0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.10 % Command : run_vampire %s %d THM 0.09/0.30 % Computer : n032.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 1440 0.09/0.30 % WCLimit : 180 0.09/0.30 % DateTime : Thu Jul 4 08:20:53 EDT 2024 0.09/0.31 % CPUTime : 0.15/0.32 This is a THF_ problem 0.15/0.32 Running higher-order theorem proving 0.15/0.33 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.uhKqkCh3KT/E---3.1_6491.p -m 16384 -t 180 0.15/0.34 % (6602)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_6491 for (1799ds/2Mi) 0.15/0.34 % (6605)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_6491 for (1799ds/18Mi) 0.15/0.34 % (6600)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_6491 for (1799ds/4Mi) 0.15/0.34 % (6602)Instruction limit reached! 0.15/0.34 % (6602)------------------------------ 0.15/0.34 % (6602)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.34 % (6602)Termination reason: Unknown 0.15/0.34 % (6602)Termination phase: Unused predicate definition removal 0.15/0.34 0.15/0.34 % (6602)Memory used [KB]: 1023 0.15/0.34 % (6602)Time elapsed: 0.002 s 0.15/0.34 % (6602)Instructions burned: 2 (million) 0.15/0.34 % (6602)------------------------------ 0.15/0.34 % (6602)------------------------------ 0.15/0.34 % (6603)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_6491 for (1799ds/2Mi) 0.15/0.34 % (6601)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_6491 for (1799ds/27Mi) 0.15/0.34 % (6604)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_6491 for (1799ds/275Mi) 0.15/0.34 % (6600)Instruction limit reached! 0.15/0.34 % (6600)------------------------------ 0.15/0.34 % (6600)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.34 % (6599)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_6491 for (1799ds/183Mi) 0.15/0.34 % (6600)Termination reason: Unknown 0.15/0.34 % (6600)Termination phase: Saturation 0.15/0.34 0.15/0.34 % (6600)Memory used [KB]: 5500 0.15/0.34 % (6600)Time elapsed: 0.004 s 0.15/0.34 % (6600)Instructions burned: 4 (million) 0.15/0.34 % (6600)------------------------------ 0.15/0.34 % (6600)------------------------------ 0.15/0.34 % (6603)Instruction limit reached! 0.15/0.34 % (6603)------------------------------ 0.15/0.34 % (6603)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.34 % (6603)Termination reason: Unknown 0.15/0.34 % (6603)Termination phase: Property scanning 0.15/0.34 0.15/0.34 % (6603)Memory used [KB]: 1023 0.15/0.34 % (6603)Time elapsed: 0.003 s 0.15/0.34 % (6603)Instructions burned: 3 (million) 0.15/0.34 % (6603)------------------------------ 0.15/0.34 % (6603)------------------------------ 0.15/0.35 % (6605)Instruction limit reached! 0.15/0.35 % (6605)------------------------------ 0.15/0.35 % (6605)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.35 % (6605)Termination reason: Unknown 0.15/0.35 % (6605)Termination phase: Saturation 0.15/0.35 0.15/0.35 % (6605)Memory used [KB]: 5628 0.15/0.35 % (6605)Time elapsed: 0.010 s 0.15/0.35 % (6605)Instructions burned: 19 (million) 0.15/0.35 % (6605)------------------------------ 0.15/0.35 % (6605)------------------------------ 0.15/0.35 % (6606)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_6491 for (1799ds/3Mi) 0.15/0.35 % (6601)Refutation not found, incomplete strategy 0.15/0.35 % (6601)------------------------------ 0.15/0.35 % (6601)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.35 % (6601)Termination reason: Refutation not found, incomplete strategy 0.15/0.35 0.15/0.35 0.15/0.35 % (6601)Memory used [KB]: 5628 0.15/0.35 % (6601)Time elapsed: 0.011 s 0.15/0.35 % (6601)Instructions burned: 16 (million) 0.15/0.35 % (6601)------------------------------ 0.15/0.35 % (6601)------------------------------ 0.15/0.35 % (6606)Instruction limit reached! 0.15/0.35 % (6606)------------------------------ 0.15/0.35 % (6606)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.35 % (6606)Termination reason: Unknown 0.15/0.35 % (6606)Termination phase: Saturation 0.15/0.35 0.15/0.35 % (6606)Memory used [KB]: 5500 0.15/0.35 % (6606)Time elapsed: 0.003 s 0.15/0.35 % (6606)Instructions burned: 4 (million) 0.15/0.35 % (6606)------------------------------ 0.15/0.35 % (6606)------------------------------ 0.18/0.35 % (6608)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_6491 for (1799ds/15Mi) 0.18/0.36 % (6607)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_6491 for (1799ds/37Mi) 0.18/0.36 % (6609)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_6491 for (1799ds/3Mi) 0.18/0.36 % (6609)Instruction limit reached! 