TSTP Solution File: SYO464^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO464^5 : 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 : n005.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 09:04:58 EDT 2024
% Result : Theorem 0.12s 0.37s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO464^5 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.13 % 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
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 10:01:53 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 This is a TH0_THM_EQU_NAR problem
% 0.12/0.34 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
% 0.12/0.36 % (4686)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.36 % (4684)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)
% 0.12/0.36 % (4683)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.36 % (4685)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)
% 0.12/0.36 % (4688)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)
% 0.12/0.36 % (4687)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)
% 0.12/0.36 % (4686)Instruction limit reached!
% 0.12/0.36 % (4686)------------------------------
% 0.12/0.36 % (4686)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (4690)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)
% 0.12/0.36 % (4686)Termination reason: Unknown
% 0.12/0.36 % (4686)Termination phase: shuffling
% 0.12/0.36
% 0.12/0.36 % (4687)Instruction limit reached!
% 0.12/0.36 % (4687)------------------------------
% 0.12/0.36 % (4687)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (4687)Termination reason: Unknown
% 0.12/0.36 % (4687)Termination phase: shuffling
% 0.12/0.36
% 0.12/0.36 % (4687)Memory used [KB]: 1023
% 0.12/0.36 % (4687)Time elapsed: 0.003 s
% 0.12/0.36 % (4687)Instructions burned: 3 (million)
% 0.12/0.36 % (4687)------------------------------
% 0.12/0.36 % (4687)------------------------------
% 0.12/0.36 % (4686)Memory used [KB]: 1023
% 0.12/0.36 % (4686)Time elapsed: 0.003 s
% 0.12/0.36 % (4686)Instructions burned: 3 (million)
% 0.12/0.36 % (4686)------------------------------
% 0.12/0.36 % (4686)------------------------------
% 0.12/0.36 % (4689)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.36 % (4684)Instruction limit reached!
% 0.12/0.36 % (4684)------------------------------
% 0.12/0.36 % (4684)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (4684)Termination reason: Unknown
% 0.12/0.36 % (4684)Termination phase: Property scanning
% 0.12/0.36
% 0.12/0.36 % (4684)Memory used [KB]: 1023
% 0.12/0.36 % (4684)Time elapsed: 0.004 s
% 0.12/0.36 % (4684)Instructions burned: 4 (million)
% 0.12/0.36 % (4684)------------------------------
% 0.12/0.36 % (4684)------------------------------
% 0.12/0.36 % (4690)Instruction limit reached!
% 0.12/0.36 % (4690)------------------------------
% 0.12/0.36 % (4690)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (4690)Termination reason: Unknown
% 0.12/0.36 % (4690)Termination phase: shuffling
% 0.12/0.36
% 0.12/0.36 % (4690)Memory used [KB]: 1023
% 0.12/0.36 % (4690)Time elapsed: 0.003 s
% 0.12/0.36 % (4690)Instructions burned: 3 (million)
% 0.12/0.36 % (4690)------------------------------
% 0.12/0.36 % (4690)------------------------------
% 0.12/0.36 % (4688)Refutation not found, incomplete strategy
% 0.12/0.36 % (4688)------------------------------
% 0.12/0.36 % (4688)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.36 % (4688)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.36
% 0.12/0.36
% 0.12/0.36 % (4688)Memory used [KB]: 5628
% 0.12/0.36 % (4688)Time elapsed: 0.007 s
% 0.12/0.36 % (4688)Instructions burned: 11 (million)
% 0.12/0.36 % (4688)------------------------------
% 0.12/0.36 % (4688)------------------------------
% 0.12/0.37 % (4683)First to succeed.
% 0.12/0.37 % (4689)Instruction limit reached!
% 0.12/0.37 % (4689)------------------------------
% 0.12/0.37 % (4689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (4689)Termination reason: Unknown
% 0.12/0.37 % (4689)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (4689)Memory used [KB]: 5756
% 0.12/0.37 % (4689)Time elapsed: 0.013 s
% 0.12/0.37 % (4689)Instructions burned: 19 (million)
% 0.12/0.37 % (4689)------------------------------
% 0.12/0.37 % (4689)------------------------------
% 0.12/0.37 % (4691)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)
% 0.12/0.37 % (4692)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.12/0.37 % (4693)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.12/0.37 % (4683)Refutation found. Thanks to Tanya!
