TSTP Solution File: SYO432^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO432^1 : 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 : 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 09:04:25 EDT 2024
% Result : Theorem 0.48s 0.56s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO432^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14 % 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 : n005.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 08:34:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 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
% 0.22/0.37 ipcrm: permission denied for id (1712291841)
% 0.22/0.37 ipcrm: permission denied for id (1712324611)
% 0.22/0.38 ipcrm: permission denied for id (1712390152)
% 0.22/0.38 ipcrm: permission denied for id (1712488459)
% 0.22/0.38 ipcrm: permission denied for id (1712521228)
% 0.22/0.39 ipcrm: permission denied for id (1712586766)
% 0.22/0.40 ipcrm: permission denied for id (1712717847)
% 0.22/0.41 ipcrm: permission denied for id (1712816158)
% 0.22/0.41 ipcrm: permission denied for id (1712881699)
% 0.22/0.43 ipcrm: permission denied for id (1713012783)
% 0.22/0.43 ipcrm: permission denied for id (1713045555)
% 0.22/0.43 ipcrm: permission denied for id (1713078325)
% 0.22/0.44 ipcrm: permission denied for id (1713209401)
% 0.22/0.45 ipcrm: permission denied for id (1713274944)
% 0.22/0.45 ipcrm: permission denied for id (1713307713)
% 0.22/0.45 ipcrm: permission denied for id (1713340483)
% 0.22/0.46 ipcrm: permission denied for id (1713504329)
% 0.22/0.46 ipcrm: permission denied for id (1713537098)
% 0.22/0.47 ipcrm: permission denied for id (1713635408)
% 0.22/0.48 ipcrm: permission denied for id (1713733722)
% 0.22/0.48 ipcrm: permission denied for id (1713766492)
% 0.22/0.48 ipcrm: permission denied for id (1713799261)
% 0.22/0.49 ipcrm: permission denied for id (1713864801)
% 0.22/0.49 ipcrm: permission denied for id (1713930339)
% 0.22/0.50 ipcrm: permission denied for id (1713963113)
% 0.22/0.50 ipcrm: permission denied for id (1713995882)
% 0.22/0.50 ipcrm: permission denied for id (1714061420)
% 0.22/0.51 ipcrm: permission denied for id (1714094190)
% 0.22/0.51 ipcrm: permission denied for id (1714126960)
% 0.22/0.51 ipcrm: permission denied for id (1714192501)
% 0.22/0.52 ipcrm: permission denied for id (1714225270)
% 0.22/0.52 ipcrm: permission denied for id (1714323579)
% 0.22/0.52 ipcrm: permission denied for id (1714356348)
% 0.22/0.53 ipcrm: permission denied for id (1714421886)
% 0.22/0.54 % (28175)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2998ds/18Mi)
% 0.22/0.54 % (28173)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 (2998ds/2Mi)
% 0.22/0.54 % (28171)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 (2998ds/27Mi)
% 0.22/0.54 % (28172)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2998ds/2Mi)
% 0.22/0.55 % (28174)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 (2998ds/275Mi)
% 0.22/0.55 % (28176)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.22/0.55 % (28172)Instruction limit reached!
% 0.22/0.55 % (28172)------------------------------
% 0.22/0.55 % (28172)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (28172)Termination reason: Unknown
% 0.22/0.55 % (28172)Termination phase: shuffling
% 0.22/0.55
% 0.22/0.55 % (28172)Memory used [KB]: 1023
% 0.22/0.55 % (28172)Time elapsed: 0.003 s
% 0.22/0.55 % (28172)Instructions burned: 2 (million)
% 0.22/0.55 % (28172)------------------------------
% 0.22/0.55 % (28172)------------------------------
% 0.22/0.55 % (28173)Instruction limit reached!
% 0.22/0.55 % (28173)------------------------------
% 0.22/0.55 % (28173)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (28173)Termination reason: Unknown
% 0.22/0.55 % (28173)Termination phase: shuffling
% 0.22/0.55
% 0.22/0.55 % (28173)Memory used [KB]: 1023
% 0.22/0.55 % (28173)Time elapsed: 0.003 s
% 0.22/0.55 % (28173)Instructions burned: 2 (million)
% 0.22/0.55 % (28173)------------------------------
% 0.22/0.55 % (28173)------------------------------
% 0.22/0.55 % (28176)Instruction limit reached!