0.18/0.36 % (6609)------------------------------ 0.18/0.36 % (6609)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.36 % (6609)Termination reason: Unknown 0.18/0.36 % (6609)Termination phase: Saturation 0.18/0.36 % (6611)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_6491 for (1799ds/7Mi) 0.18/0.36 0.18/0.36 % (6609)Memory used [KB]: 5500 0.18/0.36 % (6609)Time elapsed: 0.003 s 0.18/0.36 % (6609)Instructions burned: 4 (million) 0.18/0.36 % (6609)------------------------------ 0.18/0.36 % (6609)------------------------------ 0.18/0.36 % (6608)Instruction limit reached! 0.18/0.36 % (6608)------------------------------ 0.18/0.36 % (6608)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.36 % (6608)Termination reason: Unknown 0.18/0.36 % (6608)Termination phase: Saturation 0.18/0.36 0.18/0.36 % (6608)Memory used [KB]: 5628 0.18/0.36 % (6608)Time elapsed: 0.030 s 0.18/0.36 % (6608)Instructions burned: 16 (million) 0.18/0.36 % (6608)------------------------------ 0.18/0.36 % (6608)------------------------------ 0.18/0.36 % (6610)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on E---3.1_6491 for (1799ds/1041Mi) 0.18/0.36 % (6611)Instruction limit reached! 0.18/0.36 % (6611)------------------------------ 0.18/0.36 % (6611)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.36 % (6611)Termination reason: Unknown 0.18/0.36 % (6611)Termination phase: Saturation 0.18/0.36 0.18/0.36 % (6611)Memory used [KB]: 1023 0.18/0.36 % (6611)Time elapsed: 0.004 s 0.18/0.36 % (6611)Instructions burned: 7 (million) 0.18/0.36 % (6611)------------------------------ 0.18/0.36 % (6611)------------------------------ 0.18/0.36 % (6604)First to succeed. 0.18/0.37 % (6604)Refutation found. Thanks to Tanya! 0.18/0.37 % SZS status Theorem for E---3.1_6491 0.18/0.37 % SZS output start Proof for E---3.1_6491 0.18/0.37 thf(func_def_0, type, in: $i > $i > $o). 0.18/0.37 thf(func_def_1, type, subset: $i > $i > $o). 0.18/0.37 thf(func_def_4, type, kpair: $i > $i > $i). 0.18/0.37 thf(func_def_5, type, cartprod: $i > $i > $i). 0.18/0.37 thf(func_def_6, type, breln: $i > $i > $i > $o). 0.18/0.37 thf(func_def_14, type, sK0: $i > $i > $i). 0.18/0.37 thf(func_def_24, type, sK10: $i > $o). 0.18/0.37 thf(func_def_26, type, sK12: ($i > $o) > $i > $i > $i > $i). 0.18/0.37 thf(func_def_27, type, sK13: ($i > $o) > $i > $i > $i > $i). 0.18/0.37 thf(func_def_30, type, ph15: !>[X0: $tType]:(X0)). 0.18/0.37 thf(f185,plain,( 0.18/0.37 $false), 0.18/0.37 inference(avatar_sat_refutation,[],[f170,f184])). 0.18/0.37 thf(f184,plain,( 0.18/0.37 ~spl14_3), 0.18/0.37 inference(avatar_contradiction_clause,[],[f183])). 0.18/0.37 thf(f183,plain,( 0.18/0.37 $false | ~spl14_3), 0.18/0.37 inference(subsumption_resolution,[],[f182,f43])). 0.18/0.37 thf(f43,plain,( 0.18/0.37 ((subset @ sK5 @ sK6) != $true)), 0.18/0.37 inference(cnf_transformation,[],[f27])). 0.18/0.37 thf(f27,plain,( 0.18/0.37 (subsetI1 = $true) & (brelnall1 = $true) & ((((subset @ sK5 @ sK6) != $true) & ($true = (breln @ sK3 @ sK4 @ sK6)) & ! [X4] : (((in @ X4 @ sK3) != $true) | ! [X5] : (((in @ X5 @ sK4) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK5)) | ($true = (in @ (kpair @ X4 @ X5) @ sK6))))) & ((breln @ sK3 @ sK4 @ sK5) = $true))), 0.18/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f19,f26,f25])). 