0.11/0.18 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.18 % Command : run_vampire %s %d THM 0.11/0.42 % Computer : n023.cluster.edu 0.11/0.42 % Model : x86_64 x86_64 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.42 % Memory : 8042.1875MB 0.11/0.42 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.42 % CPULimit : 1440 0.11/0.42 % WCLimit : 180 0.11/0.42 % DateTime : Thu Jul 4 07:59:39 EDT 2024 0.11/0.43 % CPUTime : 0.19/0.58 This is a THF_ problem 0.19/0.60 Running higher-order theorem proving 0.19/0.63 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.4BHGIEY7D7/E---3.1_391.p -m 16384 -t 180 0.19/0.66 % (521)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_391 for (1799ds/18Mi) 0.19/0.67 % (521)Instruction limit reached! 0.19/0.67 % (521)------------------------------ 0.19/0.67 % (521)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.67 % (521)Termination reason: Unknown 0.19/0.67 % (521)Termination phase: Saturation 0.19/0.67 0.19/0.67 % (521)Memory used [KB]: 5628 0.19/0.67 % (521)Time elapsed: 0.011 s 0.19/0.67 % (521)Instructions burned: 19 (million) 0.19/0.67 % (521)------------------------------ 0.19/0.67 % (521)------------------------------ 0.19/0.67 % (515)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_391 for (1799ds/183Mi) 0.19/0.67 % (517)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 E---3.1_391 for (1799ds/27Mi) 0.19/0.67 % (516)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 E---3.1_391 for (1799ds/4Mi) 0.19/0.67 % (520)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_391 for (1799ds/275Mi) 0.19/0.67 % (518)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_391 for (1799ds/2Mi) 0.19/0.67 % (518)Instruction limit reached! 0.19/0.67 % (518)------------------------------ 0.19/0.67 % (518)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.67 % (518)Termination reason: Unknown 0.19/0.67 % (518)Termination phase: shuffling 0.19/0.67 0.19/0.67 % (518)Memory used [KB]: 1023 0.19/0.67 % (518)Time elapsed: 0.003 s 0.19/0.67 % (518)Instructions burned: 3 (million) 0.19/0.67 % (518)------------------------------ 0.19/0.67 % (518)------------------------------ 0.19/0.68 % (516)Instruction limit reached! 0.19/0.68 % (516)------------------------------ 0.19/0.68 % (516)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.68 % (516)Termination reason: Unknown 0.19/0.68 % (516)Termination phase: Property scanning 0.19/0.68 0.19/0.68 % (516)Memory used [KB]: 1023 0.19/0.68 % (516)Time elapsed: 0.004 s 0.19/0.68 % (516)Instructions burned: 6 (million) 0.19/0.68 % (516)------------------------------ 0.19/0.68 % (516)------------------------------ 0.19/0.68 % (519)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_391 for (1799ds/2Mi) 0.19/0.68 % (519)Instruction limit reached! 0.19/0.68 % (519)------------------------------ 0.19/0.68 % (519)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.68 % (519)Termination reason: Unknown 0.19/0.68 % (519)Termination phase: shuffling 0.19/0.68 0.19/0.68 % (519)Memory used [KB]: 1023 0.19/0.68 % (519)Time elapsed: 0.004 s 0.19/0.68 % (519)Instructions burned: 3 (million) 0.19/0.68 % (519)------------------------------ 0.19/0.68 % (519)------------------------------ 0.19/0.69 % (523)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 E---3.1_391 for (1799ds/37Mi) 0.19/0.69 % (520)First to succeed. 0.19/0.70 % (523)Instruction limit reached! 0.19/0.70 % (523)------------------------------ 0.19/0.70 % (523)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.70 % (523)Termination reason: Unknown 0.19/0.70 % (523)Termination phase: Saturation 0.19/0.70 0.19/0.70 % (523)Memory used [KB]: 6140 0.19/0.70 % (523)Time elapsed: 0.020 s 0.19/0.70 % (523)Instructions burned: 37 (million) 0.19/0.70 % (523)------------------------------ 0.19/0.70 % (523)------------------------------ 0.19/0.71 % (517)Instruction limit reached! 