% 0.22/0.55 % (28176)------------------------------
% 0.22/0.55 % (28176)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.55 % (28176)Termination reason: Unknown
% 0.22/0.55 % (28176)Termination phase: shuffling
% 0.22/0.55
% 0.22/0.55 % (28176)Memory used [KB]: 1023
% 0.22/0.55 % (28176)Time elapsed: 0.003 s
% 0.22/0.55 % (28176)Instructions burned: 3 (million)
% 0.22/0.55 % (28176)------------------------------
% 0.22/0.55 % (28176)------------------------------
% 0.22/0.55 % (28169)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2998ds/183Mi)
% 0.48/0.55 % (28174)Refutation not found, incomplete strategy
% 0.48/0.55 % (28174)------------------------------
% 0.48/0.55 % (28174)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.48/0.55 % (28174)Termination reason: Refutation not found, incomplete strategy
% 0.48/0.55
% 0.48/0.55
% 0.48/0.55 % (28174)Memory used [KB]: 5628
% 0.48/0.55 % (28174)Time elapsed: 0.011 s
% 0.48/0.55 % (28174)Instructions burned: 13 (million)
% 0.48/0.55 % (28174)------------------------------
% 0.48/0.55 % (28174)------------------------------
% 0.48/0.55 % (28175)Instruction limit reached!
% 0.48/0.55 % (28175)------------------------------
% 0.48/0.55 % (28175)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.48/0.55 % (28175)Termination reason: Unknown
% 0.48/0.55 % (28175)Termination phase: Saturation
% 0.48/0.55
% 0.48/0.55 % (28175)Memory used [KB]: 5628
% 0.48/0.55 % (28175)Time elapsed: 0.013 s
% 0.48/0.55 % (28175)Instructions burned: 19 (million)
% 0.48/0.55 % (28175)------------------------------
% 0.48/0.55 % (28175)------------------------------
% 0.48/0.56 % (28171)First to succeed.
% 0.48/0.56 % (28170)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 (2998ds/4Mi)
% 0.48/0.56 % (28177)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 (2998ds/37Mi)
% 0.48/0.56 % (28170)Instruction limit reached!
% 0.48/0.56 % (28170)------------------------------
% 0.48/0.56 % (28170)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.48/0.56 % (28170)Termination reason: Unknown
% 0.48/0.56 % (28170)Termination phase: shuffling
% 0.48/0.56
% 0.48/0.56 % (28170)Memory used [KB]: 1023
% 0.48/0.56 % (28170)Time elapsed: 0.004 s
% 0.48/0.56 % (28170)Instructions burned: 4 (million)
% 0.48/0.56 % (28170)------------------------------
% 0.48/0.56 % (28170)------------------------------
% 0.48/0.56 % (28169)Also succeeded, but the first one will report.
% 0.48/0.56 % (28178)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 (2998ds/15Mi)
% 0.48/0.56 % (28171)Refutation found. Thanks to Tanya!
% 0.48/0.56 % SZS status Theorem for theBenchmark
% 0.48/0.56 % SZS output start Proof for theBenchmark
% 0.48/0.56 thf(type_def_5, type, mu: $tType).
% 0.48/0.56 thf(func_def_0, type, mu: $tType).
% 0.48/0.56 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.48/0.56 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_15, type, mtrue: $i > $o).
% 0.48/0.56 thf(func_def_16, type, mfalse: $i > $o).
% 0.48/0.56 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.48/0.56 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.48/0.56 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.48/0.56 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.48/0.56 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.48/0.56 thf(func_def_33, type, rel_b: $i > $i > $o).
% 0.48/0.56 thf(func_def_34, type, mbox_b: ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_35, type, mdia_b: ($i > $o) > $i > $o).
% 0.48/0.56 thf(func_def_36, type, p: $i > $o).
% 0.48/0.56 thf(func_def_37, type, q: $i > $o).
% 0.48/0.56 thf(func_def_38, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.48/0.56 thf(func_def_57, type, sK3: $i > $i).
