TSTP Solution File: SYO474^6 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO474^6 : 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/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 09:05:21 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO474^6 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.15 % 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
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 10:00:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % (1708)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.15/0.40 % (1707)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.40 % (1709)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.15/0.40 % (1710)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40 % (1711)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)
% 0.22/0.40 % (1713)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.40 % (1712)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)
% 0.22/0.40 % (1710)Instruction limit reached!
% 0.22/0.40 % (1710)------------------------------
% 0.22/0.40 % (1710)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (1710)Termination reason: Unknown
% 0.22/0.40 % (1710)Termination phase: shuffling
% 0.22/0.40 % (1711)Instruction limit reached!
% 0.22/0.40 % (1711)------------------------------
% 0.22/0.40 % (1711)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40
% 0.22/0.40 % (1710)Memory used [KB]: 1023
% 0.22/0.40 % (1710)Time elapsed: 0.004 s
% 0.22/0.40 % (1710)Instructions burned: 2 (million)
% 0.22/0.40 % (1710)------------------------------
% 0.22/0.40 % (1710)------------------------------
% 0.22/0.40 % (1711)Termination reason: Unknown
% 0.22/0.40 % (1711)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (1711)Memory used [KB]: 1023
% 0.22/0.40 % (1711)Time elapsed: 0.004 s
% 0.22/0.40 % (1711)Instructions burned: 2 (million)
% 0.22/0.40 % (1711)------------------------------
% 0.22/0.40 % (1711)------------------------------
% 0.22/0.40 % (1714)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)
% 0.22/0.40 % (1708)Instruction limit reached!
% 0.22/0.40 % (1708)------------------------------
% 0.22/0.40 % (1708)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (1708)Termination reason: Unknown
% 0.22/0.40 % (1708)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (1708)Memory used [KB]: 1023
% 0.22/0.40 % (1708)Time elapsed: 0.006 s
% 0.22/0.40 % (1708)Instructions burned: 4 (million)
% 0.22/0.40 % (1708)------------------------------
% 0.22/0.40 % (1708)------------------------------
% 0.22/0.40 % (1714)Instruction limit reached!
% 0.22/0.40 % (1714)------------------------------
% 0.22/0.40 % (1714)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (1714)Termination reason: Unknown
% 0.22/0.40 % (1714)Termination phase: shuffling
% 0.22/0.40
% 0.22/0.40 % (1714)Memory used [KB]: 1023
% 0.22/0.40 % (1714)Time elapsed: 0.005 s
% 0.22/0.40 % (1714)Instructions burned: 3 (million)
% 0.22/0.40 % (1714)------------------------------
% 0.22/0.40 % (1714)------------------------------
% 0.22/0.42 % (1713)Instruction limit reached!
% 0.22/0.42 % (1713)------------------------------
% 0.22/0.42 % (1713)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (1713)Termination reason: Unknown
% 0.22/0.42 % (1713)Termination phase: Saturation
% 0.22/0.42
% 0.22/0.42 % (1713)Memory used [KB]: 5628
% 0.22/0.42 % (1713)Time elapsed: 0.019 s
% 0.22/0.42 % (1713)Instructions burned: 18 (million)
% 0.22/0.42 % (1713)------------------------------
% 0.22/0.42 % (1713)------------------------------
% 0.22/0.42 % (1712)Refutation not found, incomplete strategy
% 0.22/0.42 % (1712)------------------------------
% 0.22/0.42 % (1712)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (1712)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.42
% 0.22/0.42
% 0.22/0.42 % (1712)Memory used [KB]: 5628
% 0.22/0.42 % (1712)Time elapsed: 0.021 s
% 0.22/0.42 % (1712)Instructions burned: 19 (million)
% 0.22/0.42 % (1712)------------------------------
% 0.22/0.42 % (1712)------------------------------
% 0.22/0.42 % (1707)First to succeed.
% 0.22/0.43 % (1709)Instruction limit reached!
% 0.22/0.43 % (1709)------------------------------
% 0.22/0.43 % (1709)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (1709)Termination reason: Unknown
% 0.22/0.43 % (1709)Termination phase: Saturation
% 0.22/0.43
% 0.22/0.43 % (1709)Memory used [KB]: 5756
% 0.22/0.43 % (1709)Time elapsed: 0.029 s
% 0.22/0.43 % (1709)Instructions burned: 27 (million)
% 0.22/0.43 % (1709)------------------------------
% 0.22/0.43 % (1709)------------------------------
% 0.22/0.43 % (1715)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)
% 0.22/0.43 % (1716)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)
% 0.22/0.43 % (1717)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)
% 0.22/0.43 % (1707)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% 0.22/0.43 thf(type_def_5, type, mu: $tType).
