0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : run_vampire %s %d THM 0.13/0.34 % Computer : n007.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Thu Jul 4 05:26:54 EDT 2024 0.13/0.34 % CPUTime : 0.13/0.36 This is a THF_ problem 0.13/0.36 Running higher-order theorem proving 0.13/0.37 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.cO0QTgRBiV/E---3.1_30184.p -m 16384 -t 180 0.13/0.38 % (30416)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_30184 for (1799ds/18Mi) 0.13/0.39 % (30411)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_30184 for (1799ds/4Mi) 0.13/0.39 % (30413)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_30184 for (1799ds/2Mi) 0.13/0.39 % (30410)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_30184 for (1799ds/183Mi) 0.13/0.39 % (30412)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_30184 for (1799ds/27Mi) 0.13/0.39 % (30415)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_30184 for (1799ds/275Mi) 0.13/0.39 % (30414)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_30184 for (1799ds/2Mi) 0.13/0.39 % (30413)Instruction limit reached! 0.13/0.39 % (30413)------------------------------ 0.13/0.39 % (30413)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (30413)Termination reason: Unknown 0.13/0.39 % (30414)Instruction limit reached! 0.13/0.39 % (30414)------------------------------ 0.13/0.39 % (30414)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (30413)Termination phase: Saturation 0.13/0.39 0.13/0.39 % (30413)Memory used [KB]: 5500 0.13/0.39 % (30413)Time elapsed: 0.004 s 0.13/0.39 % (30413)Instructions burned: 2 (million) 0.13/0.39 % (30413)------------------------------ 0.13/0.39 % (30413)------------------------------ 0.13/0.39 % (30414)Termination reason: Unknown 0.13/0.39 % (30414)Termination phase: Property scanning 0.13/0.39 0.13/0.39 % (30414)Memory used [KB]: 895 0.13/0.39 % (30414)Time elapsed: 0.003 s 0.13/0.39 % (30414)Instructions burned: 2 (million) 0.13/0.39 % (30414)------------------------------ 0.13/0.39 % (30414)------------------------------ 0.13/0.39 % (30416)Instruction limit reached! 0.13/0.39 % (30416)------------------------------ 0.13/0.39 % (30416)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (30416)Termination reason: Unknown 0.13/0.39 % (30416)Termination phase: Saturation 0.13/0.39 0.13/0.39 % (30416)Memory used [KB]: 5628 0.13/0.39 % (30416)Time elapsed: 0.008 s 0.13/0.39 % (30416)Instructions burned: 18 (million) 0.13/0.39 % (30416)------------------------------ 0.13/0.39 % (30416)------------------------------ 0.13/0.39 % (30411)Instruction limit reached! 0.13/0.39 % (30411)------------------------------ 0.13/0.39 % (30411)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (30411)Termination reason: Unknown 0.13/0.39 % (30411)Termination phase: Saturation 0.13/0.39 0.13/0.39 % (30411)Memory used [KB]: 5500 0.13/0.39 % (30411)Time elapsed: 0.005 s 0.13/0.39 % (30411)Instructions burned: 4 (million) 0.13/0.39 % (30411)------------------------------ 0.13/0.39 % (30411)------------------------------ 0.13/0.39 % (30412)Refutation not found, incomplete strategy 0.13/0.39 % (30412)------------------------------ 0.13/0.39 % (30412)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (30412)Termination reason: Refutation not found, incomplete strategy 0.13/0.39 0.13/0.39 0.13/0.39 % (30412)Memory used [KB]: 5500 0.13/0.39 % (30412)Time elapsed: 0.006 s 0.13/0.39 % (30412)Instructions burned: 6 (million) 0.13/0.39 % (30412)------------------------------ 0.13/0.39 % (30412)------------------------------ 0.22/0.40 % (30426)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 E---3.1_30184 for (1799ds/15Mi) 0.22/0.40 % (30415)Refutation not found, incomplete strategy 0.22/0.40 % (30415)------------------------------ 0.22/0.40 % (30415)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.40 % (30415)Termination reason: Refutation not found, incomplete strategy 0.22/0.40 0.22/0.40 0.22/0.40 % (30415)Memory used [KB]: 5628 0.22/0.40 % (30415)Time elapsed: 0.015 s 0.22/0.40 % (30415)Instructions burned: 20 (million) 0.22/0.40 % (30415)------------------------------ 0.22/0.40 % (30415)------------------------------ 0.22/0.40 % (30426)First to succeed. 