0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : run_vampire %s %d THM 0.10/0.31 % Computer : n025.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1920 0.10/0.31 % WCLimit : 240 0.10/0.31 % DateTime : Wed Jul 30 04:32:49 EDT 2025 0.10/0.31 % 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.4wXKxDnKE1/E---3.1_13738.p -m 16384 -t 240 0.15/0.35 % (13848)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_13738 for (2399ds/4Mi) 0.15/0.35 % (13849)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_13738 for (2399ds/27Mi) 0.15/0.35 % (13852)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_13738 for (2399ds/275Mi) 0.15/0.35 % (13847)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_13738 for (2399ds/183Mi) 0.15/0.35 % (13851)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_13738 for (2399ds/2Mi) 0.15/0.35 % (13853)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_13738 for (2399ds/18Mi) 0.15/0.35 % (13850)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_13738 for (2399ds/2Mi) 0.15/0.35 % (13850)Instruction limit reached! 0.15/0.35 % (13850)------------------------------ 0.15/0.35 % (13850)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.35 % (13850)Termination reason: Unknown 0.15/0.35 % (13850)Termination phase: Property scanning 0.15/0.35 % (13851)Instruction limit reached! 0.15/0.35 % (13851)------------------------------ 0.15/0.35 % (13851)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.35 0.15/0.35 % (13850)Memory used [KB]: 895 0.15/0.35 % (13850)Time elapsed: 0.002 s 0.15/0.35 % (13850)Instructions burned: 2 (million) 0.15/0.35 % (13850)------------------------------ 0.15/0.35 % (13850)------------------------------ 0.15/0.35 % (13851)Termination reason: Unknown 0.15/0.35 % (13851)Termination phase: Saturation 0.15/0.35 0.15/0.35 % (13851)Memory used [KB]: 1023 0.15/0.35 % (13851)Time elapsed: 0.004 s 0.15/0.35 % (13851)Instructions burned: 4 (million) 0.15/0.35 % (13851)------------------------------ 0.15/0.35 % (13851)------------------------------ 0.15/0.35 % (13848)Instruction limit reached! 0.15/0.35 % (13848)------------------------------ 0.15/0.35 % (13848)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.35 % (13848)Termination reason: Unknown 0.15/0.35 % (13848)Termination phase: Saturation 0.15/0.35 0.15/0.35 % (13848)Memory used [KB]: 5500 0.15/0.35 % (13848)Time elapsed: 0.005 s 0.15/0.35 % (13848)Instructions burned: 4 (million) 0.15/0.35 % (13848)------------------------------ 0.15/0.35 % (13848)------------------------------ 0.15/0.36 % (13853)Instruction limit reached! 0.15/0.36 % (13853)------------------------------ 0.15/0.36 % (13853)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.36 % (13853)Termination reason: Unknown 0.15/0.36 % (13853)Termination phase: Saturation 0.15/0.36 0.15/0.36 % (13853)Memory used [KB]: 5628 0.15/0.36 % (13853)Time elapsed: 0.012 s 0.15/0.36 % (13853)Instructions burned: 18 (million) 0.15/0.36 % (13853)------------------------------ 0.15/0.36 % (13853)------------------------------ 0.15/0.36 % (13849)Instruction limit reached! 0.15/0.36 % (13849)------------------------------ 0.15/0.36 % (13849)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.36 % (13849)Termination reason: Unknown 0.15/0.36 % (13849)Termination phase: Saturation 0.15/0.36 0.15/0.36 % (13849)Memory used [KB]: 5628 0.15/0.36 % (13849)Time elapsed: 0.016 s 0.15/0.36 % (13849)Instructions burned: 29 (million) 0.15/0.36 % (13849)------------------------------ 0.15/0.36 % (13849)------------------------------ 0.15/0.36 % (13855)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_13738 for (2399ds/37Mi) 0.15/0.36 % (13856)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_13738 for (2399ds/15Mi) 0.15/0.36 % (13854)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_13738 for (2399ds/3Mi) 0.15/0.36 % (13854)Instruction limit reached! 