 (million)
% 0.14/0.39 % (20026)------------------------------
% 0.14/0.39 % (20026)------------------------------
% 0.14/0.39 % (20024)Refutation not found, incomplete strategy
% 0.14/0.39 % (20024)------------------------------
% 0.14/0.39 % (20024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (20024)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (20024)Memory used [KB]: 5628
% 0.14/0.39 % (20024)Time elapsed: 0.008 s
% 0.14/0.39 % (20024)Instructions burned: 12 (million)
% 0.14/0.39 % (20024)------------------------------
% 0.14/0.39 % (20024)------------------------------
% 0.14/0.39 % (20025)Instruction limit reached!
% 0.14/0.39 % (20025)------------------------------
% 0.14/0.39 % (20025)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (20025)Termination reason: Unknown
% 0.14/0.39 % (20025)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (20025)Memory used [KB]: 5628
% 0.14/0.39 % (20025)Time elapsed: 0.011 s
% 0.14/0.39 % (20025)Instructions burned: 18 (million)
% 0.14/0.39 % (20025)------------------------------
% 0.14/0.39 % (20025)------------------------------
% 0.14/0.39 % (20019)First to succeed.
% 0.14/0.39 % (20027)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.40 % (20021)Also succeeded, but the first one will report.
% 0.14/0.40 % (20019)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_s4: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_36, type, p: $i > $o).
% 0.14/0.40 thf(func_def_37, type, q: $i > $o).
% 0.14/0.40 thf(func_def_55, type, sK2: $i > $i).
% 0.14/0.40 thf(f344,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f239,f245,f320,f336,f343])).
% 0.14/0.40 thf(f343,plain,(
% 0.14/0.40 ~spl0_4 | ~spl0_5),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f342])).
% 0.14/0.40 thf(f342,plain,(
% 0.14/0.40 $false | (~spl0_4 | ~spl0_5)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f339])).
% 0.14/0.40 thf(f339,plain,(
% 0.14/0.40 ($true = $false) | (~spl0_4 | ~spl0_5)),
% 0.14/0.40 inference(superposition,[],[f237,f313])).
% 0.14/0.40 thf(f313,plain,(
% 0.14/0.40 ($true = (q @ (sK2 @ sK3))) | ~spl0_5),
% 0.14/0.40 inference(avatar_component_clause,[],[f311])).
% 0.14/0.40 thf(f311,plain,(
% 0.14/0.40 spl0_5 <=> ($true = (q @ (sK2 @ sK3)))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.14/0.40 thf(f237,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK3)) = $false) | ~spl0_4),
% 0.14/0.40 inference(avatar_component_clause,[],[f235])).
% 0.14/0.40 thf(f235,plain,(
% 0.14/0.40 spl0_4 <=> ((q @ (sK2 @ sK3)) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.14/0.40 thf(f336,plain,(
% 0.14/0.40 ~spl0_6),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f335])).
% 0.14/0.40 thf(f335,plain,(
% 0.14/0.40 $false | ~spl0_6),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f328])).
% 0.14/0.40 thf(f328,plain,(
% 0.14/0.40 ($true = $false) | ~spl0_6),
% 0.14/0.40 inference(superposition,[],[f317,f203])).
% 0.14/0.40 thf(f203,plain,(
% 0.14/0.40 ($true = (rel_s4 @ sK1 @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ((~ (rel_s4 @ sK1 @ sK3)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f199])).
% 0.14/0.40 thf(f199,plain,(
% 0.14/0.40 (((~ (p @ sK3)) | (~ (rel_s4 @ sK1 @ sK3))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f198])).
% 0.14/0.40 thf(f198,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK1 @ Y0)))) @ sK3) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f191])).
% 0.14/0.40 thf(f191,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f175])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK1 @ Y0))))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))) | (~ (rel_s4 @ Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))))) @ sK1) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))) | (~ (rel_s4 @ Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))))),
% 0.14/0.40 inference(boolean_simplification,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))) != $true)),
% 0.14/0.40 inference(boolean_simplification,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))))) != $true)),
% 0.14/0.40 inference(boolean_simplification,[],[f169])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (p @ Y1))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((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 > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ q))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f142,f139,f145,f144,f153,f131,f153,f144,f131])).