% 0.22/0.43 thf(func_def_0, type, mu: $tType).
% 0.22/0.43 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.43 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.43 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.43 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.43 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.22/0.43 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.22/0.43 thf(func_def_36, type, p: $i > $o).
% 0.22/0.43 thf(func_def_56, type, sK4: $i > $i).
% 0.22/0.43 thf(func_def_57, type, sK5: $i > $i).
% 0.22/0.43 thf(f344,plain,(
% 0.22/0.43 $false),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f343])).
% 0.22/0.43 thf(f343,plain,(
% 0.22/0.43 ($false = $true)),
% 0.22/0.43 inference(superposition,[],[f190,f339])).
% 0.22/0.43 thf(f339,plain,(
% 0.22/0.43 ((p @ sK2) = $true)),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f331])).
% 0.22/0.43 thf(f331,plain,(
% 0.22/0.43 ($false = $true) | ((p @ sK2) = $true)),
% 0.22/0.43 inference(superposition,[],[f325,f192])).
% 0.22/0.43 thf(f192,plain,(
% 0.22/0.43 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.22/0.43 inference(not_proxy_clausification,[],[f191])).
% 0.22/0.43 thf(f191,plain,(
% 0.22/0.43 ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f189])).
% 0.22/0.43 thf(f189,plain,(
% 0.22/0.43 ($false = ((~ (rel_s5 @ sK1 @ sK2)) | (p @ sK2)))),
% 0.22/0.43 inference(beta_eta_normalization,[],[f188])).
% 0.22/0.43 thf(f188,plain,(
% 0.22/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0))) @ sK2) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f187])).
% 0.22/0.43 thf(f187,plain,(
% 0.22/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0)))))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f185])).
% 0.22/0.43 thf(f185,plain,(
% 0.22/0.43 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f183])).
% 0.22/0.43 thf(f183,plain,(
% 0.22/0.43 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (p @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))) | (~ (p @ Y1))))))))))))))),
% 0.22/0.43 inference(beta_eta_normalization,[],[f182])).
% 0.22/0.43 thf(f182,plain,(
% 0.22/0.43 (((^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))) | (~ (p @ Y2)))))))))))))) @ sK1) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f181])).
% 0.22/0.43 thf(f181,plain,(
% 0.22/0.43 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))) | (~ (p @ Y2))))))))))))))) != $true)),
% 0.22/0.43 inference(boolean_simplification,[],[f180])).
% 0.22/0.43 thf(f180,plain,(
% 0.22/0.43 ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (p @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (p @ Y3)))) | (~ (p @ Y2))))))))))))))) != $true)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f160])).
% 0.22/0.43 thf(f160,plain,(
% 0.22/0.43 (((^[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]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p))) @ ((^[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]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))) != $true)),
% 0.22/0.43 inference(definition_unfolding,[],[f127,f145,f149,f135,f149,f135,f149,f135,f135,f149,f157,f135,f135])).
% 0.22/0.43 thf(f157,plain,(
% 0.22/0.43 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.22/0.43 inference(definition_unfolding,[],[f139,f147,f135,f147])).
% 0.22/0.43 thf(f147,plain,(
% 0.22/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f86])).
% 0.22/0.43 thf(f86,plain,(
% 0.22/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.43 inference(fool_elimination,[],[f85])).
% 0.22/0.43 thf(f85,plain,(
% 0.22/0.43 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.22/0.43 inference(rectify,[],[f3])).
% 0.22/0.43 thf(f3,axiom,(
% 0.22/0.43 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.22/0.43 thf(f139,plain,(
% 0.22/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.22/0.43 inference(cnf_transformation,[],[f66])).
% 0.22/0.43 thf(f66,plain,(
% 0.22/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.22/0.43 inference(fool_elimination,[],[f65])).
% 0.22/0.43 thf(f65,plain,(
% 0.22/0.43 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.22/0.43 inference(rectify,[],[f33])).
% 0.22/0.43 thf(f33,axiom,(
% 0.22/0.43 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.22/0.43 thf(f135,plain,(
% 0.22/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f56])).
% 0.22/0.43 thf(f56,plain,(
% 0.22/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f55])).