0.15/0.36 % (13854)------------------------------ 0.15/0.36 % (13854)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.36 % (13854)Termination reason: Unknown 0.15/0.36 % (13854)Termination phase: Saturation 0.15/0.36 0.15/0.36 % (13854)Memory used [KB]: 5500 0.15/0.36 % (13854)Time elapsed: 0.004 s 0.15/0.36 % (13854)Instructions burned: 4 (million) 0.15/0.36 % (13854)------------------------------ 0.15/0.36 % (13854)------------------------------ 0.15/0.37 % (13852)First to succeed. 0.15/0.37 % (13852)Refutation found. Thanks to Tanya! 0.15/0.37 % SZS status Theorem for E---3.1_13738 0.15/0.37 % SZS output start Proof for E---3.1_13738 0.15/0.37 thf(func_def_0, type, in: $i > $i > $o). 0.15/0.37 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i). 0.15/0.37 thf(func_def_2, type, subset: $i > $i > $o). 0.15/0.37 thf(func_def_7, type, binintersect: $i > $i > $i). 0.15/0.37 thf(func_def_27, type, sK12: $i > $i > $i). 0.15/0.37 thf(f256,plain,( 0.15/0.37 $false), 0.15/0.37 inference(subsumption_resolution,[],[f255,f75])). 0.15/0.37 thf(f75,plain,( 0.15/0.37 ((subset @ sK10 @ sK11) = $true)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 thf(f49,plain,( 0.15/0.37 (((subset @ sK10 @ sK11) = $true) & ((binintersect @ sK10 @ sK11) != sK10)) & (subsetI1 = $true) & (binintersectI = $true) & (subsetE = $true) & (binintersectLsub = $true) & (setextsub = $true)), 0.15/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f24,f48])). 0.15/0.37 thf(f48,plain,( 0.15/0.37 ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((binintersect @ X0 @ X1) != X0)) => (((subset @ sK10 @ sK11) = $true) & ((binintersect @ sK10 @ sK11) != sK10))), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f24,plain,( 0.15/0.37 ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((binintersect @ X0 @ X1) != X0)) & (subsetI1 = $true) & (binintersectI = $true) & (subsetE = $true) & (binintersectLsub = $true) & (setextsub = $true)), 0.15/0.37 inference(flattening,[],[f23])). 0.15/0.37 thf(f23,plain,( 0.15/0.37 ((((? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((binintersect @ X0 @ X1) != X0)) & (binintersectLsub = $true)) & (binintersectI = $true)) & (setextsub = $true)) & (subsetE = $true)) & (subsetI1 = $true)), 0.15/0.37 inference(ennf_transformation,[],[f13])). 0.15/0.37 thf(f13,plain,( 0.15/0.37 ~((subsetI1 = $true) => ((subsetE = $true) => ((setextsub = $true) => ((binintersectI = $true) => ((binintersectLsub = $true) => ! [X0,X1] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X0 @ X1) = X0)))))))), 0.15/0.37 inference(fool_elimination,[],[f12])). 0.15/0.37 thf(f12,plain,( 0.15/0.37 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)))))))), 0.15/0.37 inference(rectify,[],[f8])). 0.15/0.37 thf(f8,negated_conjecture,( 0.15/0.37 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)))))))), 0.15/0.37 inference(negated_conjecture,[],[f7])). 0.15/0.37 thf(f7,conjecture,( 0.15/0.37 subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectLsub => ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0))))))), 0.15/0.37 file('/export/starexec/sandbox/tmp/tmp.4wXKxDnKE1/E---3.1_13738.p',binintersectSubset2)). 