0.18/0.37 thf(f25,plain,( 0.18/0.37 ? [X0,X1,X2] : (? [X3] : (($true != (subset @ X2 @ X3)) & ((breln @ X0 @ X1 @ X3) = $true) & ! [X4] : (((in @ X4 @ X0) != $true) | ! [X5] : (($true != (in @ X5 @ X1)) | ($true != (in @ (kpair @ X4 @ X5) @ X2)) | ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) & ((breln @ X0 @ X1 @ X2) = $true)) => (? [X3] : (((subset @ sK5 @ X3) != $true) & ($true = (breln @ sK3 @ sK4 @ X3)) & ! [X4] : (((in @ X4 @ sK3) != $true) | ! [X5] : (((in @ X5 @ sK4) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK5)) | ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) & ((breln @ sK3 @ sK4 @ sK5) = $true))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f26,plain,( 0.18/0.37 ? [X3] : (((subset @ sK5 @ X3) != $true) & ($true = (breln @ sK3 @ sK4 @ X3)) & ! [X4] : (((in @ X4 @ sK3) != $true) | ! [X5] : (((in @ X5 @ sK4) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK5)) | ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) => (((subset @ sK5 @ sK6) != $true) & ($true = (breln @ sK3 @ sK4 @ sK6)) & ! [X4] : (((in @ X4 @ sK3) != $true) | ! [X5] : (((in @ X5 @ sK4) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK5)) | ($true = (in @ (kpair @ X4 @ X5) @ sK6)))))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f19,plain,( 0.18/0.37 (subsetI1 = $true) & (brelnall1 = $true) & ? [X0,X1,X2] : (? [X3] : (($true != (subset @ X2 @ X3)) & ((breln @ X0 @ X1 @ X3) = $true) & ! [X4] : (((in @ X4 @ X0) != $true) | ! [X5] : (($true != (in @ X5 @ X1)) | ($true != (in @ (kpair @ X4 @ X5) @ X2)) | ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) & ((breln @ X0 @ X1 @ X2) = $true))), 0.18/0.37 inference(flattening,[],[f18])). 0.18/0.37 thf(f18,plain,( 0.18/0.37 (? [X0,X1,X2] : (? [X3] : ((($true != (subset @ X2 @ X3)) & ! [X4] : (! [X5] : ((((in @ (kpair @ X4 @ X5) @ X3) = $true) | ($true != (in @ (kpair @ X4 @ X5) @ X2))) | ($true != (in @ X5 @ X1))) | ((in @ X4 @ X0) != $true))) & ((breln @ X0 @ X1 @ X3) = $true)) & ((breln @ X0 @ X1 @ X2) = $true)) & (brelnall1 = $true)) & (subsetI1 = $true)), 0.18/0.37 inference(ennf_transformation,[],[f12])). 0.18/0.37 thf(f12,plain,( 0.18/0.37 ~((subsetI1 = $true) => ((brelnall1 = $true) => ! [X0,X1,X2] : (((breln @ X0 @ X1 @ X2) = $true) => ! [X3] : (((breln @ X0 @ X1 @ X3) = $true) => (! [X4] : (((in @ X4 @ X0) = $true) => ! [X5] : (($true = (in @ X5 @ X1)) => (($true = (in @ (kpair @ X4 @ X5) @ X2)) => ((in @ (kpair @ X4 @ X5) @ X3) = $true)))) => ($true = (subset @ X2 @ X3)))))))), 0.18/0.37 inference(fool_elimination,[],[f11])). 0.18/0.37 thf(f11,plain,( 0.18/0.37 ~(subsetI1 => (brelnall1 => ! [X0,X1,X2] : ((breln @ X0 @ X1 @ X2) => ! [X3] : ((breln @ X0 @ X1 @ X3) => (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3))))))), 0.18/0.37 inference(rectify,[],[f5])). 0.18/0.37 thf(f5,negated_conjecture,( 0.18/0.37 ~(subsetI1 => (brelnall1 => ! [X0,X1,X4] : ((breln @ X0 @ X1 @ X4) => ! [X7] : ((breln @ X0 @ X1 @ X7) => (! [X2] : ((in @ X2 @ X0) => ! [X6] : ((in @ X6 @ X1) => ((in @ (kpair @ X2 @ X6) @ X4) => (in @ (kpair @ X2 @ X6) @ X7)))) => (subset @ X4 @ X7))))))), 0.18/0.37 inference(negated_conjecture,[],[f4])). 0.18/0.37 thf(f4,conjecture,( 0.18/0.37 subsetI1 => (brelnall1 => ! [X0,X1,X4] : ((breln @ X0 @ X1 @ X4) => ! [X7] : ((breln @ X0 @ X1 @ X7) => (! [X2] : ((in @ X2 @ X0) => ! [X6] : ((in @ X6 @ X1) => ((in @ (kpair @ X2 @ X6) @ X4) => (in @ (kpair @ X2 @ X6) @ X7)))) => (subset @ X4 @ X7)))))), 0.18/0.37 file('/export/starexec/sandbox/tmp/tmp.uhKqkCh3KT/E---3.1_6491.p',subbreln)). 0.18/0.37 thf(f182,plain,( 0.18/0.37 ((subset @ sK5 @ sK6) = $true) | ~spl14_3), 0.18/0.37 inference(equality_resolution,[],[f181])). 0.18/0.37 thf(f181,plain,( 0.18/0.37 ( ! [X0 : $i] : (((sK0 @ sK6 @ sK5) != (sK0 @ X0 @ sK5)) | ((subset @ sK5 @ X0) = $true)) ) | ~spl14_3), 0.18/0.37 inference(trivial_inequality_removal,[],[f174])). 0.18/0.37 thf(f174,plain,( 0.18/0.37 ( ! [X0 : $i] : (($true != $true) | ((sK0 @ sK6 @ sK5) != (sK0 @ X0 @ sK5)) | ((subset @ sK5 @ X0) = $true)) ) | ~spl14_3), 0.18/0.37 inference(superposition,[],[f169,f66])). 0.18/0.37 thf(f66,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X0) = $true) | ((subset @ X0 @ X1) = $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f55])). 0.18/0.37 thf(f55,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X0) = $true) | ((subset @ X0 @ X1) = $true) | ($true != $true)) )), 0.18/0.37 inference(definition_unfolding,[],[f38,f45])). 0.18/0.37 thf(f45,plain,( 0.18/0.37 (subsetI1 = $true)), 0.18/0.37 inference(cnf_transformation,[],[f27])). 0.18/0.37 thf(f38,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK0 @ X1 @ X0) @ X0) = $true) | (subsetI1 != $true)) )), 0.18/0.37 inference(cnf_transformation,[],[f24])). 