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37 % SZS output start Proof for theBenchmark
% 0.12/0.37 thf(type_def_5, type, mu: $tType).
% 0.12/0.37 thf(func_def_0, type, mu: $tType).
% 0.12/0.37 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.12/0.37 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_15, type, mtrue: $i > $o).
% 0.12/0.37 thf(func_def_16, type, mfalse: $i > $o).
% 0.12/0.37 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.12/0.37 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.12/0.37 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.12/0.37 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.12/0.37 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.12/0.37 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.12/0.37 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.12/0.37 thf(func_def_36, type, p: $i > $o).
% 0.12/0.37 thf(func_def_37, type, q: $i > $o).
% 0.12/0.37 thf(f301,plain,(
% 0.12/0.37 $false),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f300])).
% 0.12/0.37 thf(f300,plain,(
% 0.12/0.37 ($true = $false)),
% 0.12/0.37 inference(superposition,[],[f243,f295])).
% 0.12/0.37 thf(f295,plain,(
% 0.12/0.37 ((q @ sK3) = $true)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f289])).
% 0.12/0.37 thf(f289,plain,(
% 0.12/0.37 ((q @ sK3) = $true) | ($true = $false)),
% 0.12/0.37 inference(superposition,[],[f285,f207])).
% 0.12/0.37 thf(f207,plain,(
% 0.12/0.37 ((rel_s4 @ sK2 @ sK3) = $true)),
% 0.12/0.37 inference(not_proxy_clausification,[],[f191])).
% 0.12/0.37 thf(f191,plain,(
% 0.12/0.37 ((~ (rel_s4 @ sK2 @ sK3)) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f190])).
% 0.12/0.37 thf(f190,plain,(
% 0.12/0.37 ((((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK3 @ Y0))))))) | (~ (rel_s4 @ sK2 @ sK3))) = $false)),
% 0.12/0.37 inference(beta_eta_normalization,[],[f189])).
% 0.12/0.37 thf(f189,plain,(
% 0.12/0.37 (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK2 @ Y0)))) @ sK3) = $false)),
% 0.12/0.37 inference(sigma_clausification,[],[f188])).
% 0.12/0.37 thf(f188,plain,(
% 0.12/0.37 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK2 @ Y0))))) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f186])).
% 0.12/0.37 thf(f186,plain,(
% 0.12/0.37 (((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s4 @ Y0 @ Y1))))))) | (~ (rel_s4 @ sK2 @ Y0))))) | (~ (rel_s4 @ sK1 @ sK2))) = $false)),
% 0.12/0.37 inference(beta_eta_normalization,[],[f185])).
% 0.12/0.37 thf(f185,plain,(
% 0.12/0.37 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (rel_s4 @ sK1 @ Y0)))) @ sK2))),
% 0.12/0.37 inference(sigma_clausification,[],[f173])).
% 0.12/0.37 thf(f173,plain,(
% 0.12/0.37 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (rel_s4 @ sK1 @ Y0))))) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.12/0.37 thf(f172,plain,(
% 0.12/0.37 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (p @ Y0)) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s4 @ Y1 @ Y2))))))) | (~ (rel_s4 @ Y0 @ Y1))))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.12/0.37 inference(beta_eta_normalization,[],[f171])).
% 0.12/0.37 thf(f171,plain,(
% 0.12/0.37 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (p @ Y1)) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (q @ Y3)) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (rel_s4 @ Y0 @ Y1))))))) @ sK1) = $false)),
% 0.12/0.37 inference(sigma_clausification,[],[f170])).
% 0.12/0.37 thf(f170,plain,(
% 0.12/0.37 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (p @ Y1)) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (q @ Y3)) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (rel_s4 @ Y0 @ Y1)))))))))),
% 0.12/0.37 inference(boolean_simplification,[],[f169])).
% 0.12/0.37 thf(f169,plain,(
% 0.12/0.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((~ (p @ Y1)) | (~ (q @ Y1)))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (((~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (q @ Y3)) | (~ (rel_s4 @ Y2 @ Y3))))))) | (~ (rel_s4 @ Y1 @ Y2))))) | (~ (rel_s4 @ Y0 @ Y1)))))))) != $true)),
% 0.12/0.37 inference(beta_eta_normalization,[],[f154])).
% 0.12/0.37 thf(f154,plain,(
% 0.12/0.37 (((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[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 > $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)))) @ q)))))) != $true)),
% 0.12/0.37 inference(definition_unfolding,[],[f113,f136,f145,f125,f144,f125,f125,f145,f153,f153])).