0.15/0.37 thf(f255,plain,( 0.15/0.37 ((subset @ sK10 @ sK11) != $true)), 0.15/0.37 inference(trivial_inequality_removal,[],[f240])). 0.15/0.37 thf(f240,plain,( 0.15/0.37 (sK10 != sK10) | ((subset @ sK10 @ sK11) != $true)), 0.15/0.37 inference(superposition,[],[f74,f230])). 0.15/0.37 thf(f230,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ((subset @ X0 @ X1) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f224])). 0.15/0.37 thf(f224,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X0) | ($true != $true) | ((subset @ X0 @ X1) != $true)) )), 0.15/0.37 inference(superposition,[],[f107,f222])). 0.15/0.37 thf(f222,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ X1) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f221])). 0.15/0.37 thf(f221,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ X1) != $true) | ($true != $true)) )), 0.15/0.37 inference(duplicate_literal_removal,[],[f216])). 0.15/0.37 thf(f216,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ X1) != $true) | ($true != $true) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true)) )), 0.15/0.37 inference(superposition,[],[f154,f98])). 0.15/0.37 thf(f98,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK12 @ X1 @ X0) @ X1) = $true) | ((subset @ X1 @ X0) = $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f95])). 0.15/0.37 thf(f95,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK12 @ X1 @ X0) @ X1) = $true) | ($true != $true) | ((subset @ X1 @ X0) = $true)) )), 0.15/0.37 inference(definition_unfolding,[],[f78,f73])). 0.15/0.37 thf(f73,plain,( 0.15/0.37 (subsetI1 = $true)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 thf(f78,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK12 @ X1 @ X0) @ X1) = $true) | ((subset @ X1 @ X0) = $true) | (subsetI1 != $true)) )), 0.15/0.37 inference(cnf_transformation,[],[f54])). 0.15/0.37 thf(f54,plain,( 0.15/0.37 (! [X0,X1] : ((((in @ (sK12 @ X1 @ X0) @ X0) != $true) & ((in @ (sK12 @ X1 @ X0) @ X1) = $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | (! [X5] : (((in @ X5 @ sK13) = $true) | ((in @ X5 @ sK14) != $true)) & ($true != (subset @ sK14 @ sK13))))), 0.15/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f51,f53,f52])). 0.15/0.37 thf(f52,plain,( 0.15/0.37 ! [X0,X1] : (? [X2] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) => (((in @ (sK12 @ X1 @ X0) @ X0) != $true) & ((in @ (sK12 @ X1 @ X0) @ X1) = $true)))), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f53,plain,( 0.15/0.37 ? [X3,X4] : (! [X5] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true)) & ((subset @ X4 @ X3) != $true)) => (! [X5] : (((in @ X5 @ sK13) = $true) | ((in @ X5 @ sK14) != $true)) & ($true != (subset @ sK14 @ sK13)))), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f51,plain,( 0.15/0.37 (! [X0,X1] : (? [X2] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3,X4] : (! [X5] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true)) & ((subset @ X4 @ X3) != $true)))), 0.15/0.37 inference(rectify,[],[f50])). 0.15/0.37 thf(f50,plain,( 0.15/0.37 (! [X0,X1] : (? [X2] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0,X1] : (! [X2] : (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) & ((subset @ X1 @ X0) != $true)))), 0.15/0.37 inference(nnf_transformation,[],[f25])). 0.15/0.37 thf(f25,plain,( 0.15/0.37 ! [X0,X1] : (? [X2] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) | ((subset @ X1 @ X0) = $true)) <=> (subsetI1 = $true)), 0.15/0.37 inference(ennf_transformation,[],[f11])). 