0.19/0.71 % (517)------------------------------ 0.19/0.71 % (517)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.71 % (517)Termination reason: Unknown 0.19/0.71 % (517)Termination phase: Saturation 0.19/0.71 0.19/0.71 % (517)Memory used [KB]: 5756 0.19/0.71 % (517)Time elapsed: 0.045 s 0.19/0.71 % (517)Instructions burned: 27 (million) 0.19/0.71 % (517)------------------------------ 0.19/0.71 % (517)------------------------------ 0.19/0.71 % (522)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_391 for (1799ds/3Mi) 0.19/0.71 % (522)Instruction limit reached! 0.19/0.71 % (522)------------------------------ 0.19/0.71 % (522)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.71 % (522)Termination reason: Unknown 0.19/0.71 % (522)Termination phase: Property scanning 0.19/0.71 0.19/0.71 % (522)Memory used [KB]: 1023 0.19/0.71 % (522)Time elapsed: 0.004 s 0.19/0.71 % (522)Instructions burned: 5 (million) 0.19/0.71 % (522)------------------------------ 0.19/0.71 % (522)------------------------------ 0.19/0.71 % (520)Refutation found. Thanks to Tanya! 0.19/0.71 % SZS status Theorem for E---3.1_391 0.19/0.71 % SZS output start Proof for E---3.1_391 0.19/0.71 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o). 0.19/0.71 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o). 0.19/0.71 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o). 0.19/0.71 thf(func_def_6, type, refl: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_9, type, symm: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_11, type, asymm: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_13, type, trans: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_17, type, po: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_18, type, so: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_19, type, total: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_20, type, term: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_21, type, ind: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o). 0.19/0.71 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_24, type, norm: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o). 0.19/0.71 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_28, type, confl: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_29, type, cr: ($i > $i > $o) > $o). 0.19/0.71 thf(func_def_49, type, sK1: $i > $i > $o). 0.19/0.71 thf(func_def_50, type, sK2: $i > $i > $o). 0.19/0.71 thf(func_def_53, type, sK5: ($i > $i > $o) > $i). 0.19/0.71 thf(func_def_54, type, sK6: ($i > $i > $o) > $i). 0.19/0.71 thf(func_def_55, type, sK7: $i > $i > $o). 0.19/0.71 thf(func_def_56, type, ph8: !>[X0: $tType]:(X0)). 0.19/0.71 thf(f306,plain,( 0.19/0.71 $false), 0.19/0.71 inference(trivial_inequality_removal,[],[f305])). 0.19/0.71 thf(f305,plain,( 0.19/0.71 ($true = $false)), 0.19/0.71 inference(forward_demodulation,[],[f304,f129])). 0.19/0.71 thf(f129,plain,( 0.19/0.71 ($false = (sK7 @ sK4 @ sK3))), 0.19/0.71 inference(binary_proxy_clausification,[],[f128])). 0.19/0.71 thf(f128,plain,( 0.19/0.71 ((((trans @ sK7) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1 @ Y0) => (sK7 @ Y1 @ Y0))))))) => (sK7 @ sK4 @ sK3)) = $false)), 0.19/0.71 inference(beta_eta_normalization,[],[f127])). 0.19/0.71 thf(f127,plain,( 0.19/0.71 ($false = ((^[Y0 : $i > $i > $o]: (((trans @ Y0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))) @ sK7))), 0.19/0.71 inference(sigma_clausification,[],[f115])). 0.19/0.71 thf(f115,plain,( 0.19/0.71 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((trans @ Y0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3)))) = $false)), 0.19/0.71 inference(binary_proxy_clausification,[],[f114])). 