TSTP Solution File: SEU472^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU472^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n023.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 03:49:02 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU472^1 : TPTP v8.2.0. Released v3.6.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n023.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 : Sun May 19 18:09:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (15787)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.37 % (15788)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (15789)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (15792)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (15788)Instruction limit reached!
% 0.14/0.37 % (15788)------------------------------
% 0.14/0.37 % (15788)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15788)Termination reason: Unknown
% 0.14/0.37 % (15788)Termination phase: shuffling
% 0.14/0.37 % (15789)Instruction limit reached!
% 0.14/0.37 % (15789)------------------------------
% 0.14/0.37 % (15789)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37
% 0.14/0.37 % (15788)Memory used [KB]: 1023
% 0.14/0.37 % (15788)Time elapsed: 0.003 s
% 0.14/0.37 % (15788)Instructions burned: 3 (million)
% 0.14/0.37 % (15788)------------------------------
% 0.14/0.37 % (15788)------------------------------
% 0.14/0.37 % (15789)Termination reason: Unknown
% 0.14/0.37 % (15789)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (15789)Memory used [KB]: 1023
% 0.14/0.37 % (15789)Time elapsed: 0.003 s
% 0.14/0.37 % (15789)Instructions burned: 3 (million)
% 0.14/0.37 % (15789)------------------------------
% 0.14/0.37 % (15789)------------------------------
% 0.14/0.37 % (15792)Instruction limit reached!
% 0.14/0.37 % (15792)------------------------------
% 0.14/0.37 % (15792)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15792)Termination reason: Unknown
% 0.14/0.37 % (15792)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (15792)Memory used [KB]: 1023
% 0.14/0.37 % (15792)Time elapsed: 0.003 s
% 0.14/0.37 % (15792)Instructions burned: 3 (million)
% 0.14/0.37 % (15792)------------------------------
% 0.14/0.37 % (15792)------------------------------
% 0.14/0.37 % (15786)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (15786)Instruction limit reached!
% 0.14/0.37 % (15786)------------------------------
% 0.14/0.37 % (15786)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (15786)Termination reason: Unknown
% 0.14/0.37 % (15786)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (15786)Memory used [KB]: 1023
% 0.14/0.37 % (15786)Time elapsed: 0.005 s
% 0.14/0.37 % (15786)Instructions burned: 5 (million)
% 0.14/0.37 % (15786)------------------------------
% 0.14/0.37 % (15786)------------------------------
% 0.14/0.38 % (15787)First to succeed.
% 0.14/0.38 % (15787)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.14/0.38 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.14/0.38 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.14/0.38 thf(func_def_30, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.14/0.38 thf(func_def_49, type, sK1: $i > $i > $o).
% 0.14/0.38 thf(func_def_52, type, sK4: $i > $i > $o).
% 0.14/0.38 thf(func_def_53, type, sK5: $i > $i > $o).
% 0.14/0.38 thf(f215,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f214])).
% 0.14/0.38 thf(f214,plain,(
% 0.14/0.38 ($false = $true)),
% 0.14/0.38 inference(backward_demodulation,[],[f146,f199])).
% 0.14/0.38 thf(f199,plain,(
% 0.14/0.38 ((sK1 @ sK2 @ sK3) = $false)),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f198])).
% 0.14/0.38 thf(f198,plain,(
% 0.14/0.38 ((sK1 @ sK2 @ sK3) = $false) | ($false = $true)),
% 0.14/0.38 inference(superposition,[],[f175,f191])).
% 0.14/0.38 thf(f191,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (sK5 @ X1 @ X2)) | ($false = (sK1 @ X1 @ X2))) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f190])).
% 0.14/0.38 thf(f190,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1 @ X2) => (sK5 @ X1 @ X2)) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f189])).
% 0.14/0.38 thf(f189,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK1 @ X1 @ Y0) => (sK5 @ X1 @ Y0))) @ X2))) )),
% 0.14/0.38 inference(pi_clausification,[],[f188])).
% 0.14/0.38 thf(f188,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ X1 @ Y0) => (sK5 @ X1 @ Y0)))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f187])).
% 0.14/0.38 thf(f187,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f177])).
% 0.14/0.38 thf(f177,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1)))))) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f176])).
% 0.14/0.38 thf(f176,plain,(
% 0.14/0.38 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y1 @ Y0)) => (sK5 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))))) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.38 thf(f174,plain,(
% 0.14/0.38 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y1 @ Y0)) => (sK5 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (sK5 @ Y0 @ Y1))))))) => (sK5 @ sK2 @ sK3)) = $false)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f173])).
% 0.14/0.38 thf(f173,plain,(
% 0.14/0.38 ($false = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK3))) @ sK5))),
% 0.14/0.38 inference(sigma_clausification,[],[f172])).
% 0.14/0.38 thf(f172,plain,(
% 0.14/0.38 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK3)))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f147])).
% 0.14/0.38 thf(f147,plain,(
% 0.14/0.38 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK3)))) | (sK2 = sK3)) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f145])).