% 0.22/0.43 thf(f55,plain,(
% 0.22/0.43 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))))),
% 0.22/0.43 inference(rectify,[],[f32])).
% 0.22/0.43 thf(f32,axiom,(
% 0.22/0.43 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.22/0.43 thf(f149,plain,(
% 0.22/0.43 (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)))))),
% 0.22/0.43 inference(definition_unfolding,[],[f129,f142,f147])).
% 0.22/0.43 thf(f142,plain,(
% 0.22/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f90])).
% 0.22/0.43 thf(f90,plain,(
% 0.22/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f89])).
% 0.22/0.43 thf(f89,plain,(
% 0.22/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.22/0.43 inference(rectify,[],[f4])).
% 0.22/0.43 thf(f4,axiom,(
% 0.22/0.43 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.22/0.43 thf(f129,plain,(
% 0.22/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.43 inference(cnf_transformation,[],[f64])).
% 0.22/0.43 thf(f64,plain,(
% 0.22/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.43 inference(fool_elimination,[],[f63])).
% 0.22/0.43 thf(f63,plain,(
% 0.22/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.22/0.43 inference(rectify,[],[f6])).
% 0.22/0.43 thf(f6,axiom,(
% 0.22/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.43 thf(f145,plain,(
% 0.22/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.43 inference(cnf_transformation,[],[f94])).
% 0.22/0.43 thf(f94,plain,(
% 0.22/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.43 inference(fool_elimination,[],[f93])).
% 0.22/0.43 thf(f93,plain,(
% 0.22/0.43 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.22/0.43 inference(rectify,[],[f28])).
% 0.22/0.43 thf(f28,axiom,(
% 0.22/0.43 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.43 thf(f127,plain,(
% 0.22/0.43 ((mvalid @ (mimplies @ (mbox_s5 @ (mimplies @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ p))) @ (mbox_s5 @ p))) @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mbox_s5 @ p)))) != $true)),
% 0.22/0.43 inference(cnf_transformation,[],[f110])).
% 0.22/0.43 thf(f110,plain,(
% 0.22/0.43 ((mvalid @ (mimplies @ (mbox_s5 @ (mimplies @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ p))) @ (mbox_s5 @ p))) @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mbox_s5 @ p)))) != $true)),
% 0.22/0.43 inference(flattening,[],[f76])).
% 0.22/0.43 thf(f76,plain,(
% 0.22/0.43 ~((mvalid @ (mimplies @ (mbox_s5 @ (mimplies @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ p))) @ (mbox_s5 @ p))) @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mbox_s5 @ p)))) = $true)),
% 0.22/0.43 inference(fool_elimination,[],[f75])).
% 0.22/0.43 thf(f75,plain,(
% 0.22/0.43 ~(mvalid @ (mimplies @ (mbox_s5 @ (mimplies @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ p))) @ (mbox_s5 @ p))) @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mbox_s5 @ p))))),
% 0.22/0.43 inference(rectify,[],[f38])).
% 0.22/0.43 thf(f38,negated_conjecture,(
% 0.22/0.43 ~(mvalid @ (mimplies @ (mbox_s5 @ (mimplies @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ p))) @ (mbox_s5 @ p))) @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mbox_s5 @ p))))),
% 0.22/0.43 inference(negated_conjecture,[],[f37])).
% 0.22/0.43 thf(f37,conjecture,(
% 0.22/0.43 (mvalid @ (mimplies @ (mbox_s5 @ (mimplies @ (mbox_s5 @ (mimplies @ p @ (mbox_s5 @ p))) @ (mbox_s5 @ p))) @ (mimplies @ (mdia_s5 @ (mbox_s5 @ p)) @ (mbox_s5 @ p))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.22/0.43 thf(f325,plain,(
% 0.22/0.43 ( ! [X0 : $i] : (((rel_s5 @ sK1 @ X0) = $false) | ((p @ X0) = $true)) )),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f312])).
% 0.22/0.43 thf(f312,plain,(
% 0.22/0.43 ( ! [X0 : $i] : (($false = $true) | ((rel_s5 @ sK1 @ X0) = $false) | ((p @ X0) = $true)) )),
% 0.22/0.43 inference(superposition,[],[f269,f202])).
% 0.22/0.43 thf(f202,plain,(
% 0.22/0.43 ( ! [X1 : $i] : (($false = (rel_s5 @ sK3 @ X1)) | ($true = (p @ X1))) )),
% 0.22/0.43 inference(not_proxy_clausification,[],[f201])).
