0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : run_vampire %s %d THM 0.12/0.33 % Computer : n021.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 02:26:19 EDT 2025 0.12/0.34 % CPUTime : 0.12/0.35 This is a THF_ problem 0.12/0.36 Running higher-order theorem proving 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.ayrFukndGU/E---3.1_20509.p -m 16384 -t 240 0.12/0.39 % (20617)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_20509 for (2399ds/4Mi) 0.12/0.39 % (20616)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_20509 for (2399ds/183Mi) 0.12/0.39 % (20621)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_20509 for (2399ds/275Mi) 0.12/0.39 % (20619)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_20509 for (2399ds/2Mi) 0.12/0.39 % (20618)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_20509 for (2399ds/27Mi) 0.12/0.39 % (20620)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_20509 for (2399ds/2Mi) 0.12/0.39 % (20622)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_20509 for (2399ds/18Mi) 0.12/0.39 % (20619)Instruction limit reached! 0.12/0.39 % (20619)------------------------------ 0.12/0.39 % (20619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (20619)Termination reason: Unknown 0.12/0.39 % (20619)Termination phase: Property scanning 0.12/0.39 % (20620)Instruction limit reached! 0.12/0.39 % (20620)------------------------------ 0.12/0.39 % (20620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (20620)Termination reason: Unknown 0.12/0.39 % (20620)Termination phase: Property scanning 0.12/0.39 0.12/0.39 % (20620)Memory used [KB]: 1023 0.12/0.39 % (20620)Time elapsed: 0.004 s 0.12/0.39 % (20620)Instructions burned: 3 (million) 0.12/0.39 % (20620)------------------------------ 0.12/0.39 % (20620)------------------------------ 0.12/0.39 0.12/0.39 % (20619)Memory used [KB]: 1023 0.12/0.39 % (20619)Time elapsed: 0.004 s 0.12/0.39 % (20619)Instructions burned: 3 (million) 0.12/0.39 % (20619)------------------------------ 0.12/0.39 % (20619)------------------------------ 0.22/0.39 % (20617)Instruction limit reached! 0.22/0.39 % (20617)------------------------------ 0.22/0.39 % (20617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.39 % (20617)Termination reason: Unknown 0.22/0.39 % (20617)Termination phase: Function definition elimination 0.22/0.39 0.22/0.39 % (20617)Memory used [KB]: 1023 0.22/0.39 % (20617)Time elapsed: 0.005 s 0.22/0.39 % (20617)Instructions burned: 4 (million) 0.22/0.39 % (20617)------------------------------ 0.22/0.39 % (20617)------------------------------ 0.22/0.40 % (20622)Instruction limit reached! 0.22/0.40 % (20622)------------------------------ 0.22/0.40 % (20622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.40 % (20622)Termination reason: Unknown 0.22/0.40 % (20622)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (20622)Memory used [KB]: 5756 0.22/0.40 % (20622)Time elapsed: 0.013 s 0.22/0.40 % (20622)Instructions burned: 19 (million) 0.22/0.40 % (20622)------------------------------ 0.22/0.40 % (20622)------------------------------ 0.22/0.40 % (20621)First to succeed. 0.22/0.40 % (20618)Instruction limit reached! 0.22/0.40 % (20618)------------------------------ 0.22/0.40 % (20618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.40 % (20618)Termination reason: Unknown 0.22/0.40 % (20618)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (20618)Memory used [KB]: 5756 0.22/0.40 % (20621)Refutation found. Thanks to Tanya! 0.22/0.40 % SZS status Theorem for E---3.1_20509 0.22/0.40 % SZS output start Proof for E---3.1_20509 0.22/0.40 thf(func_def_0, type, in: $i > $i > $o). 0.22/0.40 thf(func_def_2, type, setadjoin: $i > $i > $i). 0.22/0.40 thf(func_def_3, type, dsetconstr: $i > ($i > $o) > $i). 