% 0.14/0.38 thf(f145,plain,(
% 0.14/0.38 ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK2)))) | (sK3 = sK2)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK3)))) | (sK2 = sK3))) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f144])).
% 0.14/0.38 thf(f144,plain,(
% 0.14/0.38 (((sK1 @ sK2 @ sK3) => (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK3 @ sK2)))) | (sK3 = sK2)) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y1 @ Y2) => (Y0 @ Y1 @ Y2))))))) => (Y0 @ sK2 @ sK3)))) | (sK2 = sK3)))) = $false)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f143])).
% 0.14/0.38 thf(f143,plain,(
% 0.14/0.38 (((^[Y0 : $i]: ((sK1 @ sK2 @ Y0) => (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK2)))) | (Y0 = sK2)) | ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK2 @ Y0)))) | (sK2 = Y0))))) @ sK3) = $false)),
% 0.14/0.38 inference(sigma_clausification,[],[f142])).
% 0.14/0.38 thf(f142,plain,(
% 0.14/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ sK2 @ Y0) => (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ Y0 @ sK2)))) | (Y0 = sK2)) | ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))) => (Y1 @ sK2 @ Y0)))) | (sK2 = Y0)))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f141])).
% 0.14/0.38 thf(f141,plain,(
% 0.14/0.38 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0)))) | (Y1 = Y0)) | ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (Y0 = Y1))))))) @ sK2))),
% 0.14/0.38 inference(sigma_clausification,[],[f140])).
% 0.14/0.38 thf(f140,plain,(
% 0.14/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y0 @ Y1) => (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y1 @ Y0)))) | (Y1 = Y0)) | ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5)))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y3 @ Y4) => (Y2 @ Y3 @ Y4))))))) => (Y2 @ Y0 @ Y1)))) | (Y0 = Y1)))))))))),
% 0.14/0.38 inference(beta_eta_normalization,[],[f139])).
% 0.14/0.38 thf(f139,plain,(
% 0.14/0.38 ($false = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1)))) | (Y2 = Y1)) | ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (Y1 = Y2))))))))) @ sK1))),
% 0.14/0.38 inference(sigma_clausification,[],[f138])).
% 0.14/0.38 thf(f138,plain,(
% 0.14/0.38 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y2 @ Y1)))) | (Y2 = Y1)) | ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6)))))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))) => (Y3 @ Y1 @ Y2)))) | (Y1 = Y2)))))))))) != $true)),
% 0.14/0.38 inference(beta_eta_normalization,[],[f137])).
% 0.14/0.38 thf(f137,plain,(
% 0.14/0.38 ($true != ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))))) @ Y1 @ (Y0 @ Y1))))) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (Y1 @ Y2 @ Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y2 = Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) @ Y4) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))))) @ Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f107,f122,f126])).
% 0.14/0.38 thf(f126,plain,(
% 0.14/0.38 (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (Y1 @ Y2 @ Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (Y2 = Y3))))))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) @ Y4) & ((^[Y5 : $i > $i > $o]: ((^[Y6 : $i > $i > $o]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y5 @ Y7 @ Y8) => (Y6 @ Y7 @ Y8))))))))) @ Y1 @ Y4)) => (Y4 @ Y2 @ Y3))))))))) @ Y0)))))),
% 0.14/0.38 inference(definition_unfolding,[],[f116,f108,f118,f124])).
% 0.14/0.38 thf(f124,plain,(
% 0.14/0.38 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y6 @ Y7) => (Y5 @ Y6 @ Y7))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f103,f112,f117])).
% 0.14/0.38 thf(f117,plain,(
% 0.14/0.38 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f56])).
% 0.14/0.38 thf(f56,plain,(
% 0.14/0.38 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y2 @ Y3))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f55])).
% 0.14/0.38 thf(f55,plain,(
% 0.14/0.38 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X3 @ X2) => (X1 @ X3 @ X2)))))),
% 0.14/0.38 inference(rectify,[],[f1])).
% 0.14/0.38 thf(f1,axiom,(
% 0.14/0.38 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X3,X2] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subrel)).
% 0.14/0.38 thf(f112,plain,(
% 0.14/0.38 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f64])).
% 0.14/0.38 thf(f64,plain,(
% 0.14/0.38 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f63])).
% 0.14/0.38 thf(f63,plain,(
% 0.14/0.38 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X1)) => (X0 @ X2 @ X1)))) = trans)),
% 0.14/0.38 inference(rectify,[],[f13])).
% 0.14/0.38 thf(f13,axiom,(
% 0.14/0.38 ((^[X0 : $i > $i > $o] : (! [X5,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))) = trans)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive)).
% 0.14/0.38 thf(f103,plain,(
% 0.14/0.38 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f69])).
% 0.14/0.38 thf(f69,plain,(
% 0.14/0.38 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f68])).
% 0.14/0.38 thf(f68,plain,(
% 0.14/0.38 (tc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))))),
% 0.14/0.38 inference(rectify,[],[f14])).