0.22/0.40 % (30424)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_30184 for (1799ds/3Mi) 0.22/0.40 % (30425)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_30184 for (1799ds/37Mi) 0.22/0.41 % (30426)Refutation found. Thanks to Tanya! 0.22/0.41 % SZS status Theorem for E---3.1_30184 0.22/0.41 % SZS output start Proof for E---3.1_30184 0.22/0.41 thf(func_def_3, type, sP0: (($i > $o) > ($i > $o) > $o) > $o). 0.22/0.41 thf(func_def_4, type, sP1: (($i > $o) > ($i > $o) > $o) > $o). 0.22/0.41 thf(func_def_5, type, sK2: (($i > $o) > ($i > $o) > $o) > $i > $o). 0.22/0.41 thf(func_def_6, type, sK3: (($i > $o) > ($i > $o) > $o) > $i > $o). 0.22/0.41 thf(func_def_7, type, sK4: (($i > $o) > ($i > $o) > $o) > $i > $o). 0.22/0.41 thf(func_def_8, type, sK5: (($i > $o) > ($i > $o) > $o) > $i > $o). 0.22/0.41 thf(func_def_9, type, sK6: (($i > $o) > ($i > $o) > $o) > $i > $o). 0.22/0.41 thf(func_def_10, type, sK7: (($i > $o) > ($i > $o) > $o) > $i). 0.22/0.41 thf(func_def_11, type, sK8: (($i > $o) > ($i > $o) > $o) > $i > $o). 0.22/0.41 thf(func_def_13, type, ph10: !>[X0: $tType]:(X0)). 0.22/0.41 thf(f189,plain,( 0.22/0.41 $false), 0.22/0.41 inference(avatar_sat_refutation,[],[f55,f74,f83,f133,f142,f151,f169,f174,f179,f181,f184,f185,f188])). 0.22/0.41 thf(f188,plain,( 0.22/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))), 0.22/0.41 introduced(theory_tautology_sat_conflict,[])). 0.22/0.41 thf(f185,plain,( 0.22/0.41 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))), 0.22/0.41 introduced(theory_tautology_sat_conflict,[])). 0.22/0.41 thf(f184,plain,( 0.22/0.41 ($false != (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($false != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true)), 0.22/0.41 introduced(theory_tautology_sat_conflict,[])). 0.22/0.41 thf(f181,plain,( 0.22/0.41 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ($false != (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($false != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true)), 0.22/0.41 introduced(theory_tautology_sat_conflict,[])). 0.22/0.41 thf(f179,plain,( 0.22/0.41 ~spl9_17 | ~spl9_1), 0.22/0.41 inference(avatar_split_clause,[],[f158,f48,f176])). 0.22/0.41 thf(f176,plain,( 0.22/0.41 spl9_17 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_17])])). 0.22/0.41 thf(f48,plain,( 0.22/0.41 spl9_1 <=> ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_1])])). 0.22/0.41 thf(f158,plain,( 0.22/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) != (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1), 0.22/0.41 inference(equality_proxy_clausification,[],[f157])). 0.22/0.41 thf(f157,plain,( 0.22/0.41 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_1), 0.22/0.41 inference(beta_eta_normalization,[],[f156])). 0.22/0.41 thf(f156,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ~spl9_1), 0.22/0.41 inference(trivial_inequality_removal,[],[f155])). 0.22/0.41 thf(f155,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ($true != $true) | ~spl9_1), 0.22/0.41 inference(superposition,[],[f23,f50])). 0.22/0.41 thf(f50,plain,( 0.22/0.41 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ~spl9_1), 0.22/0.41 inference(avatar_component_clause,[],[f48])). 