0.07/0.13 % Problem : Vampire---4.8_16233 : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.15/0.35 % Computer : n015.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1440 0.15/0.35 % WCLimit : 180 0.15/0.35 % DateTime : Mon Jul 3 13:11:10 EDT 2023 0.15/0.35 % CPUTime : 0.15/0.36 This is a THF_ problem 0.15/0.36 Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.6tj3RTaWcM/Vampire---4.8_16233 -m 12000 -t 180 0.15/0.38 % (16427)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1799ds/385Mi) 0.23/0.39 % (16428)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.23/0.39 % (16429)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on Vampire---4 for (1799ds/74Mi) 0.23/0.39 % (16424)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.23/0.39 % (16425)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.23/0.39 % (16426)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1799ds/34Mi) 0.23/0.39 % (16430)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1799ds/4Mi) 0.23/0.39 % (16431)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1799ds/915Mi) 0.23/0.39 % (16430)Instruction limit reached! 0.23/0.39 % (16430)------------------------------ 0.23/0.39 % (16430)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.39 % (16430)Termination reason: Unknown 0.23/0.39 % (16430)Termination phase: Function definition elimination 0.23/0.39 0.23/0.39 % (16430)Memory used [KB]: 1023 0.23/0.39 % (16430)Time elapsed: 0.006 s 0.23/0.39 % (16430)Instructions burned: 5 (million) 0.23/0.39 % (16430)------------------------------ 0.23/0.39 % (16430)------------------------------ 0.23/0.40 % (16428)Instruction limit reached! 0.23/0.40 % (16428)------------------------------ 0.23/0.40 % (16428)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.40 % (16428)Termination reason: Unknown 0.23/0.40 % (16428)Termination phase: Saturation 0.23/0.40 0.23/0.40 % (16428)Memory used [KB]: 5628 0.23/0.40 % (16428)Time elapsed: 0.016 s 0.23/0.40 % (16428)Instructions burned: 17 (million) 0.23/0.40 % (16428)------------------------------ 0.23/0.40 % (16428)------------------------------ 0.23/0.41 % (16431)First to succeed. 0.23/0.41 % (16431)Refutation found. Thanks to Tanya! 0.23/0.41 % SZS status Theorem for Vampire---4 0.23/0.41 % SZS output start Proof for Vampire---4 0.23/0.41 thf(func_def_0, type, in: $i > $i > $o). 0.23/0.41 thf(func_def_2, type, setadjoin: $i > $i > $i). 0.23/0.41 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i). 0.23/0.41 thf(func_def_4, type, subset: $i > $i > $o). 0.23/0.41 thf(func_def_5, type, kpair: $i > $i > $i). 0.23/0.41 thf(func_def_6, type, cartprod: $i > $i > $i). 0.23/0.41 thf(func_def_7, type, singleton: $i > $o). 0.23/0.41 thf(func_def_9, type, ex1: $i > ($i > $o) > $o). 0.23/0.41 thf(func_def_10, type, breln: $i > $i > $i > $o). 0.23/0.41 thf(func_def_11, type, func: $i > $i > $i > $o). 0.23/0.41 thf(func_def_12, type, ap: $i > $i > $i > $i > $i). 0.23/0.41 thf(func_def_43, type, ph16: !>[X0: $tType]:(X0)). 