0.22/0.40 thf(func_def_4, type, subset: $i > $i > $o). 0.22/0.40 thf(func_def_5, type, kpair: $i > $i > $i). 0.22/0.40 thf(func_def_6, type, cartprod: $i > $i > $i). 0.22/0.40 thf(func_def_7, type, singleton: $i > $o). 0.22/0.40 thf(func_def_9, type, ex1: $i > ($i > $o) > $o). 0.22/0.40 thf(func_def_10, type, breln: $i > $i > $i > $o). 0.22/0.40 thf(func_def_11, type, func: $i > $i > $i > $o). 0.22/0.40 thf(func_def_12, type, ap: $i > $i > $i > $i > $i). 0.22/0.40 thf(f107,plain,( 0.22/0.40 $false), 0.22/0.40 inference(subsumption_resolution,[status(thm)],[f106,f59])). 0.22/0.40 thf(f59,plain,( 0.22/0.40 ($true = (in @ sK14 @ sK11))), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f44,plain,( 0.22/0.40 (funcGraphProp2 = $true) & (funcGraphProp1 = $true) & ((! [X4 : $i] : (((in @ X4 @ sK10) != $true) | ((ap @ sK10 @ sK11 @ sK9 @ X4) = (ap @ sK10 @ sK11 @ sK12 @ X4))) & (($true = (in @ sK13 @ sK10)) & (($true = (in @ sK14 @ sK11)) & ($true != (in @ (kpair @ sK13 @ sK14) @ sK9)) & ($true = (in @ (kpair @ sK13 @ sK14) @ sK12)))) & ($true = (func @ sK10 @ sK11 @ sK12))) & ((func @ sK10 @ sK11 @ sK9) = $true))), 0.22/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13,sK14])],[f25,f43,f42,f41,f40])). 0.22/0.40 thf(f40,plain,( 0.22/0.40 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ X1)) & ? [X6 : $i] : (($true = (in @ X6 @ X2)) & ($true != (in @ (kpair @ X5 @ X6) @ X0)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)))) & ($true = (func @ X1 @ X2 @ X3))) & ($true = (func @ X1 @ X2 @ X0))) => (? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ sK10) != $true) | ((ap @ sK10 @ sK11 @ sK9 @ X4) = (ap @ sK10 @ sK11 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ sK10)) & ? [X6 : $i] : (($true = (in @ X6 @ sK11)) & ($true != (in @ (kpair @ X5 @ X6) @ sK9)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)))) & ($true = (func @ sK10 @ sK11 @ X3))) & ((func @ sK10 @ sK11 @ sK9) = $true))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f41,plain,( 0.22/0.40 ? [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ sK10) != $true) | ((ap @ sK10 @ sK11 @ sK9 @ X4) = (ap @ sK10 @ sK11 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ sK10)) & ? [X6 : $i] : (($true = (in @ X6 @ sK11)) & ($true != (in @ (kpair @ X5 @ X6) @ sK9)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)))) & ($true = (func @ sK10 @ sK11 @ X3))) => (! [X4 : $i] : (((in @ X4 @ sK10) != $true) | ((ap @ sK10 @ sK11 @ sK9 @ X4) = (ap @ sK10 @ sK11 @ sK12 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ sK10)) & ? [X6 : $i] : (($true = (in @ X6 @ sK11)) & ($true != (in @ (kpair @ X5 @ X6) @ sK9)) & ($true = (in @ (kpair @ X5 @ X6) @ sK12)))) & ($true = (func @ sK10 @ sK11 @ sK12)))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f42,plain,( 0.22/0.40 ? [X5 : $i] : (($true = (in @ X5 @ sK10)) & ? [X6 : $i] : (($true = (in @ X6 @ sK11)) & ($true != (in @ (kpair @ X5 @ X6) @ sK9)) & ($true = (in @ (kpair @ X5 @ X6) @ sK12)))) => (($true = (in @ sK13 @ sK10)) & ? [X6 : $i] : (($true = (in @ X6 @ sK11)) & ($true != (in @ (kpair @ sK13 @ X6) @ sK9)) & ($true = (in @ (kpair @ sK13 @ X6) @ sK12))))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f43,plain,( 0.22/0.40 ? [X6 : $i] : (($true = (in @ X6 @ sK11)) & ($true != (in @ (kpair @ sK13 @ X6) @ sK9)) & ($true = (in @ (kpair @ sK13 @ X6) @ sK12))) => (($true = (in @ sK14 @ sK11)) & ($true != (in @ (kpair @ sK13 @ sK14) @ sK9)) & ($true = (in @ (kpair @ sK13 @ sK14) @ sK12)))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f25,plain,( 0.22/0.40 (funcGraphProp2 = $true) & (funcGraphProp1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ X1)) & ? [X6 : $i] : (($true = (in @ X6 @ X2)) & ($true != (in @ (kpair @ X5 @ X6) @ X0)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)))) & ($true = (func @ X1 @ X2 @ X3))) & ($true = (func @ X1 @ X2 @ X0)))), 0.22/0.40 inference(flattening,[status(thm)],[f24])). 