% 0.14/0.40 thf(f131,plain,(
% 0.14/0.40 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f102])).
% 0.14/0.40 thf(f102,plain,(
% 0.14/0.40 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f101])).
% 0.14/0.40 thf(f101,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))) = mbox_s4)),
% 0.14/0.40 inference(rectify,[],[f32])).
% 0.14/0.40 thf(f32,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s4 @ X2 @ X7) | (X3 @ X7)))) = mbox_s4)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f137,f116,f131,f116])).
% 0.14/0.40 thf(f116,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f61])).
% 0.14/0.40 thf(f61,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f60])).
% 0.14/0.40 thf(f60,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/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f137,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f106])).
% 0.14/0.40 thf(f106,plain,(
% 0.14/0.40 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.14/0.40 inference(fool_elimination,[],[f105])).
% 0.14/0.40 thf(f105,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.14/0.40 thf(f144,plain,(
% 0.14/0.40 (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)))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f130,f116,f143,f116,f116])).
% 0.14/0.40 thf(f143,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f90])).
% 0.14/0.40 thf(f90,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f89])).
% 0.14/0.40 thf(f89,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f130,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f57])).
% 0.14/0.40 thf(f57,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f56])).
% 0.14/0.40 thf(f56,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.14/0.40 inference(rectify,[],[f5])).
% 0.14/0.40 thf(f5,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.14/0.40 thf(f145,plain,(
% 0.14/0.40 (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)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f126,f143,f116])).
% 0.14/0.40 thf(f126,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f94])).
% 0.14/0.40 thf(f94,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f93])).
% 0.14/0.40 thf(f93,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f139,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f46])).
% 0.14/0.40 thf(f46,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f45])).
% 0.14/0.40 thf(f45,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f142,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mand @ (mdia_s4 @ p) @ (mbox_s4 @ q)) @ (mdia_s4 @ (mand @ p @ (mbox_s4 @ q))))) != $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f107])).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 ((mvalid @ (mimplies @ (mand @ (mdia_s4 @ p) @ (mbox_s4 @ q)) @ (mdia_s4 @ (mand @ p @ (mbox_s4 @ q))))) != $true)),
% 0.14/0.40 inference(flattening,[],[f81])).
% 0.14/0.40 thf(f81,plain,(
% 0.14/0.40 ~((mvalid @ (mimplies @ (mand @ (mdia_s4 @ p) @ (mbox_s4 @ q)) @ (mdia_s4 @ (mand @ p @ (mbox_s4 @ q))))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f80])).
% 0.14/0.40 thf(f80,plain,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mand @ (mdia_s4 @ p) @ (mbox_s4 @ q)) @ (mdia_s4 @ (mand @ p @ (mbox_s4 @ q)))))),
% 0.14/0.40 inference(rectify,[],[f37])).
% 0.14/0.40 thf(f37,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mimplies @ (mand @ (mdia_s4 @ p) @ (mbox_s4 @ q)) @ (mdia_s4 @ (mand @ p @ (mbox_s4 @ q)))))),
% 0.14/0.40 inference(negated_conjecture,[],[f36])).
% 0.14/0.40 thf(f36,conjecture,(
% 0.14/0.40 (mvalid @ (mimplies @ (mand @ (mdia_s4 @ p) @ (mbox_s4 @ q)) @ (mdia_s4 @ (mand @ p @ (mbox_s4 @ q)))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.40 thf(f317,plain,(
% 0.14/0.40 ((rel_s4 @ sK1 @ sK3) = $false) | ~spl0_6),
% 0.14/0.40 inference(avatar_component_clause,[],[f315])).
% 0.14/0.40 thf(f315,plain,(
% 0.14/0.40 spl0_6 <=> ((rel_s4 @ sK1 @ sK3) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.14/0.40 thf(f320,plain,(
% 0.14/0.40 spl0_6 | spl0_5 | spl0_3),
% 0.14/0.40 inference(avatar_split_clause,[],[f319,f231,f311,f315])).