% 0.48/0.56 thf(f284,plain,(
% 0.48/0.56 $false),
% 0.48/0.56 inference(trivial_inequality_removal,[],[f283])).
% 0.48/0.56 thf(f283,plain,(
% 0.48/0.56 ($false = $true)),
% 0.48/0.56 inference(forward_demodulation,[],[f282,f166])).
% 0.48/0.56 thf(f166,plain,(
% 0.48/0.56 ((q @ sK2) = $false)),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f164])).
% 0.48/0.56 thf(f164,plain,(
% 0.48/0.56 (((q @ sK2) | (~ (rel_b @ sK1 @ sK2))) = $false)),
% 0.48/0.56 inference(beta_eta_normalization,[],[f163])).
% 0.48/0.56 thf(f163,plain,(
% 0.48/0.56 ($false = ((^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ sK2))),
% 0.48/0.56 inference(sigma_clausification,[],[f162])).
% 0.48/0.56 thf(f162,plain,(
% 0.48/0.56 ($false = (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))))),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f160])).
% 0.48/0.56 thf(f160,plain,(
% 0.48/0.56 (((!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_b @ sK1 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: (((q @ Y2) | (~ (p @ Y2))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))) = $false)),
% 0.48/0.56 inference(beta_eta_normalization,[],[f159])).
% 0.48/0.56 thf(f159,plain,(
% 0.48/0.56 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: (((q @ Y3) | (~ (p @ Y3))) | (~ (rel_b @ Y2 @ Y3)))))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1))))))))) @ sK1) = $false)),
% 0.48/0.56 inference(sigma_clausification,[],[f158])).
% 0.48/0.56 thf(f158,plain,(
% 0.48/0.56 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: (((q @ Y3) | (~ (p @ Y3))) | (~ (rel_b @ Y2 @ Y3)))))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))))))) != $true)),
% 0.48/0.56 inference(boolean_simplification,[],[f157])).
% 0.48/0.56 thf(f157,plain,(
% 0.48/0.56 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_b @ Y0 @ Y1))))) | (~ (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: (((q @ Y3) | (~ (p @ Y3))) | (~ (rel_b @ Y2 @ Y3)))))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_b @ Y0 @ Y1)))))))))))) != $true)),
% 0.48/0.56 inference(beta_eta_normalization,[],[f155])).
% 0.48/0.56 thf(f155,plain,(
% 0.48/0.56 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ 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 @ q))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))) @ q))) != $true)),
% 0.48/0.56 inference(definition_unfolding,[],[f117,f114,f145,f144,f128,f128,f153,f128,f145,f128])).
% 0.48/0.56 thf(f153,plain,(
% 0.48/0.56 (mdia_b = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_b @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.48/0.56 inference(definition_unfolding,[],[f116,f110,f128,f110])).
% 0.48/0.56 thf(f110,plain,(
% 0.48/0.56 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.48/0.56 inference(cnf_transformation,[],[f71])).
% 0.48/0.56 thf(f71,plain,(
% 0.48/0.56 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.48/0.56 inference(fool_elimination,[],[f70])).
% 0.48/0.56 thf(f70,plain,(
% 0.48/0.56 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.48/0.56 inference(rectify,[],[f3])).
% 0.48/0.56 thf(f3,axiom,(
% 0.48/0.56 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.48/0.56 thf(f116,plain,(
% 0.48/0.56 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.48/0.56 inference(cnf_transformation,[],[f87])).
% 0.48/0.56 thf(f87,plain,(
% 0.48/0.56 (mdia_b = (^[Y0 : $i > $o]: (mnot @ (mbox_b @ (mnot @ Y0)))))),
% 0.48/0.56 inference(fool_elimination,[],[f86])).
% 0.48/0.56 thf(f86,plain,(
% 0.48/0.56 ((^[X0 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X0)))) = mdia_b)),
% 0.48/0.56 inference(rectify,[],[f33])).
% 0.48/0.56 thf(f33,axiom,(
% 0.48/0.56 ((^[X3 : $i > $o] : (mnot @ (mbox_b @ (mnot @ X3)))) = mdia_b)),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_b)).