0.23/0.41 thf(f101,plain,( 0.23/0.41 $false), 0.23/0.41 inference(subsumption_resolution,[],[f100,f61])). 0.23/0.41 thf(f61,plain,( 0.23/0.41 ($true = (in @ sK14 @ sK9))), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f44,plain,( 0.23/0.41 (funcGraphProp2 = $true) & (((func @ sK11 @ sK9 @ sK10) = $true) & (! [X4] : (((ap @ sK11 @ sK9 @ sK10 @ X4) = (ap @ sK11 @ sK9 @ sK12 @ X4)) | ((in @ X4 @ sK11) != $true)) & (((in @ sK13 @ sK11) = $true) & (((in @ (kpair @ sK13 @ sK14) @ sK10) != $true) & ($true = (in @ sK14 @ sK9)) & ((in @ (kpair @ sK13 @ sK14) @ sK12) = $true))) & ($true = (func @ sK11 @ sK9 @ sK12)))) & (funcGraphProp1 = $true)), 0.23/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13,sK14])],[f26,f43,f42,f41,f40])). 0.23/0.41 thf(f40,plain,( 0.23/0.41 ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (! [X4] : (((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4)) | ((in @ X4 @ X2) != $true)) & ? [X5] : (((in @ X5 @ X2) = $true) & ? [X6] : (((in @ (kpair @ X5 @ X6) @ X1) != $true) & ((in @ X6 @ X0) = $true) & ((in @ (kpair @ X5 @ X6) @ X3) = $true))) & ((func @ X2 @ X0 @ X3) = $true))) => (((func @ sK11 @ sK9 @ sK10) = $true) & ? [X3] : (! [X4] : (((ap @ sK11 @ sK9 @ sK10 @ X4) = (ap @ sK11 @ sK9 @ X3 @ X4)) | ((in @ X4 @ sK11) != $true)) & ? [X5] : (((in @ X5 @ sK11) = $true) & ? [X6] : (((in @ (kpair @ X5 @ X6) @ sK10) != $true) & ((in @ X6 @ sK9) = $true) & ((in @ (kpair @ X5 @ X6) @ X3) = $true))) & ($true = (func @ sK11 @ sK9 @ X3))))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f41,plain,( 0.23/0.41 ? [X3] : (! [X4] : (((ap @ sK11 @ sK9 @ sK10 @ X4) = (ap @ sK11 @ sK9 @ X3 @ X4)) | ((in @ X4 @ sK11) != $true)) & ? [X5] : (((in @ X5 @ sK11) = $true) & ? [X6] : (((in @ (kpair @ X5 @ X6) @ sK10) != $true) & ((in @ X6 @ sK9) = $true) & ((in @ (kpair @ X5 @ X6) @ X3) = $true))) & ($true = (func @ sK11 @ sK9 @ X3))) => (! [X4] : (((ap @ sK11 @ sK9 @ sK10 @ X4) = (ap @ sK11 @ sK9 @ sK12 @ X4)) | ((in @ X4 @ sK11) != $true)) & ? [X5] : (((in @ X5 @ sK11) = $true) & ? [X6] : (((in @ (kpair @ X5 @ X6) @ sK10) != $true) & ((in @ X6 @ sK9) = $true) & ((in @ (kpair @ X5 @ X6) @ sK12) = $true))) & ($true = (func @ sK11 @ sK9 @ sK12)))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f42,plain,( 0.23/0.41 ? [X5] : (((in @ X5 @ sK11) = $true) & ? [X6] : (((in @ (kpair @ X5 @ X6) @ sK10) != $true) & ((in @ X6 @ sK9) = $true) & ((in @ (kpair @ X5 @ X6) @ sK12) = $true))) => (((in @ sK13 @ sK11) = $true) & ? [X6] : (($true != (in @ (kpair @ sK13 @ X6) @ sK10)) & ((in @ X6 @ sK9) = $true) & ((in @ (kpair @ sK13 @ X6) @ sK12) = $true)))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f43,plain,( 0.23/0.41 ? [X6] : (($true != (in @ (kpair @ sK13 @ X6) @ sK10)) & ((in @ X6 @ sK9) = $true) & ((in @ (kpair @ sK13 @ X6) @ sK12) = $true)) => (((in @ (kpair @ sK13 @ sK14) @ sK10) != $true) & ($true = (in @ sK14 @ sK9)) & ((in @ (kpair @ sK13 @ sK14) @ sK12) = $true))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f26,plain,( 0.23/0.41 (funcGraphProp2 = $true) & ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (! [X4] : (((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4)) | ((in @ X4 @ X2) != $true)) & ? [X5] : (((in @ X5 @ X2) = $true) & ? [X6] : (((in @ (kpair @ X5 @ X6) @ X1) != $true) & ((in @ X6 @ X0) = $true) & ((in @ (kpair @ X5 @ X6) @ X3) = $true))) & ((func @ X2 @ X0 @ X3) = $true))) & (funcGraphProp1 = $true)), 0.23/0.41 inference(flattening,[],[f25])). 