0.19/0.71 thf(f114,plain,( 0.19/0.71 (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((trans @ Y0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3)))) => (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((trans @ Y0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))))) = $false)), 0.19/0.71 inference(beta_eta_normalization,[],[f113])). 0.19/0.71 thf(f113,plain,( 0.19/0.71 (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((trans @ Y1) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3)))) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((trans @ Y1) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3)))))) @ sK4) = $false)), 0.19/0.71 inference(sigma_clausification,[],[f112])). 0.19/0.71 thf(f112,plain,( 0.19/0.71 ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((trans @ Y1) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3)))) => (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((trans @ Y1) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (Y1 @ Y0 @ sK3))))))) = $false)), 0.19/0.71 inference(beta_eta_normalization,[],[f111])). 0.19/0.71 thf(f111,plain,( 0.19/0.71 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((trans @ Y2) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((trans @ Y2) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))))))) @ sK3) = $false)), 0.19/0.71 inference(sigma_clausification,[],[f104])). 0.19/0.71 thf(f104,plain,( 0.19/0.71 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((trans @ Y2) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((trans @ Y2) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0))))))))))), 0.19/0.71 inference(binary_proxy_clausification,[],[f103])). 0.19/0.71 thf(f103,plain,( 0.19/0.71 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK1 @ Y1 @ Y0)))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((trans @ Y2) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))) => (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((trans @ Y2) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (Y2 @ Y1 @ Y0)))))))))) = $false)), 0.19/0.71 inference(beta_eta_normalization,[],[f102])). 0.19/0.71 thf(f102,plain,( 0.19/0.71 (((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (sK1 @ Y2 @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1))))))))))) @ sK2) = $false)), 0.19/0.71 inference(sigma_clausification,[],[f101])). 0.19/0.71 thf(f101,plain,( 0.19/0.71 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (sK1 @ Y2 @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))) => (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))) => (Y3 @ Y2 @ Y1)))))))))))) = $false)), 0.19/0.71 inference(beta_eta_normalization,[],[f100])). 0.19/0.71 thf(f100,plain,( 0.19/0.71 (((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (Y0 @ Y3 @ Y2)))))) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((trans @ Y4) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((trans @ Y4) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2))))))))))))) @ sK1) = $false)), 0.19/0.71 inference(sigma_clausification,[],[f99])). 0.19/0.71 thf(f99,plain,( 0.19/0.71 ($true != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (Y0 @ Y3 @ Y2)))))) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((trans @ Y4) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))) => (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((trans @ Y4) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))) => (Y4 @ Y3 @ Y2)))))))))))))))), 0.19/0.71 inference(beta_eta_normalization,[],[f98])). 0.19/0.71 thf(f98,plain,( 0.19/0.71 ($true != ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) @ Y2 @ Y1) => ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) @ (Y0 @ Y2) @ (Y0 @ Y1)))))))) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2)))))))))))), 0.19/0.71 inference(definition_unfolding,[],[f92,f97,f96])). 