% 0.12/0.37 thf(f153,plain,(
% 0.12/0.37 (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)))))),
% 0.12/0.37 inference(definition_unfolding,[],[f119,f111,f125,f111])).
% 0.12/0.37 thf(f111,plain,(
% 0.12/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.12/0.37 inference(cnf_transformation,[],[f64])).
% 0.12/0.37 thf(f64,plain,(
% 0.12/0.37 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.12/0.37 inference(fool_elimination,[],[f63])).
% 0.12/0.37 thf(f63,plain,(
% 0.12/0.37 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.12/0.37 inference(rectify,[],[f3])).
% 0.12/0.37 thf(f3,axiom,(
% 0.12/0.37 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.12/0.37 thf(f119,plain,(
% 0.12/0.37 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.12/0.37 inference(cnf_transformation,[],[f92])).
% 0.12/0.37 thf(f92,plain,(
% 0.12/0.37 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.12/0.37 inference(fool_elimination,[],[f91])).
% 0.12/0.37 thf(f91,plain,(
% 0.12/0.37 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.12/0.37 inference(rectify,[],[f33])).
% 0.12/0.37 thf(f33,axiom,(
% 0.12/0.37 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.12/0.37 thf(f144,plain,(
% 0.12/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.12/0.37 inference(definition_unfolding,[],[f127,f111,f134,f111,f111])).
% 0.12/0.37 thf(f134,plain,(
% 0.12/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.12/0.37 inference(cnf_transformation,[],[f98])).
% 0.12/0.37 thf(f98,plain,(
% 0.12/0.37 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.12/0.37 inference(fool_elimination,[],[f97])).
% 0.12/0.37 thf(f97,plain,(
% 0.12/0.37 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.12/0.37 inference(rectify,[],[f4])).
% 0.12/0.37 thf(f4,axiom,(
% 0.12/0.37 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.12/0.37 thf(f127,plain,(
% 0.12/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.12/0.37 inference(cnf_transformation,[],[f78])).
% 0.12/0.37 thf(f78,plain,(
% 0.12/0.37 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.12/0.37 inference(fool_elimination,[],[f77])).
% 0.12/0.37 thf(f77,plain,(
% 0.12/0.37 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.12/0.37 inference(rectify,[],[f5])).
% 0.12/0.37 thf(f5,axiom,(
% 0.12/0.37 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.12/0.37 thf(f125,plain,(
% 0.12/0.37 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.12/0.37 inference(cnf_transformation,[],[f106])).
% 0.12/0.37 thf(f106,plain,(
% 0.12/0.37 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.12/0.37 inference(fool_elimination,[],[f105])).
% 0.12/0.37 thf(f105,plain,(
% 0.12/0.37 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))) = mbox_s4)),
% 0.12/0.37 inference(rectify,[],[f32])).
% 0.12/0.37 thf(f32,axiom,(
% 0.12/0.37 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s4 @ X2 @ X7) | (X3 @ X7)))) = mbox_s4)),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.12/0.37 thf(f145,plain,(
% 0.12/0.37 (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)))))),
% 0.12/0.37 inference(definition_unfolding,[],[f121,f134,f111])).
% 0.12/0.37 thf(f121,plain,(
% 0.12/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.12/0.37 inference(cnf_transformation,[],[f70])).
% 0.12/0.37 thf(f70,plain,(
% 0.12/0.37 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.12/0.37 inference(fool_elimination,[],[f69])).
% 0.12/0.37 thf(f69,plain,(
% 0.12/0.37 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.12/0.37 inference(rectify,[],[f6])).
% 0.12/0.37 thf(f6,axiom,(
% 0.12/0.37 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.12/0.37 thf(f136,plain,(
% 0.12/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.12/0.37 inference(cnf_transformation,[],[f52])).
% 0.12/0.37 thf(f52,plain,(
% 0.12/0.37 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.12/0.37 inference(fool_elimination,[],[f51])).
% 0.12/0.37 thf(f51,plain,(
% 0.12/0.37 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.12/0.37 inference(rectify,[],[f28])).
% 0.12/0.37 thf(f28,axiom,(
% 0.12/0.37 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.12/0.37 thf(f113,plain,(
% 0.12/0.37 ((mvalid @ (mimplies @ (mbox_s4 @ (mand @ p @ q)) @ (mbox_s4 @ (mbox_s4 @ (mimplies @ (mdia_s4 @ p) @ (mdia_s4 @ q)))))) != $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f107])).