0.18/0.37 thf(f24,plain,( 0.18/0.37 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | (((in @ (sK0 @ X1 @ X0) @ X1) != $true) & ((in @ (sK0 @ X1 @ X0) @ X0) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != (subset @ sK1 @ sK2)) & ! [X5] : (((in @ X5 @ sK2) = $true) | ($true != (in @ X5 @ sK1)))))), 0.18/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f23,f22])). 0.18/0.37 thf(f22,plain,( 0.18/0.37 ! [X0,X1] : (? [X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)) => (((in @ (sK0 @ X1 @ X0) @ X1) != $true) & ((in @ (sK0 @ X1 @ X0) @ X0) = $true)))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f23,plain,( 0.18/0.37 ? [X3,X4] : (((subset @ X3 @ X4) != $true) & ! [X5] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true))) => (($true != (subset @ sK1 @ sK2)) & ! [X5] : (((in @ X5 @ sK2) = $true) | ($true != (in @ X5 @ sK1))))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f21,plain,( 0.18/0.37 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3,X4] : (((subset @ X3 @ X4) != $true) & ! [X5] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true))))), 0.18/0.37 inference(rectify,[],[f20])). 0.18/0.37 thf(f20,plain,( 0.18/0.37 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0,X1] : (((subset @ X0 @ X1) != $true) & ! [X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))))), 0.18/0.37 inference(nnf_transformation,[],[f15])). 0.18/0.37 thf(f15,plain,( 0.18/0.37 ! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) <=> (subsetI1 = $true)), 0.18/0.37 inference(ennf_transformation,[],[f8])). 0.18/0.37 thf(f8,plain,( 0.18/0.37 (subsetI1 = $true) <=> ! [X0,X1] : (! [X2] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))), 0.18/0.37 inference(fool_elimination,[],[f7])). 0.18/0.37 thf(f7,plain,( 0.18/0.37 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)), 0.18/0.37 inference(rectify,[],[f1])). 0.18/0.37 thf(f1,axiom,( 0.18/0.37 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)), 0.18/0.37 file('/export/starexec/sandbox/tmp/tmp.uhKqkCh3KT/E---3.1_6491.p',subsetI1)). 0.18/0.37 thf(f169,plain,( 0.18/0.37 ( ! [X0 : $i] : (((in @ X0 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X0)) ) | ~spl14_3), 0.18/0.37 inference(avatar_component_clause,[],[f168])). 0.18/0.37 thf(f168,plain,( 0.18/0.37 spl14_3 <=> ! [X0] : (((in @ X0 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X0))), 0.18/0.37 introduced(avatar_definition,[new_symbols(naming,[spl14_3])])). 0.18/0.37 thf(f170,plain,( 0.18/0.37 spl14_3 | spl14_3), 0.18/0.37 inference(avatar_split_clause,[],[f166,f168,f168])). 0.18/0.37 thf(f166,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK5) != $true) | ((in @ X0 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X1) | ((sK0 @ sK6 @ sK5) != X0)) )), 0.18/0.37 inference(subsumption_resolution,[],[f165,f43])). 0.18/0.37 thf(f165,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X1) | ((in @ X1 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X0) | ((subset @ sK5 @ sK6) = $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f164])). 0.18/0.37 thf(f164,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ sK5 @ sK6) = $true) | ((sK0 @ sK6 @ sK5) != X1) | ((in @ X0 @ sK5) != $true) | ((in @ X1 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X0) | ($true != $true)) )), 0.18/0.37 inference(duplicate_literal_removal,[],[f163])). 0.18/0.37 thf(f163,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((sK0 @ sK6 @ sK5) != X0) | ((in @ X1 @ sK5) != $true) | ((sK0 @ sK6 @ sK5) != X1) | ((in @ X0 @ sK5) != $true) | ((subset @ sK5 @ sK6) = $true) | ((subset @ sK5 @ sK6) = $true) | ($true != $true)) )), 0.18/0.37 inference(superposition,[],[f154,f66])). 0.18/0.37 thf(f154,plain,( 0.18/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK0 @ sK6 @ X0) @ sK5) != $true) | ((sK0 @ sK6 @ X0) != X1) | ((in @ X2 @ sK5) != $true) | ((sK0 @ sK6 @ X0) != X2) | ((in @ X1 @ sK5) != $true) | ($true = (subset @ X0 @ sK6))) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f153])). 