0.19/0.71 thf(f96,plain,( 0.19/0.71 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))), 0.19/0.71 inference(definition_unfolding,[],[f93,f94])). 0.19/0.71 thf(f94,plain,( 0.19/0.71 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))), 0.19/0.71 inference(cnf_transformation,[],[f74])). 0.19/0.71 thf(f74,plain,( 0.19/0.71 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))), 0.19/0.71 inference(fool_elimination,[],[f73])). 0.19/0.71 thf(f73,plain,( 0.19/0.71 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))), 0.19/0.71 inference(rectify,[],[f1])). 0.19/0.71 thf(f1,axiom,( 0.19/0.71 (subrel = (^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))))), 0.19/0.71 file('/export/starexec/sandbox2/tmp/tmp.4BHGIEY7D7/E---3.1_391.p',subrel)). 0.19/0.71 thf(f93,plain,( 0.19/0.71 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))), 0.19/0.71 inference(cnf_transformation,[],[f68])). 0.19/0.71 thf(f68,plain,( 0.19/0.71 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((trans @ Y3) & (subrel @ Y0 @ Y3)) => (Y3 @ Y1 @ Y2))))))))))), 0.19/0.71 inference(fool_elimination,[],[f67])). 0.19/0.71 thf(f67,plain,( 0.19/0.71 ((^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((subrel @ X0 @ X3) & (trans @ X3)) => (X3 @ X1 @ X2)))) = tc)), 0.19/0.71 inference(rectify,[],[f14])). 0.19/0.71 thf(f14,axiom,( 0.19/0.71 ((^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((subrel @ X0 @ X1) & (trans @ X1)) => (X1 @ X2 @ X3)))) = tc)), 0.19/0.71 file('/export/starexec/sandbox2/tmp/tmp.4BHGIEY7D7/E---3.1_391.p',transitive_closure)). 0.19/0.71 thf(f97,plain,( 0.19/0.71 (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) @ Y2 @ Y1) => ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) @ (Y0 @ Y2) @ (Y0 @ Y1)))))))))), 0.19/0.71 inference(definition_unfolding,[],[f95,f94,f94])). 0.19/0.71 thf(f95,plain,( 0.19/0.71 (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((subrel @ Y2 @ Y1) => (subrel @ (Y0 @ Y2) @ (Y0 @ Y1)))))))))), 0.19/0.71 inference(cnf_transformation,[],[f88])). 0.19/0.71 thf(f88,plain,( 0.19/0.71 (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((subrel @ Y2 @ Y1) => (subrel @ (Y0 @ Y2) @ (Y0 @ Y1)))))))))), 0.19/0.71 inference(fool_elimination,[],[f87])). 0.19/0.71 thf(f87,plain,( 0.19/0.71 ((^[X0 : ($i > $i > $o) > $i > $i > $o] : (! [X1 : $i > $i > $o,X2 : $i > $i > $o] : ((subrel @ X1 @ X2) => (subrel @ (X0 @ X1) @ (X0 @ X2))))) = mono)), 0.19/0.71 inference(rectify,[],[f5])). 0.19/0.71 thf(f5,axiom,( 0.19/0.71 ((^[X4 : ($i > $i > $o) > $i > $i > $o] : (! [X0 : $i > $i > $o,X1 : $i > $i > $o] : ((subrel @ X0 @ X1) => (subrel @ (X4 @ X0) @ (X4 @ X1))))) = mono)), 0.19/0.71 file('/export/starexec/sandbox2/tmp/tmp.4BHGIEY7D7/E---3.1_391.p',monotonic)). 0.19/0.71 thf(f92,plain,( 0.19/0.71 ((mono @ tc) != $true)), 0.19/0.71 inference(cnf_transformation,[],[f91])). 0.19/0.71 thf(f91,plain,( 0.19/0.71 ((mono @ tc) != $true)), 0.19/0.71 inference(flattening,[],[f62])). 0.19/0.71 thf(f62,plain,( 0.19/0.71 ~((mono @ tc) = $true)), 0.19/0.71 inference(fool_elimination,[],[f61])). 0.19/0.71 thf(f61,plain,( 0.19/0.71 ~(mono @ tc)), 0.19/0.71 inference(rectify,[],[f31])). 0.19/0.71 thf(f31,negated_conjecture,( 0.19/0.71 ~(mono @ tc)), 0.19/0.71 inference(negated_conjecture,[],[f30])). 0.19/0.71 thf(f30,conjecture,( 0.19/0.71 (mono @ tc)), 0.19/0.71 file('/export/starexec/sandbox2/tmp/tmp.4BHGIEY7D7/E---3.1_391.p',transitive_closure_op_is_monotonic)). 0.19/0.71 thf(f304,plain,( 0.19/0.71 ($true = (sK7 @ sK4 @ sK3))), 0.19/0.71 inference(trivial_inequality_removal,[],[f303])). 