0.22/0.41 thf(f23,plain,( 0.22/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true) | ($true != (sP1 @ X0))) )), 0.22/0.41 inference(cnf_transformation,[],[f13])). 0.22/0.41 thf(f13,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK4 @ X0) @ (sK3 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true) & ($true = (X0 @ (sK2 @ X0) @ (sK4 @ X0)))) | ($true != (sP1 @ X0)))), 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f11,f12])). 0.22/0.41 thf(f12,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X1 @ X2) != $true) & ((X0 @ X1 @ X3) = $true)) => (((X0 @ (sK4 @ X0) @ (sK3 @ X0)) = $true) & ((X0 @ (sK2 @ X0) @ (sK3 @ X0)) != $true) & ($true = (X0 @ (sK2 @ X0) @ (sK4 @ X0)))))), 0.22/0.41 introduced(choice_axiom,[])). 0.22/0.41 thf(f11,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X1 @ X2) != $true) & ((X0 @ X1 @ X3) = $true)) | ($true != (sP1 @ X0)))), 0.22/0.41 inference(nnf_transformation,[],[f9])). 0.22/0.41 thf(f9,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X1 @ X2) != $true) & ((X0 @ X1 @ X3) = $true)) | ~($true = (sP1 @ X0)))), 0.22/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])). 0.22/0.41 thf(f174,plain,( 0.22/0.41 spl9_16 | ~spl9_1), 0.22/0.41 inference(avatar_split_clause,[],[f161,f48,f171])). 0.22/0.41 thf(f171,plain,( 0.22/0.41 spl9_16 <=> ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_16])])). 0.22/0.41 thf(f161,plain,( 0.22/0.41 ((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1), 0.22/0.41 inference(equality_proxy_clausification,[],[f160])). 0.22/0.41 thf(f160,plain,( 0.22/0.41 (((sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1), 0.22/0.41 inference(beta_eta_normalization,[],[f159])). 0.22/0.41 thf(f159,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1), 0.22/0.41 inference(trivial_inequality_removal,[],[f153])). 0.22/0.41 thf(f153,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true) | ~spl9_1), 0.22/0.41 inference(superposition,[],[f24,f50])). 0.22/0.41 thf(f24,plain,( 0.22/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK4 @ X0) @ (sK3 @ X0)) = $true) | ($true != (sP1 @ X0))) )), 0.22/0.41 inference(cnf_transformation,[],[f13])). 0.22/0.41 thf(f169,plain,( 0.22/0.41 spl9_15 | ~spl9_1), 0.22/0.41 inference(avatar_split_clause,[],[f164,f48,f166])). 0.22/0.41 thf(f166,plain,( 0.22/0.41 spl9_15 <=> ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_15])])). 0.22/0.41 thf(f164,plain,( 0.22/0.41 ((sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_1), 0.22/0.41 inference(equality_proxy_clausification,[],[f163])). 0.22/0.41 thf(f163,plain,( 0.22/0.41 (((sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1), 0.22/0.41 inference(beta_eta_normalization,[],[f162])). 0.22/0.41 thf(f162,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1), 0.22/0.41 inference(trivial_inequality_removal,[],[f154])). 0.22/0.41 thf(f154,plain,( 0.22/0.41 ($true != $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK4 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_1), 0.22/0.41 inference(superposition,[],[f22,f50])). 0.22/0.41 thf(f22,plain,( 0.22/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true != (sP1 @ X0)) | ($true = (X0 @ (sK2 @ X0) @ (sK4 @ X0)))) )), 0.22/0.41 inference(cnf_transformation,[],[f13])). 0.22/0.41 thf(f151,plain,( 0.22/0.41 spl9_13 | spl9_14 | ~spl9_2), 0.22/0.41 inference(avatar_split_clause,[],[f121,f52,f148,f144])). 0.22/0.41 thf(f144,plain,( 0.22/0.41 spl9_13 <=> ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_13])])). 0.22/0.41 thf(f148,plain,( 0.22/0.41 spl9_14 <=> ($false = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_14])])). 0.22/0.41 thf(f52,plain,( 0.22/0.41 spl9_2 <=> ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_2])])). 