% 0.12/0.37 thf(f107,plain,(
% 0.12/0.37 ((mvalid @ (mimplies @ (mbox_s4 @ (mand @ p @ q)) @ (mbox_s4 @ (mbox_s4 @ (mimplies @ (mdia_s4 @ p) @ (mdia_s4 @ q)))))) != $true)),
% 0.12/0.37 inference(flattening,[],[f56])).
% 0.12/0.37 thf(f56,plain,(
% 0.12/0.37 ~((mvalid @ (mimplies @ (mbox_s4 @ (mand @ p @ q)) @ (mbox_s4 @ (mbox_s4 @ (mimplies @ (mdia_s4 @ p) @ (mdia_s4 @ q)))))) = $true)),
% 0.12/0.37 inference(fool_elimination,[],[f55])).
% 0.12/0.37 thf(f55,plain,(
% 0.12/0.37 ~(mvalid @ (mimplies @ (mbox_s4 @ (mand @ p @ q)) @ (mbox_s4 @ (mbox_s4 @ (mimplies @ (mdia_s4 @ p) @ (mdia_s4 @ q))))))),
% 0.12/0.37 inference(rectify,[],[f37])).
% 0.12/0.37 thf(f37,negated_conjecture,(
% 0.12/0.37 ~(mvalid @ (mimplies @ (mbox_s4 @ (mand @ p @ q)) @ (mbox_s4 @ (mbox_s4 @ (mimplies @ (mdia_s4 @ p) @ (mdia_s4 @ q))))))),
% 0.12/0.37 inference(negated_conjecture,[],[f36])).
% 0.12/0.37 thf(f36,conjecture,(
% 0.12/0.37 (mvalid @ (mimplies @ (mbox_s4 @ (mand @ p @ q)) @ (mbox_s4 @ (mbox_s4 @ (mimplies @ (mdia_s4 @ p) @ (mdia_s4 @ q))))))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.12/0.37 thf(f285,plain,(
% 0.12/0.37 ( ! [X0 : $i] : (((rel_s4 @ sK2 @ X0) = $false) | ((q @ X0) = $true)) )),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f278])).
% 0.12/0.37 thf(f278,plain,(
% 0.12/0.37 ( ! [X0 : $i] : (((q @ X0) = $true) | ((rel_s4 @ sK2 @ X0) = $false) | ($true = $false)) )),
% 0.12/0.37 inference(superposition,[],[f208,f234])).
% 0.12/0.37 thf(f234,plain,(
% 0.12/0.37 ( ! [X0 : $i,X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((rel_s4 @ X1 @ X0) = $false) | ((q @ X0) = $true)) )),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f225])).
% 0.12/0.37 thf(f225,plain,(
% 0.12/0.37 ( ! [X0 : $i,X1 : $i] : (((q @ X0) = $true) | ((rel_s4 @ sK1 @ X1) = $false) | ($true = $false) | ((rel_s4 @ X1 @ X0) = $false)) )),
% 0.12/0.37 inference(superposition,[],[f165,f184])).
% 0.12/0.37 thf(f184,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((q @ X1) = $true)) )),
% 0.12/0.37 inference(not_proxy_clausification,[],[f181])).
% 0.12/0.37 thf(f181,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (($false = (~ (q @ X1))) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f180])).
% 0.12/0.37 thf(f180,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((~ (p @ X1)) | (~ (q @ X1))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.12/0.37 inference(not_proxy_clausification,[],[f179])).
% 0.12/0.37 thf(f179,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((~ ((~ (p @ X1)) | (~ (q @ X1)))) = $true) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.12/0.37 inference(not_proxy_clausification,[],[f178])).
% 0.12/0.37 thf(f178,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((~ (rel_s4 @ sK1 @ X1)) = $true) | ((~ ((~ (p @ X1)) | (~ (q @ X1)))) = $true)) )),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f177])).
% 0.12/0.37 thf(f177,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((~ ((~ (p @ X1)) | (~ (q @ X1)))) | (~ (rel_s4 @ sK1 @ X1))) = $true)) )),
% 0.12/0.37 inference(beta_eta_normalization,[],[f176])).
% 0.12/0.37 thf(f176,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ ((~ (p @ Y0)) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.12/0.37 inference(pi_clausification,[],[f175])).