0.15/0.37 thf(f11,plain,( 0.15/0.37 ! [X0,X1] : (! [X2] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true)) <=> (subsetI1 = $true)), 0.15/0.37 inference(fool_elimination,[],[f10])). 0.15/0.37 thf(f10,plain,( 0.15/0.37 (subsetI1 = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))), 0.15/0.37 inference(rectify,[],[f1])). 0.15/0.37 thf(f1,axiom,( 0.15/0.37 (subsetI1 = ! [X1,X0] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))), 0.15/0.37 file('/export/starexec/sandbox/tmp/tmp.4wXKxDnKE1/E---3.1_13738.p',subsetI1)). 0.15/0.37 thf(f154,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK12 @ X0 @ (binintersect @ X0 @ X1)) @ X2) != $true) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X2 @ X1) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f152])). 0.15/0.37 thf(f152,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X1) != $true) | ((in @ (sK12 @ X0 @ (binintersect @ X0 @ X1)) @ X2) != $true) | ($true != $true) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true)) )), 0.15/0.37 inference(superposition,[],[f144,f103])). 0.15/0.37 thf(f103,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true) | ((subset @ X2 @ X1) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f90])). 0.15/0.37 thf(f90,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X1) != $true) | ($true != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true)) )), 0.15/0.37 inference(definition_unfolding,[],[f68,f71])). 0.15/0.37 thf(f71,plain,( 0.15/0.37 (subsetE = $true)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 thf(f68,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true) | (subsetE != $true)) )), 0.15/0.37 inference(cnf_transformation,[],[f47])). 0.15/0.37 thf(f47,plain,( 0.15/0.37 (! [X0,X1,X2] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | (($true = (in @ sK7 @ sK9)) & ((in @ sK7 @ sK8) != $true) & ($true = (subset @ sK9 @ sK8))))), 0.15/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f45,f46])). 0.15/0.37 thf(f46,plain,( 0.15/0.37 ? [X3,X4,X5] : (((in @ X3 @ X5) = $true) & ($true != (in @ X3 @ X4)) & ((subset @ X5 @ X4) = $true)) => (($true = (in @ sK7 @ sK9)) & ((in @ sK7 @ sK8) != $true) & ($true = (subset @ sK9 @ sK8)))), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f45,plain,( 0.15/0.37 (! [X0,X1,X2] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3,X4,X5] : (((in @ X3 @ X5) = $true) & ($true != (in @ X3 @ X4)) & ((subset @ X5 @ X4) = $true)))), 0.15/0.37 inference(rectify,[],[f44])). 0.15/0.37 thf(f44,plain,( 0.15/0.37 (! [X0,X1,X2] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X0,X1,X2] : (((in @ X0 @ X2) = $true) & ((in @ X0 @ X1) != $true) & ((subset @ X2 @ X1) = $true)))), 0.15/0.37 inference(nnf_transformation,[],[f29])). 0.15/0.37 thf(f29,plain,( 0.15/0.37 ! [X0,X1,X2] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) <=> (subsetE = $true)), 0.15/0.37 inference(flattening,[],[f28])). 0.15/0.37 thf(f28,plain,( 0.15/0.37 ! [X0,X1,X2] : ((((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) != $true)) | ((subset @ X2 @ X1) != $true)) <=> (subsetE = $true)), 0.15/0.37 inference(ennf_transformation,[],[f15])). 0.15/0.37 thf(f15,plain,( 0.15/0.37 ! [X0,X1,X2] : (((subset @ X2 @ X1) = $true) => (((in @ X0 @ X2) = $true) => ((in @ X0 @ X1) = $true))) <=> (subsetE = $true)), 0.15/0.37 inference(fool_elimination,[],[f14])). 0.15/0.37 thf(f14,plain,( 0.15/0.37 (! [X0,X1,X2] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))) = subsetE)), 0.15/0.37 inference(rectify,[],[f2])). 