0.22/0.41 thf(f121,plain,( 0.22/0.41 ($false = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ($false = (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2), 0.22/0.41 inference(binary_proxy_clausification,[],[f119])). 0.22/0.41 thf(f119,plain,( 0.22/0.41 ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2), 0.22/0.41 inference(trivial_inequality_removal,[],[f117])). 0.22/0.41 thf(f117,plain,( 0.22/0.41 ($true != $true) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))) | ~spl9_2), 0.22/0.41 inference(superposition,[],[f26,f54])). 0.22/0.41 thf(f54,plain,( 0.22/0.41 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ~spl9_2), 0.22/0.41 inference(avatar_component_clause,[],[f52])). 0.22/0.41 thf(f26,plain,( 0.22/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP0 @ X0) != $true) | ((sK6 @ X0 @ (sK7 @ X0)) != (sK5 @ X0 @ (sK7 @ X0)))) )), 0.22/0.41 inference(cnf_transformation,[],[f18])). 0.22/0.41 thf(f18,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : ((((X0 @ (sK6 @ X0) @ (sK5 @ X0)) = $true) & ((sK6 @ X0 @ (sK7 @ X0)) != (sK5 @ X0 @ (sK7 @ X0))) & ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true)) | ((sP0 @ X0) != $true))), 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f15,f17,f16])). 0.22/0.41 thf(f16,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) = $true) & ? [X3] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true)) => (((X0 @ (sK6 @ X0) @ (sK5 @ X0)) = $true) & ? [X3] : ((sK6 @ X0 @ X3) != (sK5 @ X0 @ X3)) & ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true)))), 0.22/0.41 introduced(choice_axiom,[])). 0.22/0.41 thf(f17,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X3] : ((sK6 @ X0 @ X3) != (sK5 @ X0 @ X3)) => ((sK6 @ X0 @ (sK7 @ X0)) != (sK5 @ X0 @ (sK7 @ X0))))), 0.22/0.41 introduced(choice_axiom,[])). 0.22/0.41 thf(f15,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) = $true) & ? [X3] : ((X2 @ X3) != (X1 @ X3)) & ((X0 @ X1 @ X2) = $true)) | ((sP0 @ X0) != $true))), 0.22/0.41 inference(rectify,[],[f14])). 0.22/0.41 thf(f14,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ? [X7] : ((X5 @ X7) != (X6 @ X7)) & ((X0 @ X6 @ X5) = $true)) | ((sP0 @ X0) != $true))), 0.22/0.41 inference(nnf_transformation,[],[f8])). 0.22/0.41 thf(f8,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ? [X7] : ((X5 @ X7) != (X6 @ X7)) & ((X0 @ X6 @ X5) = $true)) | ~((sP0 @ X0) = $true))), 0.22/0.41 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])). 0.22/0.41 thf(f142,plain,( 0.22/0.41 spl9_11 | spl9_12 | ~spl9_2), 0.22/0.41 inference(avatar_split_clause,[],[f120,f52,f139,f135])). 0.22/0.41 thf(f135,plain,( 0.22/0.41 spl9_11 <=> ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_11])])). 0.22/0.41 thf(f139,plain,( 0.22/0.41 spl9_12 <=> ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true)), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_12])])). 0.22/0.41 thf(f120,plain,( 0.22/0.41 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ((sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK7 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_2), 0.22/0.41 inference(binary_proxy_clausification,[],[f119])). 0.22/0.41 thf(f133,plain,( 0.22/0.41 spl9_10 | ~spl9_2), 0.22/0.41 inference(avatar_split_clause,[],[f124,f52,f129])). 0.22/0.41 thf(f129,plain,( 0.22/0.41 spl9_10 <=> ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_10])])). 0.22/0.41 thf(f124,plain,( 0.22/0.41 ((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) | ~spl9_2), 0.22/0.41 inference(equality_proxy_clausification,[],[f123])). 0.22/0.41 thf(f123,plain,( 0.22/0.41 (((sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_2), 0.22/0.41 inference(beta_eta_normalization,[],[f122])). 