% 0.22/0.43 thf(f201,plain,(
% 0.22/0.43 ( ! [X1 : $i] : (($true = (p @ X1)) | ((~ (rel_s5 @ sK3 @ X1)) = $true)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f200])).
% 0.22/0.43 thf(f200,plain,(
% 0.22/0.43 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK3 @ X1)) | (p @ X1)) = $true)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f199])).
% 0.22/0.43 thf(f199,plain,(
% 0.22/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0))) @ X1) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f198])).
% 0.22/0.43 thf(f198,plain,(
% 0.22/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0)))))),
% 0.22/0.43 inference(not_proxy_clausification,[],[f195])).
% 0.22/0.43 thf(f195,plain,(
% 0.22/0.43 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0))))))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f194])).
% 0.22/0.43 thf(f194,plain,(
% 0.22/0.43 ($false = ((~ (rel_s5 @ sK1 @ sK3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (p @ Y0)))))))),
% 0.22/0.43 inference(beta_eta_normalization,[],[f193])).
% 0.22/0.43 thf(f193,plain,(
% 0.22/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK3) = $false)),
% 0.22/0.43 inference(sigma_clausification,[],[f186])).
% 0.22/0.43 thf(f186,plain,(
% 0.22/0.43 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (p @ Y1)))))))))),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f185])).
% 0.22/0.43 thf(f269,plain,(
% 0.22/0.43 ( ! [X0 : $i] : (((rel_s5 @ sK3 @ X0) = $true) | ((rel_s5 @ sK1 @ X0) = $false)) )),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f257])).
% 0.22/0.43 thf(f257,plain,(
% 0.22/0.43 ( ! [X0 : $i] : (($false = $true) | ((rel_s5 @ sK3 @ X0) = $true) | ((rel_s5 @ sK1 @ X0) = $false)) )),
% 0.22/0.43 inference(superposition,[],[f240,f170])).
% 0.22/0.43 thf(f170,plain,(
% 0.22/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (rel_s5 @ X1 @ X3)) | ((rel_s5 @ X1 @ X2) = $true) | ((rel_s5 @ X3 @ X2) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f169])).
% 0.22/0.43 thf(f169,plain,(
% 0.22/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s5 @ X1 @ X2) = $true) | (((rel_s5 @ X3 @ X2) & (rel_s5 @ X1 @ X3)) = $false)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f168])).
% 0.22/0.43 thf(f168,plain,(
% 0.22/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X3 @ X2) & (rel_s5 @ X1 @ X3)) => (rel_s5 @ X1 @ X2)) = $true)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f167])).
% 0.22/0.43 thf(f167,plain,(
% 0.22/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s5 @ Y0 @ X2) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ X1 @ X2))) @ X3) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f166])).
% 0.22/0.43 thf(f166,plain,(
% 0.22/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ Y0 @ X2) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ X1 @ X2)))) = $true)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f165])).
% 0.22/0.43 thf(f165,plain,(
% 0.22/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ X1 @ Y1)) => (rel_s5 @ X1 @ Y0))))) @ X2) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f164])).
% 0.22/0.43 thf(f164,plain,(
% 0.22/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ X1 @ Y1)) => (rel_s5 @ X1 @ Y0)))))) = $true)) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f163])).
% 0.22/0.43 thf(f163,plain,(
% 0.22/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y1) & (rel_s5 @ Y0 @ Y2)) => (rel_s5 @ Y0 @ Y1))))))) @ X1) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f162])).
% 0.22/0.43 thf(f162,plain,(
% 0.22/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y2 @ Y1) & (rel_s5 @ Y0 @ Y2)) => (rel_s5 @ Y0 @ Y1)))))))) = $true)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f161])).
% 0.22/0.43 thf(f161,plain,(
% 0.22/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s5) = $true)),
% 0.22/0.43 inference(definition_unfolding,[],[f144,f134])).
% 0.22/0.43 thf(f134,plain,(
% 0.22/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f96])).
% 0.22/0.43 thf(f96,plain,(
% 0.22/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f95])).
% 0.22/0.43 thf(f95,plain,(
% 0.22/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))) = mtransitive)),
% 0.22/0.43 inference(rectify,[],[f21])).
% 0.22/0.43 thf(f21,axiom,(
% 0.22/0.43 ((^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.22/0.43 thf(f144,plain,(
% 0.22/0.43 ((mtransitive @ rel_s5) = $true)),
% 0.22/0.43 inference(cnf_transformation,[],[f107])).