0.15/0.37 thf(f2,axiom,( 0.15/0.37 (! [X2,X1,X0] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)), 0.15/0.37 file('/export/starexec/sandbox/tmp/tmp.4wXKxDnKE1/E---3.1_13738.p',subsetE)). 0.15/0.37 thf(f144,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK12 @ X0 @ (binintersect @ X0 @ X1)) @ X1)) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f143])). 0.15/0.37 thf(f143,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK12 @ X0 @ (binintersect @ X0 @ X1)) @ X1)) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ($true != $true)) )), 0.15/0.37 inference(duplicate_literal_removal,[],[f138])). 0.15/0.37 thf(f138,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X0 @ (binintersect @ X0 @ X1)) = $true) | ($true != (in @ (sK12 @ X0 @ (binintersect @ X0 @ X1)) @ X1)) | ($true != $true)) )), 0.15/0.37 inference(superposition,[],[f124,f98])). 0.15/0.37 thf(f124,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X1)) | ((subset @ X0 @ (binintersect @ X1 @ X2)) = $true) | ((in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X2) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f123])). 0.15/0.37 thf(f123,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X1 @ X2)) = $true) | ($true != (in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X1)) | ((in @ (sK12 @ X0 @ (binintersect @ X1 @ X2)) @ X2) != $true) | ($true != $true)) )), 0.15/0.37 inference(superposition,[],[f101,f100])). 0.15/0.37 thf(f100,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f82])). 0.15/0.37 thf(f82,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) != $true)) )), 0.15/0.37 inference(definition_unfolding,[],[f60,f72])). 0.15/0.37 thf(f72,plain,( 0.15/0.37 (binintersectI = $true)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 thf(f60,plain,( 0.15/0.37 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true) | (binintersectI != $true)) )), 0.15/0.37 inference(cnf_transformation,[],[f39])). 0.15/0.37 thf(f39,plain,( 0.15/0.37 (! [X0,X1,X2] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | (((in @ sK4 @ (binintersect @ sK3 @ sK2)) != $true) & ((in @ sK4 @ sK2) = $true) & ((in @ sK4 @ sK3) = $true)))), 0.15/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f37,f38])). 0.15/0.37 thf(f38,plain,( 0.15/0.37 ? [X3,X4,X5] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) & ((in @ X5 @ X3) = $true) & ((in @ X5 @ X4) = $true)) => (((in @ sK4 @ (binintersect @ sK3 @ sK2)) != $true) & ((in @ sK4 @ sK2) = $true) & ((in @ sK4 @ sK3) = $true))), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f37,plain,( 0.15/0.37 (! [X0,X1,X2] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X3,X4,X5] : (((in @ X5 @ (binintersect @ X4 @ X3)) != $true) & ((in @ X5 @ X3) = $true) & ((in @ X5 @ X4) = $true)))), 0.15/0.37 inference(rectify,[],[f36])). 0.15/0.37 thf(f36,plain,( 0.15/0.37 (! [X0,X1,X2] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) | (binintersectI != $true)) & ((binintersectI = $true) | ? [X0,X1,X2] : (((in @ X2 @ (binintersect @ X1 @ X0)) != $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) = $true)))), 0.15/0.37 inference(nnf_transformation,[],[f31])). 0.15/0.37 thf(f31,plain,( 0.15/0.37 ! [X0,X1,X2] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) != $true)) <=> (binintersectI = $true)), 0.15/0.37 inference(flattening,[],[f30])). 0.15/0.37 thf(f30,plain,( 0.15/0.37 ! [X0,X1,X2] : ((((in @ X2 @ (binintersect @ X1 @ X0)) = $true) | ((in @ X2 @ X0) != $true)) | ((in @ X2 @ X1) != $true)) <=> (binintersectI = $true)), 0.15/0.37 inference(ennf_transformation,[],[f20])). 