0.19/0.71 thf(f303,plain,( 0.19/0.71 ($true = $false) | ($true = (sK7 @ sK4 @ sK3))), 0.19/0.71 inference(forward_demodulation,[],[f302,f132])). 0.19/0.71 thf(f132,plain,( 0.19/0.71 ((trans @ sK7) = $true)), 0.19/0.71 inference(binary_proxy_clausification,[],[f130])). 0.19/0.71 thf(f130,plain,( 0.19/0.71 ($true = ((trans @ sK7) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1 @ Y0) => (sK7 @ Y1 @ Y0))))))))), 0.19/0.71 inference(binary_proxy_clausification,[],[f128])). 0.19/0.71 thf(f302,plain,( 0.19/0.71 ((trans @ sK7) = $false) | ($true = (sK7 @ sK4 @ sK3))), 0.19/0.71 inference(trivial_inequality_removal,[],[f299])). 0.19/0.71 thf(f299,plain,( 0.19/0.71 ((trans @ sK7) = $false) | ($true = $false) | ($true = (sK7 @ sK4 @ sK3))), 0.19/0.71 inference(superposition,[],[f256,f126])). 0.19/0.71 thf(f126,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (($true = (sK2 @ (sK6 @ X1) @ (sK5 @ X1))) | ((trans @ X1) = $false) | ((X1 @ sK4 @ sK3) = $true)) )), 0.19/0.71 inference(binary_proxy_clausification,[],[f124])). 0.19/0.71 thf(f124,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (((trans @ X1) = $false) | (((sK2 @ (sK6 @ X1) @ (sK5 @ X1)) => (X1 @ (sK6 @ X1) @ (sK5 @ X1))) = $false) | ((X1 @ sK4 @ sK3) = $true)) )), 0.19/0.71 inference(beta_eta_normalization,[],[f123])). 0.19/0.71 thf(f123,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i]: ((sK2 @ Y0 @ (sK5 @ X1)) => (X1 @ Y0 @ (sK5 @ X1)))) @ (sK6 @ X1)) = $false) | ((trans @ X1) = $false) | ((X1 @ sK4 @ sK3) = $true)) )), 0.19/0.71 inference(sigma_clausification,[],[f122])). 0.19/0.71 thf(f122,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ (sK5 @ X1)) => (X1 @ Y0 @ (sK5 @ X1)))))) | ((X1 @ sK4 @ sK3) = $true) | ((trans @ X1) = $false)) )), 0.19/0.71 inference(beta_eta_normalization,[],[f121])). 0.19/0.71 thf(f121,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))) @ (sK5 @ X1)) = $false) | ((X1 @ sK4 @ sK3) = $true) | ((trans @ X1) = $false)) )), 0.19/0.71 inference(sigma_clausification,[],[f120])). 0.19/0.71 thf(f120,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (((X1 @ sK4 @ sK3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) | ((trans @ X1) = $false)) )), 0.19/0.71 inference(binary_proxy_clausification,[],[f119])). 0.19/0.71 thf(f119,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (((X1 @ sK4 @ sK3) = $true) | (((trans @ X1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) = $false)) )), 0.19/0.71 inference(binary_proxy_clausification,[],[f118])). 0.19/0.71 thf(f118,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (($true = (((trans @ X1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0))))))) => (X1 @ sK4 @ sK3)))) )), 0.19/0.71 inference(beta_eta_normalization,[],[f117])). 0.19/0.71 thf(f117,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((trans @ Y0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3))) @ X1))) )), 0.19/0.71 inference(pi_clausification,[],[f116])). 0.19/0.71 thf(f116,plain,( 0.19/0.71 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((trans @ Y0) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (Y0 @ sK4 @ sK3)))))), 0.19/0.71 inference(binary_proxy_clausification,[],[f114])). 0.19/0.71 thf(f256,plain,( 0.19/0.71 ($false = (sK2 @ (sK6 @ sK7) @ (sK5 @ sK7)))), 0.19/0.71 inference(trivial_inequality_removal,[],[f255])). 0.19/0.71 thf(f255,plain,( 0.19/0.71 ($true = $false) | ($false = (sK2 @ (sK6 @ sK7) @ (sK5 @ sK7)))), 0.19/0.71 inference(forward_demodulation,[],[f254,f132])). 0.19/0.71 thf(f254,plain,( 0.19/0.71 ($false = (sK2 @ (sK6 @ sK7) @ (sK5 @ sK7))) | ((trans @ sK7) = $false)), 0.19/0.71 inference(trivial_inequality_removal,[],[f253])). 0.19/0.71 thf(f253,plain,( 0.19/0.71 ((trans @ sK7) = $false) | ($false = (sK2 @ (sK6 @ sK7) @ (sK5 @ sK7))) | ($true = $false)), 0.19/0.71 inference(forward_demodulation,[],[f252,f129])). 