0.18/0.37 thf(f153,plain,( 0.18/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sK0 @ sK6 @ X0) != X1) | ((sK0 @ sK6 @ X0) != X2) | ($true = (subset @ X0 @ sK6)) | ((in @ X2 @ sK5) != $true) | ((in @ X1 @ sK5) != $true) | ((in @ (sK0 @ sK6 @ X0) @ sK5) != $true) | ($true != $true)) )), 0.18/0.37 inference(superposition,[],[f67,f152])). 0.18/0.37 thf(f152,plain,( 0.18/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ sK6) = $true) | ((in @ X1 @ sK5) != $true) | ((in @ X0 @ sK5) != $true) | ((in @ X2 @ sK5) != $true) | (X0 != X2) | (X0 != X1)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f151])). 0.18/0.37 thf(f151,plain,( 0.18/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true) | (X0 != X1) | ((in @ X1 @ sK5) != $true) | ((in @ X2 @ sK5) != $true) | (X0 != X2) | ($true != $true)) )), 0.18/0.37 inference(duplicate_literal_removal,[],[f146])). 0.18/0.37 thf(f146,plain,( 0.18/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 != X2) | ((in @ X0 @ sK5) != $true) | (X0 != X1) | ((in @ X2 @ sK5) != $true) | ($true != $true) | ((in @ X1 @ sK5) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true)) )), 0.18/0.37 inference(superposition,[],[f145,f40])). 0.18/0.37 thf(f40,plain,( 0.18/0.37 ((breln @ sK3 @ sK4 @ sK5) = $true)), 0.18/0.37 inference(cnf_transformation,[],[f27])). 0.18/0.37 thf(f145,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (breln @ sK3 @ sK4 @ X1)) | ((in @ X0 @ sK5) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ X1) != $true) | (X0 != X2) | (X0 != X3)) )), 0.18/0.37 inference(equality_proxy_clausification,[],[f144])). 0.18/0.37 thf(f144,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((X0 = X3) = $false) | ($true != (breln @ sK3 @ sK4 @ X1)) | ((in @ X0 @ X1) != $true) | (X0 != X2) | ((in @ X0 @ sK5) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X3 @ X1) != $true)) )), 0.18/0.37 inference(not_proxy_clausification,[],[f143])). 0.18/0.37 thf(f143,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((~ (X0 = X3)) = $true) | ((in @ X0 @ sK5) != $true) | ($true != (breln @ sK3 @ sK4 @ X1)) | (X0 != X2) | ((in @ X0 @ X1) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X3 @ X1) != $true)) )), 0.18/0.37 inference(beta_eta_normalization,[],[f142])). 0.18/0.37 thf(f142,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ sK5) != $true) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ((in @ X3 @ X1) != $true) | (X0 != X2) | ((in @ X2 @ X1) != $true) | ($true != (breln @ sK3 @ sK4 @ X1)) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ X1) != $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f141])). 0.18/0.37 thf(f141,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (breln @ sK3 @ sK4 @ X1)) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true) | ((in @ X2 @ X1) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ X1) != $true) | (X0 != X2) | ($true != $true)) )), 0.18/0.37 inference(duplicate_literal_removal,[],[f140])). 0.18/0.37 thf(f140,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ sK5) != $true) | ((in @ X0 @ sK6) = $true) | ($true != $true) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ($true != (breln @ sK3 @ sK4 @ X1)) | ((in @ X3 @ X1) != $true) | ($true != (breln @ sK3 @ sK4 @ X1)) | (X0 != X2) | ((in @ X2 @ X1) != $true) | ((in @ X0 @ X1) != $true)) )), 0.18/0.37 inference(superposition,[],[f139,f70])). 0.18/0.37 thf(f70,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (((in @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X7) = $true) | ($true != (breln @ X7 @ X9 @ X8)) | ((in @ X13 @ X8) != $true) | ((X10 @ X13) = $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f65])). 0.18/0.37 thf(f65,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (((in @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X7) = $true) | ((X10 @ X13) = $true) | ($true != $true) | ((in @ X13 @ X8) != $true) | ($true != (breln @ X7 @ X9 @ X8))) )), 0.18/0.37 inference(definition_unfolding,[],[f46,f44])). 0.18/0.37 thf(f44,plain,( 0.18/0.37 (brelnall1 = $true)), 0.18/0.37 inference(cnf_transformation,[],[f27])). 0.18/0.37 thf(f46,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (breln @ X7 @ X9 @ X8)) | ((in @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X7) = $true) | ((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true) | (brelnall1 != $true)) )), 0.18/0.37 inference(cnf_transformation,[],[f35])). 