0.15/0.37 thf(f20,plain,( 0.15/0.37 ! [X0,X1,X2] : (((in @ X2 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ (binintersect @ X1 @ X0)) = $true))) <=> (binintersectI = $true)), 0.15/0.37 inference(fool_elimination,[],[f19])). 0.15/0.37 thf(f19,plain,( 0.15/0.37 (binintersectI = ! [X0,X1,X2] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ (binintersect @ X1 @ X0)))))), 0.15/0.37 inference(rectify,[],[f5])). 0.15/0.37 thf(f5,axiom,( 0.15/0.37 (binintersectI = ! [X1,X0,X2] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))), 0.15/0.37 file('/export/starexec/sandbox/tmp/tmp.4wXKxDnKE1/E---3.1_13738.p',binintersectI)). 0.15/0.37 thf(f101,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK12 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f94])). 0.15/0.37 thf(f94,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK12 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true) | ($true != $true)) )), 0.15/0.37 inference(definition_unfolding,[],[f79,f73])). 0.15/0.37 thf(f79,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK12 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true) | (subsetI1 != $true)) )), 0.15/0.37 inference(cnf_transformation,[],[f54])). 0.15/0.37 thf(f107,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) != $true) | ((binintersect @ X0 @ X1) = X0)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f105])). 0.15/0.37 thf(f105,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ (binintersect @ X0 @ X1)) != $true) | ($true != $true) | ((binintersect @ X0 @ X1) = X0)) )), 0.15/0.37 inference(superposition,[],[f99,f102])). 0.15/0.37 thf(f102,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f80])). 0.15/0.37 thf(f80,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | ($true != $true)) )), 0.15/0.37 inference(definition_unfolding,[],[f56,f70])). 0.15/0.37 thf(f70,plain,( 0.15/0.37 (binintersectLsub = $true)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 thf(f56,plain,( 0.15/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) )), 0.15/0.37 inference(cnf_transformation,[],[f35])). 0.15/0.37 thf(f35,plain,( 0.15/0.37 (! [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ((subset @ (binintersect @ sK1 @ sK0) @ sK1) != $true))), 0.15/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f33,f34])). 0.15/0.37 thf(f34,plain,( 0.15/0.37 ? [X2,X3] : ((subset @ (binintersect @ X3 @ X2) @ X3) != $true) => ((subset @ (binintersect @ sK1 @ sK0) @ sK1) != $true)), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f33,plain,( 0.15/0.37 (! [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X2,X3] : ((subset @ (binintersect @ X3 @ X2) @ X3) != $true))), 0.15/0.37 inference(rectify,[],[f32])). 0.15/0.37 thf(f32,plain,( 0.15/0.37 (! [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true))), 0.15/0.37 inference(nnf_transformation,[],[f22])). 0.15/0.37 thf(f22,plain,( 0.15/0.37 ! [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) <=> (binintersectLsub = $true)), 0.15/0.37 inference(fool_elimination,[],[f21])). 0.15/0.37 thf(f21,plain,( 0.15/0.37 (binintersectLsub = ! [X0,X1] : (subset @ (binintersect @ X1 @ X0) @ X1))), 0.15/0.37 inference(rectify,[],[f6])). 0.15/0.37 thf(f6,axiom,( 0.15/0.37 (binintersectLsub = ! [X1,X0] : (subset @ (binintersect @ X0 @ X1) @ X0))), 0.15/0.37 file('/export/starexec/sandbox/tmp/tmp.4wXKxDnKE1/E---3.1_13738.p',binintersectLsub)). 