% 0.48/0.56 thf(f128,plain,(
% 0.48/0.56 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.48/0.56 inference(cnf_transformation,[],[f83])).
% 0.48/0.56 thf(f83,plain,(
% 0.48/0.56 (mbox_b = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_b @ Y1 @ Y2)))))))))),
% 0.48/0.56 inference(fool_elimination,[],[f82])).
% 0.48/0.56 thf(f82,plain,(
% 0.48/0.56 (mbox_b = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_b @ X1 @ X2) | (X0 @ X2)))))),
% 0.48/0.56 inference(rectify,[],[f32])).
% 0.48/0.56 thf(f32,axiom,(
% 0.48/0.56 (mbox_b = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_b @ X2 @ X7) | (X3 @ X7)))))),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_b)).
% 0.48/0.56 thf(f144,plain,(
% 0.48/0.56 (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)))))))),
% 0.48/0.56 inference(definition_unfolding,[],[f139,f110,f112,f110,f110])).
% 0.48/0.56 thf(f112,plain,(
% 0.48/0.56 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.48/0.56 inference(cnf_transformation,[],[f77])).
% 0.48/0.56 thf(f77,plain,(
% 0.48/0.56 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.48/0.56 inference(fool_elimination,[],[f76])).
% 0.48/0.56 thf(f76,plain,(
% 0.48/0.56 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.48/0.56 inference(rectify,[],[f4])).
% 0.48/0.56 thf(f4,axiom,(
% 0.48/0.56 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.48/0.56 thf(f139,plain,(
% 0.48/0.56 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.48/0.56 inference(cnf_transformation,[],[f42])).
% 0.48/0.56 thf(f42,plain,(
% 0.48/0.56 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.48/0.56 inference(fool_elimination,[],[f41])).
% 0.48/0.56 thf(f41,plain,(
% 0.48/0.56 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.48/0.56 inference(rectify,[],[f5])).
% 0.48/0.56 thf(f5,axiom,(
% 0.48/0.56 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.48/0.56 thf(f145,plain,(
% 0.48/0.56 (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)))))),
% 0.48/0.56 inference(definition_unfolding,[],[f132,f112,f110])).
% 0.48/0.56 thf(f132,plain,(
% 0.48/0.56 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.48/0.56 inference(cnf_transformation,[],[f69])).
% 0.48/0.56 thf(f69,plain,(
% 0.48/0.56 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.48/0.56 inference(fool_elimination,[],[f68])).
% 0.48/0.56 thf(f68,plain,(
% 0.48/0.56 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.48/0.56 inference(rectify,[],[f6])).
% 0.48/0.56 thf(f6,axiom,(
% 0.48/0.56 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.48/0.56 thf(f114,plain,(
% 0.48/0.56 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.48/0.56 inference(cnf_transformation,[],[f55])).
% 0.48/0.56 thf(f55,plain,(
% 0.48/0.56 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.48/0.56 inference(fool_elimination,[],[f54])).
% 0.48/0.56 thf(f54,plain,(
% 0.48/0.56 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.48/0.56 inference(rectify,[],[f28])).
% 0.48/0.56 thf(f28,axiom,(
% 0.48/0.56 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.48/0.56 thf(f117,plain,(
% 0.48/0.56 ((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mdia_b @ (mbox_b @ (mimplies @ p @ q))))) @ (mbox_b @ q))) != $true)),
% 0.48/0.56 inference(cnf_transformation,[],[f107])).
% 0.48/0.56 thf(f107,plain,(
% 0.48/0.56 ((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mdia_b @ (mbox_b @ (mimplies @ p @ q))))) @ (mbox_b @ q))) != $true)),
% 0.48/0.56 inference(flattening,[],[f50])).
% 0.48/0.56 thf(f50,plain,(
% 0.48/0.56 ~((mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mdia_b @ (mbox_b @ (mimplies @ p @ q))))) @ (mbox_b @ q))) = $true)),
% 0.48/0.56 inference(fool_elimination,[],[f49])).
% 0.48/0.56 thf(f49,plain,(
% 0.48/0.56 ~(mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mdia_b @ (mbox_b @ (mimplies @ p @ q))))) @ (mbox_b @ q)))),
% 0.48/0.56 inference(rectify,[],[f37])).