% 0.12/0.37 thf(f175,plain,(
% 0.12/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (p @ Y0)) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0))))))),
% 0.12/0.37 inference(not_proxy_clausification,[],[f174])).
% 0.12/0.37 thf(f174,plain,(
% 0.12/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (p @ Y0)) | (~ (q @ Y0)))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f172])).
% 0.12/0.37 thf(f165,plain,(
% 0.12/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s4 @ X1 @ X2)) | ((rel_s4 @ X1 @ X3) = $false) | ((rel_s4 @ X3 @ X2) = $false)) )),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f164])).
% 0.12/0.37 thf(f164,plain,(
% 0.12/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((rel_s4 @ X3 @ X2) & (rel_s4 @ X1 @ X3))) | ($true = (rel_s4 @ X1 @ X2))) )),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f163])).
% 0.12/0.37 thf(f163,plain,(
% 0.12/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s4 @ X3 @ X2) & (rel_s4 @ X1 @ X3)) => (rel_s4 @ X1 @ X2)))) )),
% 0.12/0.37 inference(beta_eta_normalization,[],[f162])).
% 0.12/0.37 thf(f162,plain,(
% 0.12/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s4 @ Y0 @ X2) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X1 @ X2))) @ X3) = $true)) )),
% 0.12/0.37 inference(pi_clausification,[],[f161])).
% 0.12/0.37 thf(f161,plain,(
% 0.12/0.37 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ Y0 @ X2) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ X1 @ X2)))))) )),
% 0.12/0.37 inference(beta_eta_normalization,[],[f160])).
% 0.12/0.37 thf(f160,plain,(
% 0.12/0.37 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ X1 @ Y1)) => (rel_s4 @ X1 @ Y0))))) @ X2))) )),
% 0.12/0.37 inference(pi_clausification,[],[f159])).
% 0.12/0.37 thf(f159,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ Y0) & (rel_s4 @ X1 @ Y1)) => (rel_s4 @ X1 @ Y0)))))) = $true)) )),
% 0.12/0.37 inference(beta_eta_normalization,[],[f158])).
% 0.12/0.37 thf(f158,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y1) & (rel_s4 @ Y0 @ Y2)) => (rel_s4 @ Y0 @ Y1))))))) @ X1) = $true)) )),
% 0.12/0.37 inference(pi_clausification,[],[f157])).
% 0.12/0.37 thf(f157,plain,(
% 0.12/0.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y1) & (rel_s4 @ Y0 @ Y2)) => (rel_s4 @ Y0 @ Y1)))))))) = $true)),
% 0.12/0.37 inference(beta_eta_normalization,[],[f155])).
% 0.12/0.37 thf(f155,plain,(
% 0.12/0.37 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s4))),
% 0.12/0.37 inference(definition_unfolding,[],[f130,f120])).
% 0.12/0.37 thf(f120,plain,(
% 0.12/0.37 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.12/0.37 inference(cnf_transformation,[],[f44])).
% 0.12/0.37 thf(f44,plain,(
% 0.12/0.37 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.12/0.37 inference(fool_elimination,[],[f43])).
% 0.12/0.37 thf(f43,plain,(
% 0.12/0.37 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))))),
% 0.12/0.37 inference(rectify,[],[f21])).
% 0.12/0.37 thf(f21,axiom,(
% 0.12/0.37 (mtransitive = (^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.12/0.37 thf(f130,plain,(
% 0.12/0.37 ((mtransitive @ rel_s4) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f48])).
% 0.12/0.37 thf(f48,plain,(
% 0.12/0.37 ((mtransitive @ rel_s4) = $true)),
% 0.12/0.37 inference(fool_elimination,[],[f47])).
% 0.12/0.37 thf(f47,plain,(
% 0.12/0.37 (mtransitive @ rel_s4)),
% 0.12/0.37 inference(rectify,[],[f35])).
% 0.12/0.37 thf(f35,axiom,(
% 0.12/0.37 (mtransitive @ rel_s4)),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.12/0.37 thf(f208,plain,(
% 0.12/0.37 ($true = (rel_s4 @ sK1 @ sK2))),
% 0.12/0.37 inference(not_proxy_clausification,[],[f187])).
% 0.12/0.37 thf(f187,plain,(
% 0.12/0.37 ((~ (rel_s4 @ sK1 @ sK2)) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f186])).