% 0.14/0.38 thf(f14,axiom,(
% 0.14/0.38 (tc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)))))),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure)).
% 0.14/0.38 thf(f118,plain,(
% 0.14/0.38 (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f71])).
% 0.14/0.38 thf(f71,plain,(
% 0.14/0.38 (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y1 = Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f70])).
% 0.14/0.38 thf(f70,plain,(
% 0.14/0.38 ((^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : ((X1 = X2) | (X0 @ X1 @ X2))) = rc)),
% 0.14/0.38 inference(rectify,[],[f8])).
% 0.14/0.38 thf(f8,axiom,(
% 0.14/0.38 ((^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : ((X2 = X3) | (X0 @ X2 @ X3))) = rc)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexive_closure)).
% 0.14/0.38 thf(f108,plain,(
% 0.14/0.38 (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f36])).
% 0.14/0.38 thf(f36,plain,(
% 0.14/0.38 (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (Y0 @ Y1 @ Y2))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f35])).
% 0.14/0.38 thf(f35,plain,(
% 0.14/0.38 ((^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : ((X0 @ X1 @ X2) | (X0 @ X2 @ X1))) = sc)),
% 0.14/0.38 inference(rectify,[],[f12])).
% 0.14/0.38 thf(f12,axiom,(
% 0.14/0.38 ((^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : ((X0 @ X2 @ X3) | (X0 @ X3 @ X2))) = sc)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_closure)).
% 0.14/0.38 thf(f116,plain,(
% 0.14/0.38 (trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 0.14/0.38 inference(cnf_transformation,[],[f65])).
% 0.14/0.38 thf(f65,plain,(
% 0.14/0.38 (trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 0.14/0.38 inference(fool_elimination,[],[f16])).
% 0.14/0.38 thf(f16,axiom,(
% 0.14/0.38 ((^[X0 : $i > $i > $o] : (sc @ (rc @ (tc @ X0)))) = trsc)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure)).
% 0.14/0.38 thf(f122,plain,(
% 0.14/0.38 (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y4 @ Y5) => (Y3 @ Y4 @ Y5))))))))) @ Y1 @ (Y0 @ Y1))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f111,f117])).
% 0.14/0.38 thf(f111,plain,(
% 0.14/0.38 (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (subrel @ Y1 @ (Y0 @ Y1))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f83])).
% 0.14/0.38 thf(f83,plain,(
% 0.14/0.38 (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (subrel @ Y1 @ (Y0 @ Y1))))))),
% 0.14/0.38 inference(fool_elimination,[],[f82])).
% 0.14/0.38 thf(f82,plain,(
% 0.14/0.38 ((^[X0 : ($i > $i > $o) > $i > $i > $o] : (! [X1 : $i > $i > $o] : (subrel @ X1 @ (X0 @ X1)))) = infl)),
% 0.14/0.38 inference(rectify,[],[f4])).
% 0.14/0.38 thf(f4,axiom,(
% 0.14/0.38 ((^[X4 : ($i > $i > $o) > $i > $i > $o] : (! [X0 : $i > $i > $o] : (subrel @ X0 @ (X4 @ X0)))) = infl)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inflationary)).
% 0.14/0.38 thf(f107,plain,(
% 0.14/0.38 ((infl @ trsc) != $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f91])).
% 0.14/0.38 thf(f91,plain,(
% 0.14/0.38 ((infl @ trsc) != $true)),
% 0.14/0.38 inference(flattening,[],[f77])).
% 0.14/0.38 thf(f77,plain,(
% 0.14/0.38 ~((infl @ trsc) = $true)),
% 0.14/0.38 inference(fool_elimination,[],[f76])).
% 0.14/0.38 thf(f76,plain,(
% 0.14/0.38 ~(infl @ trsc)),
% 0.14/0.38 inference(rectify,[],[f31])).
% 0.14/0.38 thf(f31,negated_conjecture,(
% 0.14/0.38 ~(infl @ trsc)),
% 0.14/0.38 inference(negated_conjecture,[],[f30])).
% 0.14/0.38 thf(f30,conjecture,(
% 0.14/0.38 (infl @ trsc)),
% 0.14/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure_op_is_inflationary)).
% 0.14/0.38 thf(f175,plain,(
% 0.14/0.38 ((sK5 @ sK2 @ sK3) = $false)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f174])).
% 0.14/0.38 thf(f146,plain,(
% 0.14/0.38 ((sK1 @ sK2 @ sK3) = $true)),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f144])).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (15787)------------------------------
% 0.14/0.38 % (15787)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (15787)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (15787)Memory used [KB]: 5756
% 0.14/0.38 % (15787)Time elapsed: 0.015 s
% 0.14/0.38 % (15787)Instructions burned: 19 (million)
% 0.14/0.38 % (15787)------------------------------
% 0.14/0.38 % (15787)------------------------------
% 0.14/0.38 % (15784)Success in time 0.028 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------