% 0.14/0.40 thf(f231,plain,(
% 0.14/0.40 spl0_3 <=> ((p @ sK3) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.14/0.40 thf(f319,plain,(
% 0.14/0.40 ($true = (q @ (sK2 @ sK3))) | ((rel_s4 @ sK1 @ sK3) = $false) | spl0_3),
% 0.14/0.40 inference(subsumption_resolution,[],[f303,f232])).
% 0.14/0.40 thf(f232,plain,(
% 0.14/0.40 ((p @ sK3) != $false) | spl0_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f231])).
% 0.14/0.40 thf(f303,plain,(
% 0.14/0.40 ((p @ sK3) = $false) | ((rel_s4 @ sK1 @ sK3) = $false) | ($true = (q @ (sK2 @ sK3)))),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f293])).
% 0.14/0.40 thf(f293,plain,(
% 0.14/0.40 ($true = (q @ (sK2 @ sK3))) | ($true = $false) | ((rel_s4 @ sK1 @ sK3) = $false) | ((p @ sK3) = $false)),
% 0.14/0.40 inference(superposition,[],[f190,f268])).
% 0.14/0.40 thf(f268,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (((rel_s4 @ sK3 @ X0) = $false) | ($true = (q @ X0))) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f258])).
% 0.14/0.40 thf(f258,plain,(
% 0.14/0.40 ( ! [X0 : $i] : (($true = $false) | ((rel_s4 @ sK3 @ X0) = $false) | ($true = (q @ X0))) )),
% 0.14/0.40 inference(superposition,[],[f255,f203])).
% 0.14/0.40 thf(f255,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = (q @ X0)) | ((rel_s4 @ X1 @ X0) = $false)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f249])).
% 0.14/0.40 thf(f249,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((rel_s4 @ X1 @ X0) = $false) | ($true = (q @ X0)) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(superposition,[],[f197,f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X2)) | ((rel_s4 @ X3 @ X2) = $false) | ((rel_s4 @ X1 @ X3) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X2)) | (((rel_s4 @ X1 @ X3) & (rel_s4 @ X3 @ X2)) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s4 @ X1 @ X3) & (rel_s4 @ X3 @ X2)) => (rel_s4 @ X1 @ X2)) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y0 @ X2)) => (rel_s4 @ X1 @ X2))) @ X3))) )),
% 0.14/0.40 inference(pi_clausification,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y0 @ X2)) => (rel_s4 @ X1 @ X2)))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y1) & (rel_s4 @ Y1 @ Y0)) => (rel_s4 @ X1 @ Y0))))) @ X2))) )),
% 0.14/0.40 inference(pi_clausification,[],[f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y1) & (rel_s4 @ Y1 @ Y0)) => (rel_s4 @ X1 @ Y0)))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y2) & (rel_s4 @ Y2 @ Y1)) => (rel_s4 @ Y0 @ Y1))))))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y2) & (rel_s4 @ Y2 @ Y1)) => (rel_s4 @ Y0 @ Y1)))))))) = $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f154])).
% 0.14/0.40 thf(f154,plain,(
% 0.14/0.40 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s4))),
% 0.14/0.40 inference(definition_unfolding,[],[f108,f125])).
% 0.14/0.40 thf(f125,plain,(
% 0.14/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f40])).
% 0.14/0.40 thf(f40,plain,(
% 0.14/0.40 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f39])).
% 0.14/0.40 thf(f39,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X3 @ X2)))) = mtransitive)),
% 0.14/0.40 inference(rectify,[],[f21])).
% 0.14/0.40 thf(f21,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.14/0.40 thf(f108,plain,(
% 0.14/0.40 ((mtransitive @ rel_s4) = $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f84])).
% 0.14/0.40 thf(f84,plain,(
% 0.14/0.40 ((mtransitive @ rel_s4) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f83])).