% 0.12/0.37 thf(f243,plain,(
% 0.12/0.37 ((q @ sK3) = $false)),
% 0.12/0.37 inference(trivial_inequality_removal,[],[f238])).
% 0.12/0.37 thf(f238,plain,(
% 0.12/0.37 ($true = $false) | ((q @ sK3) = $false)),
% 0.12/0.37 inference(superposition,[],[f168,f206])).
% 0.12/0.37 thf(f206,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.12/0.37 inference(not_proxy_clausification,[],[f205])).
% 0.12/0.37 thf(f205,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((rel_s4 @ sK3 @ X1) = $false) | ($true = (~ (q @ X1)))) )),
% 0.12/0.37 inference(not_proxy_clausification,[],[f204])).
% 0.12/0.37 thf(f204,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((~ (rel_s4 @ sK3 @ X1)) = $true) | ($true = (~ (q @ X1)))) )),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f203])).
% 0.12/0.37 thf(f203,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((~ (q @ X1)) | (~ (rel_s4 @ sK3 @ X1))) = $true)) )),
% 0.12/0.37 inference(beta_eta_normalization,[],[f202])).
% 0.12/0.37 thf(f202,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK3 @ Y0)))) @ X1) = $true)) )),
% 0.12/0.37 inference(pi_clausification,[],[f201])).
% 0.12/0.37 thf(f201,plain,(
% 0.12/0.37 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK3 @ Y0))))) = $true)),
% 0.12/0.37 inference(not_proxy_clausification,[],[f193])).
% 0.12/0.37 thf(f193,plain,(
% 0.12/0.37 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK3 @ Y0)))))) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f192])).
% 0.12/0.37 thf(f192,plain,(
% 0.12/0.37 (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK3 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s4 @ sK3 @ Y0))))))) = $false)),
% 0.12/0.37 inference(binary_proxy_clausification,[],[f190])).
% 0.12/0.37 thf(f168,plain,(
% 0.12/0.37 ( ! [X1 : $i] : (((rel_s4 @ X1 @ X1) = $true)) )),
% 0.12/0.37 inference(beta_eta_normalization,[],[f167])).
% 0.12/0.37 thf(f167,plain,(
% 0.12/0.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1) = $true)) )),
% 0.12/0.37 inference(pi_clausification,[],[f166])).
% 0.12/0.37 thf(f166,plain,(
% 0.12/0.37 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 0.12/0.37 inference(beta_eta_normalization,[],[f156])).
% 0.12/0.37 thf(f156,plain,(
% 0.12/0.37 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4) = $true)),
% 0.12/0.37 inference(definition_unfolding,[],[f133,f114])).
% 0.12/0.37 thf(f114,plain,(
% 0.12/0.37 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.12/0.37 inference(cnf_transformation,[],[f62])).
% 0.12/0.37 thf(f62,plain,(
% 0.12/0.37 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.12/0.37 inference(fool_elimination,[],[f61])).
% 0.12/0.37 thf(f61,plain,(
% 0.12/0.37 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.12/0.37 inference(rectify,[],[f18])).
% 0.12/0.37 thf(f18,axiom,(
% 0.12/0.37 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.12/0.37 thf(f133,plain,(
% 0.12/0.37 ((mreflexive @ rel_s4) = $true)),
% 0.12/0.37 inference(cnf_transformation,[],[f50])).
% 0.12/0.37 thf(f50,plain,(
% 0.12/0.37 ((mreflexive @ rel_s4) = $true)),
% 0.12/0.37 inference(fool_elimination,[],[f49])).
% 0.12/0.37 thf(f49,plain,(
% 0.12/0.37 (mreflexive @ rel_s4)),
% 0.12/0.37 inference(rectify,[],[f34])).
% 0.12/0.37 thf(f34,axiom,(
% 0.12/0.37 (mreflexive @ rel_s4)),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.12/0.37 % SZS output end Proof for theBenchmark
% 0.12/0.37 % (4683)------------------------------
% 0.12/0.37 % (4683)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (4683)Termination reason: Refutation
% 0.12/0.37
% 0.12/0.37 % (4683)Memory used [KB]: 5756
% 0.12/0.37 % (4683)Time elapsed: 0.016 s
% 0.12/0.37 % (4683)Instructions burned: 22 (million)
% 0.12/0.37 % (4683)------------------------------
% 0.12/0.37 % (4683)------------------------------
% 0.12/0.37 % (4682)Success in time 0.037 s
% 0.12/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------