% 0.48/0.56 thf(f37,negated_conjecture,(
% 0.48/0.56 ~(mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mdia_b @ (mbox_b @ (mimplies @ p @ q))))) @ (mbox_b @ q)))),
% 0.48/0.56 inference(negated_conjecture,[],[f36])).
% 0.48/0.56 thf(f36,conjecture,(
% 0.48/0.56 (mvalid @ (mimplies @ (mand @ (mbox_b @ p) @ (mbox_b @ (mdia_b @ (mbox_b @ (mimplies @ p @ q))))) @ (mbox_b @ q)))),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.48/0.56 thf(f282,plain,(
% 0.48/0.56 ((q @ sK2) = $true)),
% 0.48/0.56 inference(trivial_inequality_removal,[],[f281])).
% 0.48/0.56 thf(f281,plain,(
% 0.48/0.56 ($false = $true) | ((q @ sK2) = $true)),
% 0.48/0.56 inference(forward_demodulation,[],[f266,f218])).
% 0.48/0.56 thf(f218,plain,(
% 0.48/0.56 ((p @ sK2) = $true)),
% 0.48/0.56 inference(trivial_inequality_removal,[],[f214])).
% 0.48/0.56 thf(f214,plain,(
% 0.48/0.56 ($false = $true) | ((p @ sK2) = $true)),
% 0.48/0.56 inference(superposition,[],[f192,f167])).
% 0.48/0.56 thf(f167,plain,(
% 0.48/0.56 ((rel_b @ sK1 @ sK2) = $true)),
% 0.48/0.56 inference(not_proxy_clausification,[],[f165])).
% 0.48/0.56 thf(f165,plain,(
% 0.48/0.56 ($false = (~ (rel_b @ sK1 @ sK2)))),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f164])).
% 0.48/0.56 thf(f192,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((p @ X1) = $true)) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f191])).
% 0.48/0.56 thf(f191,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((p @ X1) = $true) | ((~ (rel_b @ sK1 @ X1)) = $true)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f190])).
% 0.48/0.56 thf(f190,plain,(
% 0.48/0.56 ( ! [X1 : $i] : ((((p @ X1) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.48/0.56 inference(beta_eta_normalization,[],[f189])).
% 0.48/0.56 thf(f189,plain,(
% 0.48/0.56 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.48/0.56 inference(pi_clausification,[],[f188])).
% 0.48/0.56 thf(f188,plain,(
% 0.48/0.56 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.48/0.56 inference(not_proxy_clausification,[],[f168])).
% 0.48/0.56 thf(f168,plain,(
% 0.48/0.56 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0)))))))),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f161])).
% 0.48/0.56 thf(f161,plain,(
% 0.48/0.56 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: (((q @ Y2) | (~ (p @ Y2))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_b @ sK1 @ Y0))))))))),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f160])).
% 0.48/0.56 thf(f266,plain,(
% 0.48/0.56 ($false = (p @ sK2)) | ((q @ sK2) = $true)),
% 0.48/0.56 inference(trivial_inequality_removal,[],[f258])).
% 0.48/0.56 thf(f258,plain,(
% 0.48/0.56 ($false = (p @ sK2)) | ($false = $true) | ((q @ sK2) = $true)),
% 0.48/0.56 inference(superposition,[],[f254,f167])).
% 0.48/0.56 thf(f254,plain,(
% 0.48/0.56 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ((q @ X0) = $true) | ((p @ X0) = $false)) )),
% 0.48/0.56 inference(trivial_inequality_removal,[],[f253])).
% 0.48/0.56 thf(f253,plain,(
% 0.48/0.56 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ((q @ X0) = $true) | ($false = $true) | ((p @ X0) = $false)) )),
% 0.48/0.56 inference(duplicate_literal_removal,[],[f247])).
% 0.48/0.56 thf(f247,plain,(
% 0.48/0.56 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ((p @ X0) = $false) | ($false = (rel_b @ sK1 @ X0)) | ($false = $true) | ((q @ X0) = $true)) )),
% 0.48/0.56 inference(superposition,[],[f227,f186])).