0.15/0.37 thf(f99,plain,( 0.15/0.37 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) != $true) | (X2 = X3) | ((subset @ X2 @ X3) != $true)) )), 0.15/0.37 inference(trivial_inequality_removal,[],[f89])). 0.15/0.37 thf(f89,plain,( 0.15/0.37 ( ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((subset @ X3 @ X2) != $true) | ($true != $true) | (X2 = X3)) )), 0.15/0.37 inference(definition_unfolding,[],[f61,f69])). 0.15/0.37 thf(f69,plain,( 0.15/0.37 (setextsub = $true)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 thf(f61,plain,( 0.15/0.37 ( ! [X2 : $i,X3 : $i] : ((X2 = X3) | ((subset @ X3 @ X2) != $true) | ((subset @ X2 @ X3) != $true) | (setextsub != $true)) )), 0.15/0.37 inference(cnf_transformation,[],[f43])). 0.15/0.37 thf(f43,plain,( 0.15/0.37 ((setextsub = $true) | ((sK5 != sK6) & ((subset @ sK6 @ sK5) = $true) & ((subset @ sK5 @ sK6) = $true))) & (! [X2,X3] : ((X2 = X3) | ((subset @ X3 @ X2) != $true) | ((subset @ X2 @ X3) != $true)) | (setextsub != $true))), 0.15/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f41,f42])). 0.15/0.37 thf(f42,plain,( 0.15/0.37 ? [X0,X1] : ((X0 != X1) & ((subset @ X1 @ X0) = $true) & ((subset @ X0 @ X1) = $true)) => ((sK5 != sK6) & ((subset @ sK6 @ sK5) = $true) & ((subset @ sK5 @ sK6) = $true))), 0.15/0.37 introduced(choice_axiom,[])). 0.15/0.37 thf(f41,plain,( 0.15/0.37 ((setextsub = $true) | ? [X0,X1] : ((X0 != X1) & ((subset @ X1 @ X0) = $true) & ((subset @ X0 @ X1) = $true))) & (! [X2,X3] : ((X2 = X3) | ((subset @ X3 @ X2) != $true) | ((subset @ X2 @ X3) != $true)) | (setextsub != $true))), 0.15/0.37 inference(rectify,[],[f40])). 0.15/0.37 thf(f40,plain,( 0.15/0.37 ((setextsub = $true) | ? [X0,X1] : ((X0 != X1) & ((subset @ X1 @ X0) = $true) & ((subset @ X0 @ X1) = $true))) & (! [X0,X1] : ((X0 = X1) | ((subset @ X1 @ X0) != $true) | ((subset @ X0 @ X1) != $true)) | (setextsub != $true))), 0.15/0.37 inference(nnf_transformation,[],[f27])). 0.15/0.37 thf(f27,plain,( 0.15/0.37 (setextsub = $true) <=> ! [X0,X1] : ((X0 = X1) | ((subset @ X1 @ X0) != $true) | ((subset @ X0 @ X1) != $true))), 0.15/0.37 inference(flattening,[],[f26])). 0.15/0.37 thf(f26,plain,( 0.15/0.37 (setextsub = $true) <=> ! [X0,X1] : (((X0 = X1) | ((subset @ X0 @ X1) != $true)) | ((subset @ X1 @ X0) != $true))), 0.15/0.37 inference(ennf_transformation,[],[f18])). 0.15/0.37 thf(f18,plain,( 0.15/0.37 (setextsub = $true) <=> ! [X0,X1] : (((subset @ X1 @ X0) = $true) => (((subset @ X0 @ X1) = $true) => (X0 = X1)))), 0.15/0.37 inference(fool_elimination,[],[f17])). 0.15/0.37 thf(f17,plain,( 0.15/0.37 (! [X0,X1] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)), 0.15/0.37 inference(rectify,[],[f3])). 0.15/0.37 thf(f3,axiom,( 0.15/0.37 (! [X1,X0] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)), 0.15/0.37 file('/export/starexec/sandbox/tmp/tmp.4wXKxDnKE1/E---3.1_13738.p',setextsub)). 0.15/0.37 thf(f74,plain,( 0.15/0.37 ((binintersect @ sK10 @ sK11) != sK10)), 0.15/0.37 inference(cnf_transformation,[],[f49])). 0.15/0.37 % SZS output end Proof for E---3.1_13738 0.15/0.37 % (13852)------------------------------ 0.15/0.37 % (13852)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.15/0.37 % (13852)Termination reason: Refutation 0.15/0.37 0.15/0.37 % (13852)Memory used [KB]: 5628 0.15/0.37 % (13852)Time elapsed: 0.024 s 0.15/0.37 % (13852)Instructions burned: 40 (million) 0.15/0.37 % (13852)------------------------------ 0.15/0.37 % (13852)------------------------------ 0.15/0.37 % (13846)Success in time 0.034 s 0.15/0.37 EOF