0.23/0.41 thf(f25,plain,( 0.23/0.41 (? [X0,X1,X2] : (? [X3] : ((? [X5] : (? [X6] : ((((in @ (kpair @ X5 @ X6) @ X1) != $true) & ((in @ (kpair @ X5 @ X6) @ X3) = $true)) & ((in @ X6 @ X0) = $true)) & ((in @ X5 @ X2) = $true)) & ! [X4] : (((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4)) | ((in @ X4 @ X2) != $true))) & ((func @ X2 @ X0 @ X3) = $true)) & ($true = (func @ X2 @ X0 @ X1))) & (funcGraphProp2 = $true)) & (funcGraphProp1 = $true)), 0.23/0.41 inference(ennf_transformation,[],[f13])). 0.23/0.41 thf(f13,plain,( 0.23/0.41 ~((funcGraphProp1 = $true) => ((funcGraphProp2 = $true) => ! [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) => ! [X3] : (((func @ X2 @ X0 @ X3) = $true) => (! [X4] : (((in @ X4 @ X2) = $true) => ((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4))) => ! [X5] : (((in @ X5 @ X2) = $true) => ! [X6] : (((in @ X6 @ X0) = $true) => (((in @ (kpair @ X5 @ X6) @ X3) = $true) => ((in @ (kpair @ X5 @ X6) @ X1) = $true)))))))))), 0.23/0.41 inference(fool_elimination,[],[f12])). 0.23/0.41 thf(f12,plain,( 0.23/0.41 ~(funcGraphProp1 => (funcGraphProp2 => ! [X0,X1,X2] : ((func @ X2 @ X0 @ X1) => ! [X3] : ((func @ X2 @ X0 @ X3) => (! [X4] : ((in @ X4 @ X2) => ((ap @ X2 @ X0 @ X3 @ X4) = (ap @ X2 @ X0 @ X1 @ X4))) => ! [X5] : ((in @ X5 @ X2) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X1)))))))))), 0.23/0.41 inference(rectify,[],[f8])). 0.23/0.41 thf(f8,negated_conjecture,( 0.23/0.41 ~(funcGraphProp1 => (funcGraphProp2 => ! [X3,X7,X0] : ((func @ X0 @ X3 @ X7) => ! [X8] : ((func @ X0 @ X3 @ X8) => (! [X1] : ((in @ X1 @ X0) => ((ap @ X0 @ X3 @ X7 @ X1) = (ap @ X0 @ X3 @ X8 @ X1))) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X8) => (in @ (kpair @ X1 @ X6) @ X7)))))))))), 0.23/0.41 inference(negated_conjecture,[],[f7])). 0.23/0.41 thf(f7,conjecture,( 0.23/0.41 funcGraphProp1 => (funcGraphProp2 => ! [X3,X7,X0] : ((func @ X0 @ X3 @ X7) => ! [X8] : ((func @ X0 @ X3 @ X8) => (! [X1] : ((in @ X1 @ X0) => ((ap @ X0 @ X3 @ X7 @ X1) = (ap @ X0 @ X3 @ X8 @ X1))) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X8) => (in @ (kpair @ X1 @ X6) @ X7))))))))), 0.23/0.41 file('/export/starexec/sandbox2/tmp/tmp.6tj3RTaWcM/Vampire---4.8_16233',funcextLem)). 0.23/0.41 thf(f100,plain,( 0.23/0.41 ($true != (in @ sK14 @ sK9))), 0.23/0.41 inference(subsumption_resolution,[],[f99,f60])). 0.23/0.41 thf(f60,plain,( 0.23/0.41 ((in @ (kpair @ sK13 @ sK14) @ sK12) = $true)), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f99,plain,( 0.23/0.41 ((in @ (kpair @ sK13 @ sK14) @ sK12) != $true) | ($true != (in @ sK14 @ sK9))), 0.23/0.41 inference(subsumption_resolution,[],[f98,f63])). 