% 0.48/0.56 thf(f186,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (((rel_b @ (sK3 @ X1) @ X2) = $false) | ((rel_b @ sK1 @ X1) = $false) | ((q @ X2) = $true) | ($false = (p @ X2))) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f185])).
% 0.48/0.56 thf(f185,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (((rel_b @ (sK3 @ X1) @ X2) = $false) | ((~ (p @ X2)) = $true) | ((rel_b @ sK1 @ X1) = $false) | ((q @ X2) = $true)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f184])).
% 0.48/0.56 thf(f184,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (((rel_b @ (sK3 @ X1) @ X2) = $false) | ((rel_b @ sK1 @ X1) = $false) | (((q @ X2) | (~ (p @ X2))) = $true)) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f183])).
% 0.48/0.56 thf(f183,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((~ (rel_b @ (sK3 @ X1) @ X2)) = $true) | (((q @ X2) | (~ (p @ X2))) = $true)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f182])).
% 0.48/0.56 thf(f182,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((((q @ X2) | (~ (p @ X2))) | (~ (rel_b @ (sK3 @ X1) @ X2))) = $true)) )),
% 0.48/0.56 inference(beta_eta_normalization,[],[f181])).
% 0.48/0.56 thf(f181,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | (((^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_b @ (sK3 @ X1) @ Y0)))) @ X2) = $true)) )),
% 0.48/0.56 inference(pi_clausification,[],[f180])).
% 0.48/0.56 thf(f180,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_b @ (sK3 @ X1) @ Y0))))) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f179])).
% 0.48/0.56 thf(f179,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_b @ (sK3 @ X1) @ Y0)))))) = $false)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f177])).
% 0.48/0.56 thf(f177,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((rel_b @ sK1 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (((q @ Y0) | (~ (p @ Y0))) | (~ (rel_b @ (sK3 @ X1) @ Y0)))))) | (~ (rel_b @ X1 @ (sK3 @ X1)))) = $false)) )),
% 0.48/0.56 inference(beta_eta_normalization,[],[f176])).
% 0.48/0.56 thf(f176,plain,(
% 0.48/0.56 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ X1 @ Y0)))) @ (sK3 @ X1)) = $false) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.48/0.56 inference(sigma_clausification,[],[f175])).
% 0.48/0.56 thf(f175,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ X1 @ Y0))))) = $false) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f174])).
% 0.48/0.56 thf(f174,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ X1 @ Y0)))))) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f173])).
% 0.48/0.56 thf(f173,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((~ (rel_b @ sK1 @ X1)) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ X1 @ Y0)))))) = $true)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f172])).
% 0.48/0.56 thf(f172,plain,(
% 0.48/0.56 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: (((q @ Y1) | (~ (p @ Y1))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ X1 @ Y0)))))) | (~ (rel_b @ sK1 @ X1))) = $true)) )),
% 0.48/0.56 inference(beta_eta_normalization,[],[f171])).
% 0.48/0.56 thf(f171,plain,(
% 0.48/0.56 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: (((q @ Y2) | (~ (p @ Y2))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.48/0.56 inference(pi_clausification,[],[f170])).
% 0.48/0.56 thf(f170,plain,(
% 0.48/0.56 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: (((q @ Y2) | (~ (p @ Y2))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0))))) = $true)),
% 0.48/0.56 inference(not_proxy_clausification,[],[f169])).
% 0.48/0.56 thf(f169,plain,(
% 0.48/0.56 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: (((q @ Y2) | (~ (p @ Y2))) | (~ (rel_b @ Y1 @ Y2)))))) | (~ (rel_b @ Y0 @ Y1)))))) | (~ (rel_b @ sK1 @ Y0)))))) = $false)),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f161])).
% 0.48/0.56 thf(f227,plain,(
% 0.48/0.56 ( ! [X0 : $i] : (((rel_b @ (sK3 @ X0) @ X0) = $true) | ($false = (rel_b @ sK1 @ X0))) )),
% 0.48/0.56 inference(trivial_inequality_removal,[],[f222])).