0.22/0.41 thf(f122,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ~spl9_2), 0.22/0.41 inference(trivial_inequality_removal,[],[f118])). 0.22/0.41 thf(f118,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK6 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) = $true) | ($true != $true) | ~spl9_2), 0.22/0.41 inference(superposition,[],[f25,f54])). 0.22/0.41 thf(f25,plain,( 0.22/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((sP0 @ X0) != $true) | ((X0 @ (sK5 @ X0) @ (sK6 @ X0)) = $true)) )), 0.22/0.41 inference(cnf_transformation,[],[f18])). 0.22/0.41 thf(f83,plain,( 0.22/0.41 spl9_5 | spl9_3), 0.22/0.41 inference(avatar_split_clause,[],[f78,f57,f80])). 0.22/0.41 thf(f80,plain,( 0.22/0.41 spl9_5 <=> ($false = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))))), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_5])])). 0.22/0.41 thf(f57,plain,( 0.22/0.41 spl9_3 <=> ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true)), 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl9_3])])). 0.22/0.41 thf(f78,plain,( 0.22/0.41 ($false = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | spl9_3), 0.22/0.41 inference(trivial_inequality_removal,[],[f77])). 0.22/0.41 thf(f77,plain,( 0.22/0.41 ($false = (sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) | ($true != $true) | spl9_3), 0.22/0.41 inference(fool_paramodulation,[],[f58])). 0.22/0.41 thf(f58,plain,( 0.22/0.41 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) != $true) | spl9_3), 0.22/0.41 inference(avatar_component_clause,[],[f57])). 0.22/0.41 thf(f74,plain,( 0.22/0.41 ~spl9_3), 0.22/0.41 inference(avatar_contradiction_clause,[],[f73])). 0.22/0.41 thf(f73,plain,( 0.22/0.41 $false | ~spl9_3), 0.22/0.41 inference(trivial_inequality_removal,[],[f72])). 0.22/0.41 thf(f72,plain,( 0.22/0.41 ($true != $true) | ~spl9_3), 0.22/0.41 inference(beta_eta_normalization,[],[f71])). 0.22/0.41 thf(f71,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) != $true) | ~spl9_3), 0.22/0.41 inference(trivial_inequality_removal,[],[f68])). 0.22/0.41 thf(f68,plain,( 0.22/0.41 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))) @ (sK2 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) @ (sK3 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true)))))) != $true) | ($true != $true) | ~spl9_3), 0.22/0.41 inference(superposition,[],[f23,f59])). 0.22/0.41 thf(f59,plain,( 0.22/0.41 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ($true))))) = $true) | ~spl9_3), 0.22/0.41 inference(avatar_component_clause,[],[f57])). 0.22/0.41 thf(f55,plain,( 0.22/0.41 spl9_1 | spl9_2), 0.22/0.41 inference(avatar_split_clause,[],[f45,f52,f48])). 0.22/0.41 thf(f45,plain,( 0.22/0.41 ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)), 0.22/0.41 inference(trivial_inequality_removal,[],[f44])). 0.22/0.41 thf(f44,plain,( 0.22/0.41 ($true != $true) | ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)), 0.22/0.41 inference(boolean_simplification,[],[f43])). 0.22/0.41 thf(f43,plain,( 0.22/0.41 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)), 0.22/0.41 inference(beta_eta_normalization,[],[f30])). 0.22/0.41 thf(f30,plain,( 0.22/0.41 ((sP1 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true) | (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) @ (sK8 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0)))))) != $true) | ((sP0 @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (Y1 = Y0))))) = $true)), 0.22/0.41 inference(primitive_instantiation,[],[f28])). 0.22/0.41 thf(f28,plain,( 0.22/0.41 ( ! [X0 : ($i > $o) > ($i > $o) > $o] : (((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true) | ($true = (sP1 @ X0)) | ((sP0 @ X0) = $true)) )), 0.22/0.41 inference(cnf_transformation,[],[f21])). 