0.18/0.37 thf(f35,plain,( 0.18/0.37 ((brelnall1 = $true) | (($true = (breln @ sK7 @ sK9 @ sK8)) & (! [X4] : (! [X5] : (((in @ X5 @ sK9) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true = (sK10 @ (kpair @ X4 @ X5)))) | ((in @ X4 @ sK7) != $true)) & (((sK10 @ sK11) != $true) & ((in @ sK11 @ sK8) = $true))))) & (! [X7,X8,X9] : (($true != (breln @ X7 @ X9 @ X8)) | ! [X10 : $i > $o] : (((($true = (in @ (sK13 @ X10 @ X9 @ X8 @ X7) @ X9)) & ((in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7)) @ X8) = $true) & ((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7))) != $true)) & ((in @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X7) = $true)) | ! [X13] : (((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true)))) | (brelnall1 != $true))), 0.18/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12,sK13])],[f29,f34,f33,f32,f31,f30])). 0.18/0.37 thf(f30,plain,( 0.18/0.37 ? [X0,X1,X2] : (($true = (breln @ X0 @ X2 @ X1)) & ? [X3 : $i > $o] : (! [X4] : (! [X5] : (((in @ X5 @ X2) != $true) | ((in @ (kpair @ X4 @ X5) @ X1) != $true) | ((X3 @ (kpair @ X4 @ X5)) = $true)) | ((in @ X4 @ X0) != $true)) & ? [X6] : (($true != (X3 @ X6)) & ((in @ X6 @ X1) = $true)))) => (($true = (breln @ sK7 @ sK9 @ sK8)) & ? [X3 : $i > $o] : (! [X4] : (! [X5] : (((in @ X5 @ sK9) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ((X3 @ (kpair @ X4 @ X5)) = $true)) | ((in @ X4 @ sK7) != $true)) & ? [X6] : (($true != (X3 @ X6)) & ((in @ X6 @ sK8) = $true))))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f31,plain,( 0.18/0.37 ? [X3 : $i > $o] : (! [X4] : (! [X5] : (((in @ X5 @ sK9) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ((X3 @ (kpair @ X4 @ X5)) = $true)) | ((in @ X4 @ sK7) != $true)) & ? [X6] : (($true != (X3 @ X6)) & ((in @ X6 @ sK8) = $true))) => (! [X4] : (! [X5] : (((in @ X5 @ sK9) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK8)) | ($true = (sK10 @ (kpair @ X4 @ X5)))) | ((in @ X4 @ sK7) != $true)) & ? [X6] : (((sK10 @ X6) != $true) & ((in @ X6 @ sK8) = $true)))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f32,plain,( 0.18/0.37 ? [X6] : (((sK10 @ X6) != $true) & ((in @ X6 @ sK8) = $true)) => (((sK10 @ sK11) != $true) & ((in @ sK11 @ sK8) = $true))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f33,plain,( 0.18/0.37 ! [X7,X8,X9,X10 : $i > $o] : (? [X11] : (? [X12] : (((in @ X12 @ X9) = $true) & ($true = (in @ (kpair @ X11 @ X12) @ X8)) & ((X10 @ (kpair @ X11 @ X12)) != $true)) & ((in @ X11 @ X7) = $true)) => (? [X12] : (((in @ X12 @ X9) = $true) & ($true = (in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X12) @ X8)) & ((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X12)) != $true)) & ((in @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X7) = $true)))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f34,plain,( 0.18/0.37 ! [X7,X8,X9,X10 : $i > $o] : (? [X12] : (((in @ X12 @ X9) = $true) & ($true = (in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X12) @ X8)) & ((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ X12)) != $true)) => (($true = (in @ (sK13 @ X10 @ X9 @ X8 @ X7) @ X9)) & ((in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7)) @ X8) = $true) & ((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7))) != $true)))), 0.18/0.37 introduced(choice_axiom,[])). 0.18/0.37 thf(f29,plain,( 0.18/0.37 ((brelnall1 = $true) | ? [X0,X1,X2] : (($true = (breln @ X0 @ X2 @ X1)) & ? [X3 : $i > $o] : (! [X4] : (! [X5] : (((in @ X5 @ X2) != $true) | ((in @ (kpair @ X4 @ X5) @ X1) != $true) | ((X3 @ (kpair @ X4 @ X5)) = $true)) | ((in @ X4 @ X0) != $true)) & ? [X6] : (($true != (X3 @ X6)) & ((in @ X6 @ X1) = $true))))) & (! [X7,X8,X9] : (($true != (breln @ X7 @ X9 @ X8)) | ! [X10 : $i > $o] : (? [X11] : (? [X12] : (((in @ X12 @ X9) = $true) & ($true = (in @ (kpair @ X11 @ X12) @ X8)) & ((X10 @ (kpair @ X11 @ X12)) != $true)) & ((in @ X11 @ X7) = $true)) | ! [X13] : (((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true)))) | (brelnall1 != $true))), 0.18/0.37 inference(rectify,[],[f28])). 