0.23/0.41 thf(f63,plain,( 0.23/0.41 ((in @ sK13 @ sK11) = $true)), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f98,plain,( 0.23/0.41 ((in @ sK13 @ sK11) != $true) | ($true != (in @ sK14 @ sK9)) | ((in @ (kpair @ sK13 @ sK14) @ sK12) != $true)), 0.23/0.41 inference(trivial_inequality_removal,[],[f97])). 0.23/0.41 thf(f97,plain,( 0.23/0.41 ((in @ (kpair @ sK13 @ sK14) @ sK12) != $true) | ($true != (in @ sK14 @ sK9)) | ($true != $true) | ((in @ sK13 @ sK11) != $true)), 0.23/0.41 inference(superposition,[],[f62,f96])). 0.23/0.41 thf(f96,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ (kpair @ X0 @ X1) @ sK10) = $true) | ((in @ X0 @ sK11) != $true) | ((in @ X1 @ sK9) != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK12))) )), 0.23/0.41 inference(subsumption_resolution,[],[f95,f65])). 0.23/0.41 thf(f65,plain,( 0.23/0.41 ((func @ sK11 @ sK9 @ sK10) = $true)), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f95,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK9) != $true) | ((func @ sK11 @ sK9 @ sK10) != $true) | ((in @ (kpair @ X0 @ X1) @ sK10) = $true) | ((in @ X0 @ sK11) != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK12))) )), 0.23/0.41 inference(subsumption_resolution,[],[f88,f58])). 0.23/0.41 thf(f58,plain,( 0.23/0.41 (funcGraphProp1 = $true)), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f88,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ((in @ (kpair @ X0 @ X1) @ sK10) = $true) | (funcGraphProp1 != $true) | ((in @ X0 @ sK11) != $true) | ((in @ X1 @ sK9) != $true) | ((func @ sK11 @ sK9 @ sK10) != $true)) )), 0.23/0.41 inference(duplicate_literal_removal,[],[f87])). 0.23/0.41 thf(f87,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK9) != $true) | ((in @ X0 @ sK11) != $true) | (funcGraphProp1 != $true) | ((in @ (kpair @ X0 @ X1) @ sK10) = $true) | ((func @ sK11 @ sK9 @ sK10) != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ((in @ X0 @ sK11) != $true)) )), 0.23/0.41 inference(superposition,[],[f54,f78])). 0.23/0.41 thf(f78,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (((ap @ sK11 @ sK9 @ sK10 @ X0) = X1) | ((in @ X1 @ sK9) != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ((in @ X0 @ sK11) != $true)) )), 0.23/0.41 inference(subsumption_resolution,[],[f77,f59])). 0.23/0.41 thf(f59,plain,( 0.23/0.41 ($true = (func @ sK11 @ sK9 @ sK12))), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f77,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK9) != $true) | ((in @ X0 @ sK11) != $true) | ((ap @ sK11 @ sK9 @ sK10 @ X0) = X1) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ($true != (func @ sK11 @ sK9 @ sK12))) )), 0.23/0.41 inference(subsumption_resolution,[],[f73,f66])). 0.23/0.41 thf(f66,plain,( 0.23/0.41 (funcGraphProp2 = $true)), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f73,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ sK9) != $true) | (funcGraphProp2 != $true) | ((ap @ sK11 @ sK9 @ sK10 @ X0) = X1) | ($true != (func @ sK11 @ sK9 @ sK12)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ((in @ X0 @ sK11) != $true)) )), 0.23/0.41 inference(duplicate_literal_removal,[],[f70])). 