0.22/0.41 thf(f21,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (sP1 @ X0)) | ((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true) | ((sP0 @ X0) = $true))), 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f19,f20])). 0.22/0.41 thf(f20,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) => ((X0 @ (sK8 @ X0) @ (sK8 @ X0)) != $true))), 0.22/0.41 introduced(choice_axiom,[])). 0.22/0.41 thf(f19,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (sP1 @ X0)) | ? [X1 : $i > $o] : ((X0 @ X1 @ X1) != $true) | ((sP0 @ X0) = $true))), 0.22/0.41 inference(rectify,[],[f10])). 0.22/0.41 thf(f10,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (($true = (sP1 @ X0)) | ? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true) | ((sP0 @ X0) = $true))), 0.22/0.41 inference(definition_folding,[],[f7,f9,f8])). 0.22/0.41 thf(f7,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X3 @ X2) = $true) & ((X0 @ X1 @ X2) != $true) & ((X0 @ X1 @ X3) = $true)) | ? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true) | ? [X6 : $i > $o,X5 : $i > $o] : (((X0 @ X5 @ X6) = $true) & ? [X7] : ((X5 @ X7) != (X6 @ X7)) & ((X0 @ X6 @ X5) = $true)))), 0.22/0.41 inference(flattening,[],[f6])). 0.22/0.41 thf(f6,plain,( 0.22/0.41 ! [X0 : ($i > $o) > ($i > $o) > $o] : (? [X4 : $i > $o] : ((X0 @ X4 @ X4) != $true) | ? [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X2) != $true) & (((X0 @ X3 @ X2) = $true) & ((X0 @ X1 @ X3) = $true))) | ? [X6 : $i > $o,X5 : $i > $o] : (? [X7] : ((X5 @ X7) != (X6 @ X7)) & (((X0 @ X6 @ X5) = $true) & ((X0 @ X5 @ X6) = $true))))), 0.22/0.41 inference(ennf_transformation,[],[f5])). 0.22/0.41 thf(f5,plain,( 0.22/0.41 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X4 : $i > $o] : ((X0 @ X4 @ X4) = $true) & ! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : ((((X0 @ X3 @ X2) = $true) & ((X0 @ X1 @ X3) = $true)) => ((X0 @ X1 @ X2) = $true)) & ! [X6 : $i > $o,X5 : $i > $o] : ((((X0 @ X6 @ X5) = $true) & ((X0 @ X5 @ X6) = $true)) => ! [X7] : ((X5 @ X7) = (X6 @ X7))))), 0.22/0.41 inference(fool_elimination,[],[f4])). 0.22/0.41 thf(f4,plain,( 0.22/0.41 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X1 : $i > $o,X2 : $i > $o,X3 : $i > $o] : (((X0 @ X1 @ X3) & (X0 @ X3 @ X2)) => (X0 @ X1 @ X2)) & ! [X4 : $i > $o] : (X0 @ X4 @ X4) & ! [X5 : $i > $o,X6 : $i > $o] : (((X0 @ X6 @ X5) & (X0 @ X5 @ X6)) => ! [X7] : ((X6 @ X7) <=> (X5 @ X7))))), 0.22/0.41 inference(rectify,[],[f2])). 0.22/0.41 thf(f2,negated_conjecture,( 0.22/0.41 ~? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X3 : $i > $o] : (X0 @ X3 @ X3) & ! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3] : ((X2 @ X3) <=> (X1 @ X3))))), 0.22/0.41 inference(negated_conjecture,[],[f1])). 0.22/0.41 thf(f1,conjecture,( 0.22/0.41 ? [X0 : ($i > $o) > ($i > $o) > $o] : (! [X3 : $i > $o,X5 : $i > $o,X4 : $i > $o] : (((X0 @ X3 @ X4) & (X0 @ X4 @ X5)) => (X0 @ X3 @ X5)) & ! [X3 : $i > $o] : (X0 @ X3 @ X3) & ! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X2)) => ! [X3] : ((X2 @ X3) <=> (X1 @ X3))))), 0.22/0.41 file('/export/starexec/sandbox/tmp/tmp.cO0QTgRBiV/E---3.1_30184.p',cTHM120I_pme)). 0.22/0.41 % SZS output end Proof for E---3.1_30184 0.22/0.41 % (30426)------------------------------ 0.22/0.41 % (30426)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.41 % (30426)Termination reason: Refutation 0.22/0.41 0.22/0.41 % (30426)Memory used [KB]: 5628 0.22/0.41 % (30426)Time elapsed: 0.008 s 0.22/0.41 % (30426)Instructions burned: 10 (million) 0.22/0.41 % (30426)------------------------------ 0.22/0.41 % (30426)------------------------------ 0.22/0.41 % (30407)Success in time 0.021 s 0.22/0.41 EOF