0.18/0.37 thf(f28,plain,( 0.18/0.37 ((brelnall1 = $true) | ? [X0,X1,X2] : (($true = (breln @ X0 @ X2 @ X1)) & ? [X3 : $i > $o] : (! [X4] : (! [X5] : (((in @ X5 @ X2) != $true) | ((in @ (kpair @ X4 @ X5) @ X1) != $true) | ((X3 @ (kpair @ X4 @ X5)) = $true)) | ((in @ X4 @ X0) != $true)) & ? [X6] : (($true != (X3 @ X6)) & ((in @ X6 @ X1) = $true))))) & (! [X0,X1,X2] : (($true != (breln @ X0 @ X2 @ X1)) | ! [X3 : $i > $o] : (? [X4] : (? [X5] : (((in @ X5 @ X2) = $true) & ((in @ (kpair @ X4 @ X5) @ X1) = $true) & ((X3 @ (kpair @ X4 @ X5)) != $true)) & ((in @ X4 @ X0) = $true)) | ! [X6] : (($true = (X3 @ X6)) | ((in @ X6 @ X1) != $true)))) | (brelnall1 != $true))), 0.18/0.37 inference(nnf_transformation,[],[f17])). 0.18/0.37 thf(f17,plain,( 0.18/0.37 (brelnall1 = $true) <=> ! [X0,X1,X2] : (($true != (breln @ X0 @ X2 @ X1)) | ! [X3 : $i > $o] : (? [X4] : (? [X5] : (((in @ X5 @ X2) = $true) & ((in @ (kpair @ X4 @ X5) @ X1) = $true) & ((X3 @ (kpair @ X4 @ X5)) != $true)) & ((in @ X4 @ X0) = $true)) | ! [X6] : (($true = (X3 @ X6)) | ((in @ X6 @ X1) != $true))))), 0.18/0.37 inference(flattening,[],[f16])). 0.18/0.37 thf(f16,plain,( 0.18/0.37 ! [X0,X1,X2] : (! [X3 : $i > $o] : (! [X6] : (($true = (X3 @ X6)) | ((in @ X6 @ X1) != $true)) | ? [X4] : (? [X5] : ((((X3 @ (kpair @ X4 @ X5)) != $true) & ((in @ (kpair @ X4 @ X5) @ X1) = $true)) & ((in @ X5 @ X2) = $true)) & ((in @ X4 @ X0) = $true))) | ($true != (breln @ X0 @ X2 @ X1))) <=> (brelnall1 = $true)), 0.18/0.37 inference(ennf_transformation,[],[f10])). 0.18/0.37 thf(f10,plain,( 0.18/0.37 ! [X0,X1,X2] : (($true = (breln @ X0 @ X2 @ X1)) => ! [X3 : $i > $o] : (! [X4] : (((in @ X4 @ X0) = $true) => ! [X5] : (((in @ X5 @ X2) = $true) => (((in @ (kpair @ X4 @ X5) @ X1) = $true) => ((X3 @ (kpair @ X4 @ X5)) = $true)))) => ! [X6] : (((in @ X6 @ X1) = $true) => ($true = (X3 @ X6))))) <=> (brelnall1 = $true)), 0.18/0.37 inference(fool_elimination,[],[f9])). 0.18/0.37 thf(f9,plain,( 0.18/0.37 (brelnall1 = ! [X0,X1,X2] : ((breln @ X0 @ X2 @ X1) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X1) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X1) => (X3 @ X6)))))), 0.18/0.37 inference(rectify,[],[f3])). 0.18/0.37 thf(f3,axiom,( 0.18/0.37 (brelnall1 = ! [X0,X4,X1] : ((breln @ X0 @ X1 @ X4) => ! [X5 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X6] : ((in @ X6 @ X1) => ((in @ (kpair @ X2 @ X6) @ X4) => (X5 @ (kpair @ X2 @ X6))))) => ! [X2] : ((in @ X2 @ X4) => (X5 @ X2)))))), 0.18/0.37 file('/export/starexec/sandbox/tmp/tmp.uhKqkCh3KT/E---3.1_6491.p',brelnall1)). 0.18/0.37 thf(f139,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ sK4 @ X1 @ X2) @ sK3) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true) | ((breln @ X2 @ sK4 @ X1) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ X1) != $true) | (X0 != X3)) )), 0.18/0.37 inference(equality_proxy_clausification,[],[f138])). 0.18/0.37 thf(f138,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((breln @ X2 @ sK4 @ X1) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ X1) != $true) | ((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ sK4 @ X1 @ X2) @ sK3) != $true) | ((X0 = X3) = $false)) )), 0.18/0.37 inference(not_proxy_clausification,[],[f137])). 0.18/0.37 thf(f137,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((~ (X0 = X3)) = $true) | ((breln @ X2 @ sK4 @ X1) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ sK5) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ sK4 @ X1 @ X2) @ sK3) != $true) | ((in @ X0 @ X1) != $true)) )), 0.18/0.37 inference(beta_eta_normalization,[],[f136])). 0.18/0.37 thf(f136,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X0 @ X1) != $true) | ((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ sK4 @ X1 @ X2) @ sK3) != $true) | ((in @ X0 @ sK5) != $true) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ((breln @ X2 @ sK4 @ X1) != $true) | ((in @ X0 @ sK6) = $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f135])). 0.18/0.37 thf(f135,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ sK4 @ X1 @ X2) @ sK3) != $true) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ((in @ X3 @ X1) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true) | ((breln @ X2 @ sK4 @ X1) != $true) | ((in @ X0 @ X1) != $true)) )), 0.18/0.37 inference(duplicate_literal_removal,[],[f134])). 