0.23/0.41 thf(f70,plain,( 0.23/0.41 ( ! [X0 : $i,X1 : $i] : ((funcGraphProp2 != $true) | ($true != (func @ sK11 @ sK9 @ sK12)) | ((in @ X1 @ sK9) != $true) | ((in @ X0 @ sK11) != $true) | ((in @ X0 @ sK11) != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ((ap @ sK11 @ sK9 @ sK10 @ X0) = X1)) )), 0.23/0.41 inference(superposition,[],[f47,f64])). 0.23/0.41 thf(f64,plain,( 0.23/0.41 ( ! [X4 : $i] : (((ap @ sK11 @ sK9 @ sK10 @ X4) = (ap @ sK11 @ sK9 @ sK12 @ X4)) | ((in @ X4 @ sK11) != $true)) )), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 thf(f47,plain,( 0.23/0.41 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) = X9) | (funcGraphProp2 != $true) | ((func @ X6 @ X7 @ X5) != $true) | ((in @ X8 @ X6) != $true) | ((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((in @ X9 @ X7) != $true)) )), 0.23/0.41 inference(cnf_transformation,[],[f34])). 0.23/0.41 thf(f34,plain,( 0.23/0.41 ((funcGraphProp2 = $true) | (((func @ sK1 @ sK2 @ sK0) = $true) & (($true = (in @ sK3 @ sK1)) & (((in @ (kpair @ sK3 @ sK4) @ sK0) = $true) & (sK4 != (ap @ sK1 @ sK2 @ sK0 @ sK3)) & ((in @ sK4 @ sK2) = $true))))) & (! [X5,X6,X7] : (((func @ X6 @ X7 @ X5) != $true) | ! [X8] : (((in @ X8 @ X6) != $true) | ! [X9] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ((in @ X9 @ X7) != $true)))) | (funcGraphProp2 != $true))), 0.23/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f30,f33,f32,f31])). 0.23/0.41 thf(f31,plain,( 0.23/0.41 ? [X0,X1,X2] : (((func @ X1 @ X2 @ X0) = $true) & ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ X0) = $true) & ((ap @ X1 @ X2 @ X0 @ X3) != X4) & ((in @ X4 @ X2) = $true)))) => (((func @ sK1 @ sK2 @ sK0) = $true) & ? [X3] : (((in @ X3 @ sK1) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ sK0) = $true) & ((ap @ sK1 @ sK2 @ sK0 @ X3) != X4) & ((in @ X4 @ sK2) = $true))))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f32,plain,( 0.23/0.41 ? [X3] : (((in @ X3 @ sK1) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ sK0) = $true) & ((ap @ sK1 @ sK2 @ sK0 @ X3) != X4) & ((in @ X4 @ sK2) = $true))) => (($true = (in @ sK3 @ sK1)) & ? [X4] : (((in @ (kpair @ sK3 @ X4) @ sK0) = $true) & ((ap @ sK1 @ sK2 @ sK0 @ sK3) != X4) & ((in @ X4 @ sK2) = $true)))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f33,plain,( 0.23/0.41 ? [X4] : (((in @ (kpair @ sK3 @ X4) @ sK0) = $true) & ((ap @ sK1 @ sK2 @ sK0 @ sK3) != X4) & ((in @ X4 @ sK2) = $true)) => (((in @ (kpair @ sK3 @ sK4) @ sK0) = $true) & (sK4 != (ap @ sK1 @ sK2 @ sK0 @ sK3)) & ((in @ sK4 @ sK2) = $true))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f30,plain,( 0.23/0.41 ((funcGraphProp2 = $true) | ? [X0,X1,X2] : (((func @ X1 @ X2 @ X0) = $true) & ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ X0) = $true) & ((ap @ X1 @ X2 @ X0 @ X3) != X4) & ((in @ X4 @ X2) = $true))))) & (! [X5,X6,X7] : (((func @ X6 @ X7 @ X5) != $true) | ! [X8] : (((in @ X8 @ X6) != $true) | ! [X9] : (((in @ (kpair @ X8 @ X9) @ X5) != $true) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ((in @ X9 @ X7) != $true)))) | (funcGraphProp2 != $true))), 0.23/0.41 inference(rectify,[],[f29])). 