% 0.22/0.43 thf(f107,plain,(
% 0.22/0.43 ((mtransitive @ rel_s5) = $true)),
% 0.22/0.43 inference(fool_elimination,[],[f106])).
% 0.22/0.43 thf(f106,plain,(
% 0.22/0.43 (mtransitive @ rel_s5)),
% 0.22/0.43 inference(rectify,[],[f35])).
% 0.22/0.43 thf(f35,axiom,(
% 0.22/0.43 (mtransitive @ rel_s5)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.22/0.43 thf(f240,plain,(
% 0.22/0.43 ((rel_s5 @ sK3 @ sK1) = $true)),
% 0.22/0.43 inference(trivial_inequality_removal,[],[f234])).
% 0.22/0.43 thf(f234,plain,(
% 0.22/0.43 ((rel_s5 @ sK3 @ sK1) = $true) | ($false = $true)),
% 0.22/0.43 inference(superposition,[],[f179,f197])).
% 0.22/0.43 thf(f197,plain,(
% 0.22/0.43 ((rel_s5 @ sK1 @ sK3) = $true)),
% 0.22/0.43 inference(not_proxy_clausification,[],[f196])).
% 0.22/0.43 thf(f196,plain,(
% 0.22/0.43 ((~ (rel_s5 @ sK1 @ sK3)) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f194])).
% 0.22/0.43 thf(f179,plain,(
% 0.22/0.43 ( ! [X2 : $i,X1 : $i] : (((rel_s5 @ X2 @ X1) = $false) | ((rel_s5 @ X1 @ X2) = $true)) )),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f178])).
% 0.22/0.43 thf(f178,plain,(
% 0.22/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)))) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f177])).
% 0.22/0.43 thf(f177,plain,(
% 0.22/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f176])).
% 0.22/0.43 thf(f176,plain,(
% 0.22/0.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))))) )),
% 0.22/0.43 inference(beta_eta_normalization,[],[f175])).
% 0.22/0.43 thf(f175,plain,(
% 0.22/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 0.22/0.43 inference(pi_clausification,[],[f174])).
% 0.22/0.43 thf(f174,plain,(
% 0.22/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))) = $true)),
% 0.22/0.43 inference(beta_eta_normalization,[],[f159])).
% 0.22/0.43 thf(f159,plain,(
% 0.22/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5) = $true)),
% 0.22/0.43 inference(definition_unfolding,[],[f119,f122])).
% 0.22/0.43 thf(f122,plain,(
% 0.22/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.22/0.43 inference(cnf_transformation,[],[f84])).
% 0.22/0.43 thf(f84,plain,(
% 0.22/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.22/0.43 inference(fool_elimination,[],[f83])).
% 0.22/0.43 thf(f83,plain,(
% 0.22/0.43 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))))),
% 0.22/0.43 inference(rectify,[],[f19])).
% 0.22/0.43 thf(f19,axiom,(
% 0.22/0.43 (msymmetric = (^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.22/0.43 thf(f119,plain,(
% 0.22/0.43 ((msymmetric @ rel_s5) = $true)),
% 0.22/0.43 inference(cnf_transformation,[],[f46])).
% 0.22/0.43 thf(f46,plain,(
% 0.22/0.43 ((msymmetric @ rel_s5) = $true)),
% 0.22/0.43 inference(fool_elimination,[],[f45])).
% 0.22/0.43 thf(f45,plain,(
% 0.22/0.43 (msymmetric @ rel_s5)),
% 0.22/0.43 inference(rectify,[],[f36])).
% 0.22/0.43 thf(f36,axiom,(
% 0.22/0.43 (msymmetric @ rel_s5)),
% 0.22/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.22/0.43 thf(f190,plain,(
% 0.22/0.43 ((p @ sK2) = $false)),
% 0.22/0.43 inference(binary_proxy_clausification,[],[f189])).
% 0.22/0.43 % SZS output end Proof for theBenchmark
% 0.22/0.43 % (1707)------------------------------
% 0.22/0.43 % (1707)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (1707)Termination reason: Refutation
% 0.22/0.43
% 0.22/0.43 % (1707)Memory used [KB]: 5756
% 0.22/0.43 % (1707)Time elapsed: 0.032 s
% 0.22/0.43 % (1707)Instructions burned: 23 (million)
% 0.22/0.43 % (1707)------------------------------
% 0.22/0.43 % (1707)------------------------------
% 0.22/0.43 % (1706)Success in time 0.043 s
% 0.22/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------