0.19/0.71 thf(f252,plain,( 0.19/0.71 ($true = (sK7 @ sK4 @ sK3)) | ($false = (sK2 @ (sK6 @ sK7) @ (sK5 @ sK7))) | ((trans @ sK7) = $false)), 0.19/0.71 inference(trivial_inequality_removal,[],[f248])). 0.19/0.71 thf(f248,plain,( 0.19/0.71 ($true = $false) | ($false = (sK2 @ (sK6 @ sK7) @ (sK5 @ sK7))) | ($true = (sK7 @ sK4 @ sK3)) | ((trans @ sK7) = $false)), 0.19/0.71 inference(superposition,[],[f125,f218])). 0.19/0.71 thf(f218,plain,( 0.19/0.71 ( ! [X0 : $i,X1 : $i] : (((sK7 @ X0 @ X1) = $true) | ((sK2 @ X0 @ X1) = $false)) )), 0.19/0.71 inference(trivial_inequality_removal,[],[f214])). 0.19/0.71 thf(f214,plain,( 0.19/0.71 ( ! [X0 : $i,X1 : $i] : (((sK7 @ X0 @ X1) = $true) | ($true = $false) | ((sK2 @ X0 @ X1) = $false)) )), 0.19/0.71 inference(superposition,[],[f110,f137])). 0.19/0.71 thf(f137,plain,( 0.19/0.71 ( ! [X2 : $i,X1 : $i] : (($false = (sK1 @ X2 @ X1)) | ((sK7 @ X2 @ X1) = $true)) )), 0.19/0.71 inference(binary_proxy_clausification,[],[f136])). 0.19/0.71 thf(f136,plain,( 0.19/0.71 ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X2 @ X1) => (sK7 @ X2 @ X1)) = $true)) )), 0.19/0.71 inference(beta_eta_normalization,[],[f135])). 0.19/0.71 thf(f135,plain,( 0.19/0.71 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK1 @ Y0 @ X1) => (sK7 @ Y0 @ X1))) @ X2))) )), 0.19/0.71 inference(pi_clausification,[],[f134])). 0.19/0.71 thf(f134,plain,( 0.19/0.71 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0 @ X1) => (sK7 @ Y0 @ X1)))))) )), 0.19/0.71 inference(beta_eta_normalization,[],[f133])). 0.19/0.71 thf(f133,plain,( 0.19/0.71 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1 @ Y0) => (sK7 @ Y1 @ Y0))))) @ X1))) )), 0.19/0.71 inference(pi_clausification,[],[f131])). 0.19/0.71 thf(f131,plain,( 0.19/0.71 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1 @ Y0) => (sK7 @ Y1 @ Y0)))))))), 0.19/0.71 inference(binary_proxy_clausification,[],[f130])). 0.19/0.71 thf(f110,plain,( 0.19/0.71 ( ! [X2 : $i,X1 : $i] : (($true = (sK1 @ X2 @ X1)) | ((sK2 @ X2 @ X1) = $false)) )), 0.19/0.71 inference(binary_proxy_clausification,[],[f109])). 0.19/0.71 thf(f109,plain,( 0.19/0.71 ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2 @ X1) => (sK1 @ X2 @ X1)))) )), 0.19/0.71 inference(beta_eta_normalization,[],[f108])). 0.19/0.71 thf(f108,plain,( 0.19/0.71 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK2 @ Y0 @ X1) => (sK1 @ Y0 @ X1))) @ X2))) )), 0.19/0.71 inference(pi_clausification,[],[f107])). 0.19/0.71 thf(f107,plain,( 0.19/0.71 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0 @ X1) => (sK1 @ Y0 @ X1)))) = $true)) )), 0.19/0.71 inference(beta_eta_normalization,[],[f106])). 0.19/0.71 thf(f106,plain,( 0.19/0.71 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK1 @ Y1 @ Y0))))) @ X1))) )), 0.19/0.71 inference(pi_clausification,[],[f105])). 0.19/0.71 thf(f105,plain,( 0.19/0.71 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK1 @ Y1 @ Y0)))))))), 0.19/0.71 inference(binary_proxy_clausification,[],[f103])). 0.19/0.71 thf(f125,plain,( 0.19/0.71 ( ! [X1 : $i > $i > $o] : (((X1 @ (sK6 @ X1) @ (sK5 @ X1)) = $false) | ((trans @ X1) = $false) | ((X1 @ sK4 @ sK3) = $true)) )), 0.19/0.71 inference(binary_proxy_clausification,[],[f124])). 0.19/0.71 % SZS output end Proof for E---3.1_391 0.19/0.71 % (520)------------------------------ 0.19/0.71 % (520)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.19/0.71 % (520)Termination reason: Refutation 0.19/0.71 0.19/0.71 % (520)Memory used [KB]: 5884 0.19/0.71 % (520)Time elapsed: 0.049 s 0.19/0.71 % (520)Instructions burned: 21 (million) 0.19/0.71 % (520)------------------------------ 0.19/0.71 % (520)------------------------------ 0.19/0.71 % (514)Success in time 0.058 s 0.19/0.73 EOF