0.23/0.41 thf(f29,plain,( 0.23/0.41 ((funcGraphProp2 = $true) | ? [X0,X1,X2] : (((func @ X1 @ X2 @ X0) = $true) & ? [X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ X0) = $true) & ((ap @ X1 @ X2 @ X0 @ X3) != X4) & ((in @ X4 @ X2) = $true))))) & (! [X0,X1,X2] : (((func @ X1 @ X2 @ X0) != $true) | ! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ((ap @ X1 @ X2 @ X0 @ X3) = X4) | ((in @ X4 @ X2) != $true)))) | (funcGraphProp2 != $true))), 0.23/0.41 inference(nnf_transformation,[],[f28])). 0.23/0.41 thf(f28,plain,( 0.23/0.41 (funcGraphProp2 = $true) <=> ! [X0,X1,X2] : (((func @ X1 @ X2 @ X0) != $true) | ! [X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ X0) != $true) | ((ap @ X1 @ X2 @ X0 @ X3) = X4) | ((in @ X4 @ X2) != $true))))), 0.23/0.41 inference(flattening,[],[f27])). 0.23/0.41 thf(f27,plain,( 0.23/0.41 (funcGraphProp2 = $true) <=> ! [X0,X1,X2] : (! [X3] : (! [X4] : ((((ap @ X1 @ X2 @ X0 @ X3) = X4) | ((in @ (kpair @ X3 @ X4) @ X0) != $true)) | ((in @ X4 @ X2) != $true)) | ((in @ X3 @ X1) != $true)) | ((func @ X1 @ X2 @ X0) != $true))), 0.23/0.41 inference(ennf_transformation,[],[f15])). 0.23/0.41 thf(f15,plain,( 0.23/0.41 (funcGraphProp2 = $true) <=> ! [X0,X1,X2] : (((func @ X1 @ X2 @ X0) = $true) => ! [X3] : (((in @ X3 @ X1) = $true) => ! [X4] : (((in @ X4 @ X2) = $true) => (((in @ (kpair @ X3 @ X4) @ X0) = $true) => ((ap @ X1 @ X2 @ X0 @ X3) = X4)))))), 0.23/0.41 inference(fool_elimination,[],[f14])). 0.23/0.41 thf(f14,plain,( 0.23/0.41 (! [X0,X1,X2] : ((func @ X1 @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))) = funcGraphProp2)), 0.23/0.41 inference(rectify,[],[f6])). 0.23/0.41 thf(f6,axiom,( 0.23/0.41 (! [X7,X0,X3] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => ! [X6] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))) = funcGraphProp2)), 0.23/0.41 file('/export/starexec/sandbox2/tmp/tmp.6tj3RTaWcM/Vampire---4.8_16233',funcGraphProp2)). 0.23/0.41 thf(f54,plain,( 0.23/0.41 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ (kpair @ X7 @ (ap @ X6 @ X5 @ X4 @ X7)) @ X4) = $true) | ((func @ X6 @ X5 @ X4) != $true) | ((in @ X7 @ X6) != $true) | (funcGraphProp1 != $true)) )), 0.23/0.41 inference(cnf_transformation,[],[f39])). 0.23/0.41 thf(f39,plain,( 0.23/0.41 ((funcGraphProp1 = $true) | ((((in @ (kpair @ sK8 @ (ap @ sK7 @ sK6 @ sK5 @ sK8)) @ sK5) != $true) & ((in @ sK8 @ sK7) = $true)) & ((func @ sK7 @ sK6 @ sK5) = $true))) & (! [X4,X5,X6] : (! [X7] : (((in @ (kpair @ X7 @ (ap @ X6 @ X5 @ X4 @ X7)) @ X4) = $true) | ((in @ X7 @ X6) != $true)) | ((func @ X6 @ X5 @ X4) != $true)) | (funcGraphProp1 != $true))), 0.23/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f36,f38,f37])). 