% 0.14/0.40 thf(f83,plain,(
% 0.14/0.40 (mtransitive @ rel_s4)),
% 0.14/0.40 inference(rectify,[],[f35])).
% 0.14/0.40 thf(f35,axiom,(
% 0.14/0.40 (mtransitive @ rel_s4)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.14/0.40 thf(f197,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = (q @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f196,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | ($true = (q @ X1))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f195])).
% 0.14/0.40 thf(f195,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((q @ X1) | (~ (rel_s4 @ sK1 @ X1))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f194])).
% 0.14/0.40 thf(f194,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f193])).
% 0.14/0.40 thf(f193,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f192])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f175])).
% 0.14/0.40 thf(f190,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ (sK2 @ X1))) | ((rel_s4 @ sK1 @ X1) = $false) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f189])).
% 0.14/0.40 thf(f189,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (rel_s4 @ X1 @ (sK2 @ X1))) = $false) | ((p @ X1) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f186])).
% 0.14/0.40 thf(f186,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (p @ X1))) | ((~ (rel_s4 @ X1 @ (sK2 @ X1))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f185])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((q @ (sK2 @ X1)) | (~ (rel_s4 @ X1 @ (sK2 @ X1)))) = $false) | ((rel_s4 @ sK1 @ X1) = $false) | ($true = (~ (p @ X1)))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f184])).
% 0.14/0.40 thf(f184,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = (~ (p @ X1))) | (((^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK2 @ X1)) = $false)) )),
% 0.14/0.40 inference(sigma_clausification,[],[f183])).
% 0.14/0.40 thf(f183,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ($true = (~ (p @ X1))) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | ($true = (~ (p @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f181])).
% 0.14/0.40 thf(f181,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ X1 @ Y0))))))) | ($true = (~ (p @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f180])).
% 0.14/0.40 thf(f180,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (p @ X1)))) | ($true = (~ (rel_s4 @ sK1 @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f179])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (p @ X1))) | (~ (rel_s4 @ sK1 @ X1))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f178])).
% 0.14/0.40 thf(f178,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f177])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f176])).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (p @ Y0))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f245,plain,(
% 0.14/0.40 ~spl0_3),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f244])).
% 0.14/0.40 thf(f244,plain,(
% 0.14/0.40 $false | ~spl0_3),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f241])).
% 0.14/0.40 thf(f241,plain,(
% 0.14/0.40 ($true = $false) | ~spl0_3),
% 0.14/0.40 inference(superposition,[],[f202,f233])).
% 0.14/0.40 thf(f233,plain,(
% 0.14/0.40 ((p @ sK3) = $false) | ~spl0_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f231])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ($true = (p @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f201])).
% 0.14/0.40 thf(f201,plain,(
% 0.14/0.40 ((~ (p @ sK3)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f199])).
% 0.14/0.40 thf(f239,plain,(
% 0.14/0.40 spl0_3 | spl0_4),
% 0.14/0.40 inference(avatar_split_clause,[],[f216,f235,f231])).
% 0.14/0.40 thf(f216,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK3)) = $false) | ((p @ sK3) = $false)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f213])).
% 0.14/0.40 thf(f213,plain,(
% 0.14/0.40 ((q @ (sK2 @ sK3)) = $false) | ((p @ sK3) = $false) | ($true = $false)),
% 0.14/0.40 inference(superposition,[],[f188,f203])).
% 0.14/0.40 thf(f188,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((q @ (sK2 @ X1)) = $false) | ((p @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f187])).
% 0.14/0.40 thf(f187,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((q @ (sK2 @ X1)) = $false) | ($true = (~ (p @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f185])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (20019)------------------------------
% 0.14/0.40 % (20019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (20019)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (20019)Memory used [KB]: 5756
% 0.14/0.40 % (20019)Time elapsed: 0.018 s
% 0.14/0.40 % (20019)Instructions burned: 23 (million)
% 0.14/0.40 % (20019)------------------------------
% 0.14/0.40 % (20019)------------------------------
% 0.14/0.40 % (20018)Success in time 0.032 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------