% 0.48/0.56 thf(f222,plain,(
% 0.48/0.56 ( ! [X0 : $i] : (($false = (rel_b @ sK1 @ X0)) | ((rel_b @ (sK3 @ X0) @ X0) = $true) | ($false = $true)) )),
% 0.48/0.56 inference(superposition,[],[f187,f201])).
% 0.48/0.56 thf(f201,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : (($false = (rel_b @ X1 @ X2)) | ((rel_b @ X2 @ X1) = $true)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f200])).
% 0.48/0.56 thf(f200,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : ((((rel_b @ X1 @ X2) => (rel_b @ X2 @ X1)) = $true)) )),
% 0.48/0.56 inference(beta_eta_normalization,[],[f199])).
% 0.48/0.56 thf(f199,plain,(
% 0.48/0.56 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_b @ X1 @ Y0) => (rel_b @ Y0 @ X1))) @ X2) = $true)) )),
% 0.48/0.56 inference(pi_clausification,[],[f198])).
% 0.48/0.56 thf(f198,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_b @ X1 @ Y0) => (rel_b @ Y0 @ X1)))) = $true)) )),
% 0.48/0.56 inference(beta_eta_normalization,[],[f197])).
% 0.48/0.56 thf(f197,plain,(
% 0.48/0.56 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y0 @ Y1) => (rel_b @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.48/0.56 inference(pi_clausification,[],[f196])).
% 0.48/0.56 thf(f196,plain,(
% 0.48/0.56 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_b @ Y0 @ Y1) => (rel_b @ Y1 @ Y0)))))) = $true)),
% 0.48/0.56 inference(beta_eta_normalization,[],[f156])).
% 0.48/0.56 thf(f156,plain,(
% 0.48/0.56 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_b))),
% 0.48/0.56 inference(definition_unfolding,[],[f123,f135])).
% 0.48/0.56 thf(f135,plain,(
% 0.48/0.56 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.48/0.56 inference(cnf_transformation,[],[f63])).
% 0.48/0.56 thf(f63,plain,(
% 0.48/0.56 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.48/0.56 inference(fool_elimination,[],[f62])).
% 0.48/0.56 thf(f62,plain,(
% 0.48/0.56 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.48/0.56 inference(rectify,[],[f19])).
% 0.48/0.56 thf(f19,axiom,(
% 0.48/0.56 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.48/0.56 thf(f123,plain,(
% 0.48/0.56 ((msymmetric @ rel_b) = $true)),
% 0.48/0.56 inference(cnf_transformation,[],[f85])).
% 0.48/0.56 thf(f85,plain,(
% 0.48/0.56 ((msymmetric @ rel_b) = $true)),
% 0.48/0.56 inference(fool_elimination,[],[f84])).
% 0.48/0.56 thf(f84,plain,(
% 0.48/0.56 (msymmetric @ rel_b)),
% 0.48/0.56 inference(rectify,[],[f35])).
% 0.48/0.56 thf(f35,axiom,(
% 0.48/0.56 (msymmetric @ rel_b)),
% 0.48/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.48/0.56 thf(f187,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((rel_b @ X1 @ (sK3 @ X1)) = $true) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.48/0.56 inference(not_proxy_clausification,[],[f178])).
% 0.48/0.56 thf(f178,plain,(
% 0.48/0.56 ( ! [X1 : $i] : (((~ (rel_b @ X1 @ (sK3 @ X1))) = $false) | ((rel_b @ sK1 @ X1) = $false)) )),
% 0.48/0.56 inference(binary_proxy_clausification,[],[f177])).
% 0.48/0.56 % SZS output end Proof for theBenchmark
% 0.48/0.56 % (28171)------------------------------
% 0.48/0.56 % (28171)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.48/0.56 % (28171)Termination reason: Refutation
% 0.48/0.56
% 0.48/0.56 % (28171)Memory used [KB]: 5756
% 0.48/0.56 % (28171)Time elapsed: 0.018 s
% 0.48/0.56 % (28171)Instructions burned: 20 (million)
% 0.48/0.56 % (28171)------------------------------
% 0.48/0.56 % (28171)------------------------------
% 0.48/0.56 % (28035)Success in time 0.199 s
% 0.48/0.56 % Vampire---4.8 exiting
%------------------------------------------------------------------------------