0.23/0.41 thf(f37,plain,( 0.23/0.41 ? [X0,X1,X2] : (? [X3] : (((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) != $true) & ((in @ X3 @ X2) = $true)) & ((func @ X2 @ X1 @ X0) = $true)) => (? [X3] : (((in @ (kpair @ X3 @ (ap @ sK7 @ sK6 @ sK5 @ X3)) @ sK5) != $true) & ((in @ X3 @ sK7) = $true)) & ((func @ sK7 @ sK6 @ sK5) = $true))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f38,plain,( 0.23/0.41 ? [X3] : (((in @ (kpair @ X3 @ (ap @ sK7 @ sK6 @ sK5 @ X3)) @ sK5) != $true) & ((in @ X3 @ sK7) = $true)) => (((in @ (kpair @ sK8 @ (ap @ sK7 @ sK6 @ sK5 @ sK8)) @ sK5) != $true) & ((in @ sK8 @ sK7) = $true))), 0.23/0.41 introduced(choice_axiom,[])). 0.23/0.41 thf(f36,plain,( 0.23/0.41 ((funcGraphProp1 = $true) | ? [X0,X1,X2] : (? [X3] : (((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) != $true) & ((in @ X3 @ X2) = $true)) & ((func @ X2 @ X1 @ X0) = $true))) & (! [X4,X5,X6] : (! [X7] : (((in @ (kpair @ X7 @ (ap @ X6 @ X5 @ X4 @ X7)) @ X4) = $true) | ((in @ X7 @ X6) != $true)) | ((func @ X6 @ X5 @ X4) != $true)) | (funcGraphProp1 != $true))), 0.23/0.41 inference(rectify,[],[f35])). 0.23/0.41 thf(f35,plain,( 0.23/0.41 ((funcGraphProp1 = $true) | ? [X0,X1,X2] : (? [X3] : (((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) != $true) & ((in @ X3 @ X2) = $true)) & ((func @ X2 @ X1 @ X0) = $true))) & (! [X0,X1,X2] : (! [X3] : (((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) = $true) | ((in @ X3 @ X2) != $true)) | ((func @ X2 @ X1 @ X0) != $true)) | (funcGraphProp1 != $true))), 0.23/0.41 inference(nnf_transformation,[],[f24])). 0.23/0.41 thf(f24,plain,( 0.23/0.41 (funcGraphProp1 = $true) <=> ! [X0,X1,X2] : (! [X3] : (((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) = $true) | ((in @ X3 @ X2) != $true)) | ((func @ X2 @ X1 @ X0) != $true))), 0.23/0.41 inference(ennf_transformation,[],[f19])). 0.23/0.41 thf(f19,plain,( 0.23/0.41 ! [X0,X1,X2] : (((func @ X2 @ X1 @ X0) = $true) => ! [X3] : (((in @ X3 @ X2) = $true) => ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0) = $true))) <=> (funcGraphProp1 = $true)), 0.23/0.41 inference(fool_elimination,[],[f18])). 0.23/0.41 thf(f18,plain,( 0.23/0.41 (funcGraphProp1 = ! [X0,X1,X2] : ((func @ X2 @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))))), 0.23/0.41 inference(rectify,[],[f5])). 0.23/0.41 thf(f5,axiom,( 0.23/0.41 (funcGraphProp1 = ! [X7,X3,X0] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))))), 0.23/0.41 file('/export/starexec/sandbox2/tmp/tmp.6tj3RTaWcM/Vampire---4.8_16233',funcGraphProp1)). 0.23/0.41 thf(f62,plain,( 0.23/0.41 ((in @ (kpair @ sK13 @ sK14) @ sK10) != $true)), 0.23/0.41 inference(cnf_transformation,[],[f44])). 0.23/0.41 % SZS output end Proof for Vampire---4 0.23/0.41 % (16431)------------------------------ 0.23/0.41 % (16431)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.41 % (16431)Termination reason: Refutation 0.23/0.41 0.23/0.41 % (16431)Memory used [KB]: 5628 0.23/0.41 % (16431)Time elapsed: 0.024 s 0.23/0.41 % (16431)Instructions burned: 16 (million) 0.23/0.41 % (16431)------------------------------ 0.23/0.41 % (16431)------------------------------ 0.23/0.41 % (16423)Success in time 0.047 s 0.23/0.41 % Vampire---4.8 exiting 0.23/0.42 EOF