0.18/0.37 thf(f134,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ sK4 @ X1 @ X2) @ sK3) != $true) | ($true = ((^[Y0 : $i]: (~ (X0 = Y0))) @ X3)) | ((in @ X0 @ sK5) != $true) | ((breln @ X2 @ sK4 @ X1) != $true) | ((in @ X3 @ X1) != $true) | ((breln @ X2 @ sK4 @ X1) != $true) | ($true != $true)) )), 0.18/0.37 inference(superposition,[],[f107,f68])). 0.18/0.37 thf(f68,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true = (in @ (sK13 @ X10 @ X9 @ X8 @ X7) @ X9)) | ($true != (breln @ X7 @ X9 @ X8)) | ((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f62])). 0.18/0.37 thf(f62,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != $true) | ($true = (in @ (sK13 @ X10 @ X9 @ X8 @ X7) @ X9)) | ($true != (breln @ X7 @ X9 @ X8)) | ((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true)) )), 0.18/0.37 inference(definition_unfolding,[],[f49,f44])). 0.18/0.37 thf(f49,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (breln @ X7 @ X9 @ X8)) | ($true = (in @ (sK13 @ X10 @ X9 @ X8 @ X7) @ X9)) | ((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true) | (brelnall1 != $true)) )), 0.18/0.37 inference(cnf_transformation,[],[f35])). 0.18/0.37 thf(f107,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK13 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3) @ sK4) != $true) | ((breln @ X3 @ X1 @ X2) != $true) | ((in @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3) @ sK3) != $true) | ((in @ X0 @ sK6) = $true) | ((in @ X0 @ sK5) != $true) | ($true != (in @ X0 @ X2))) )), 0.18/0.37 inference(superposition,[],[f41,f75])). 0.18/0.37 thf(f75,plain,( 0.18/0.37 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ (sK12 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3) @ (sK13 @ (^[Y0 : $i]: (~ (X0 = Y0))) @ X1 @ X2 @ X3)) = X0) | ((breln @ X3 @ X1 @ X2) != $true) | ($true != (in @ X0 @ X2))) )), 0.18/0.37 inference(leibniz_equality_elimination,[],[f71])). 0.18/0.37 thf(f71,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7))) != $true) | ((X10 @ X13) = $true) | ($true != (breln @ X7 @ X9 @ X8)) | ((in @ X13 @ X8) != $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f64])). 0.18/0.37 thf(f64,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (breln @ X7 @ X9 @ X8)) | ((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true) | ((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7))) != $true) | ($true != $true)) )), 0.18/0.37 inference(definition_unfolding,[],[f47,f44])). 0.18/0.37 thf(f47,plain,( 0.18/0.37 ( ! [X10 : $i > $o,X8 : $i,X9 : $i,X7 : $i,X13 : $i] : (($true != (breln @ X7 @ X9 @ X8)) | ((X10 @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7) @ (sK13 @ X10 @ X9 @ X8 @ X7))) != $true) | ((X10 @ X13) = $true) | ((in @ X13 @ X8) != $true) | (brelnall1 != $true)) )), 0.18/0.37 inference(cnf_transformation,[],[f35])). 0.18/0.37 thf(f41,plain,( 0.18/0.37 ( ! [X4 : $i,X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ sK6)) | ((in @ X5 @ sK4) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK5)) | ((in @ X4 @ sK3) != $true)) )), 0.18/0.37 inference(cnf_transformation,[],[f27])). 0.18/0.37 thf(f67,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )), 0.18/0.37 inference(trivial_inequality_removal,[],[f54])). 0.18/0.37 thf(f54,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK0 @ X1 @ X0) @ X1) != $true) | ($true != $true)) )), 0.18/0.37 inference(definition_unfolding,[],[f39,f45])). 0.18/0.37 thf(f39,plain,( 0.18/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK0 @ X1 @ X0) @ X1) != $true) | (subsetI1 != $true)) )), 0.18/0.37 inference(cnf_transformation,[],[f24])). 0.18/0.37 % SZS output end Proof for E---3.1_6491 0.18/0.37 % (6604)------------------------------ 0.18/0.37 % (6604)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.37 % (6604)Termination reason: Refutation 0.18/0.37 0.18/0.37 % (6604)Memory used [KB]: 5756 0.18/0.37 % (6604)Time elapsed: 0.026 s 0.18/0.37 % (6604)Instructions burned: 47 (million) 0.18/0.37 % (6604)------------------------------ 0.18/0.37 % (6604)------------------------------ 0.18/0.37 % (6598)Success in time 0.027 s 0.18/0.37 EOF