0.22/0.40 thf(f24,plain,( 0.22/0.40 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((? [X5 : $i] : (? [X6 : $i] : ((($true != (in @ (kpair @ X5 @ X6) @ X0)) & ($true = (in @ (kpair @ X5 @ X6) @ X3))) & ($true = (in @ X6 @ X2))) & ($true = (in @ X5 @ X1))) & ! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4)))) & ($true = (func @ X1 @ X2 @ X3))) & ($true = (func @ X1 @ X2 @ X0))) & (funcGraphProp2 = $true)) & (funcGraphProp1 = $true)), 0.22/0.40 inference(ennf_transformation,[status(thm)],[f21])). 0.22/0.40 thf(f21,plain,( 0.22/0.40 ~((funcGraphProp1 = $true) => ((funcGraphProp2 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) => ! [X3 : $i] : (($true = (func @ X1 @ X2 @ X3)) => (! [X4 : $i] : (($true = (in @ X4 @ X1)) => ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) => ! [X5 : $i] : (($true = (in @ X5 @ X1)) => ! [X6 : $i] : (($true = (in @ X6 @ X2)) => (($true = (in @ (kpair @ X5 @ X6) @ X3)) => ($true = (in @ (kpair @ X5 @ X6) @ X0))))))))))), 0.22/0.40 inference(fool_elimination,[status(thm)],[f20])). 0.22/0.40 thf(f20,plain,( 0.22/0.40 ~(funcGraphProp1 => (funcGraphProp2 => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((func @ X1 @ X2 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) => ! [X5 : $i] : ((in @ X5 @ X1) => ! [X6 : $i] : ((in @ X6 @ X2) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X0)))))))))), 0.22/0.40 inference(rectify,[status(thm)],[f8])). 0.22/0.40 thf(f8,negated_conjecture,( 0.22/0.40 ~(funcGraphProp1 => (funcGraphProp2 => ! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X8 : $i] : ((func @ X0 @ X3 @ X8) => (! [X1 : $i] : ((in @ X1 @ X0) => ((ap @ X0 @ X3 @ X7 @ X1) = (ap @ X0 @ X3 @ X8 @ X1))) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X8) => (in @ (kpair @ X1 @ X6) @ X7)))))))))), 0.22/0.40 inference(negated_conjecture,[status(cth)],[f7])). 0.22/0.40 thf(f7,conjecture,( 0.22/0.40 funcGraphProp1 => (funcGraphProp2 => ! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X8 : $i] : ((func @ X0 @ X3 @ X8) => (! [X1 : $i] : ((in @ X1 @ X0) => ((ap @ X0 @ X3 @ X7 @ X1) = (ap @ X0 @ X3 @ X8 @ X1))) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X8) => (in @ (kpair @ X1 @ X6) @ X7))))))))), 0.22/0.40 file('/export/starexec/sandbox/tmp/tmp.ayrFukndGU/E---3.1_20509.p',funcextLem)). 0.22/0.40 thf(f106,plain,( 0.22/0.40 ($true != (in @ sK14 @ sK11))), 0.22/0.40 inference(subsumption_resolution,[status(thm)],[f105,f57])). 0.22/0.40 thf(f57,plain,( 0.22/0.40 ($true = (in @ (kpair @ sK13 @ sK14) @ sK12))), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f105,plain,( 0.22/0.40 ($true != (in @ (kpair @ sK13 @ sK14) @ sK12)) | ($true != (in @ sK14 @ sK11))), 0.22/0.40 inference(subsumption_resolution,[status(thm)],[f104,f60])). 0.22/0.40 thf(f60,plain,( 0.22/0.40 ($true = (in @ sK13 @ sK10))), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f104,plain,( 0.22/0.40 ($true != (in @ sK13 @ sK10)) | ($true != (in @ sK14 @ sK11)) | ($true != (in @ (kpair @ sK13 @ sK14) @ sK12))), 0.22/0.40 inference(trivial_inequality_removal,[status(thm)],[f103])). 0.22/0.40 thf(f103,plain,( 0.22/0.40 ($true != (in @ sK13 @ sK10)) | ($true != $true) | ($true != (in @ sK14 @ sK11)) | ($true != (in @ (kpair @ sK13 @ sK14) @ sK12))), 0.22/0.40 inference(superposition,[status(thm)],[f58,f102])). 0.22/0.40 thf(f102,plain,( 0.22/0.40 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (kpair @ X0 @ X1) @ sK9)) | ($true != (in @ X0 @ sK10)) | ($true != (in @ X1 @ sK11)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12))) )), 0.22/0.40 inference(subsumption_resolution,[status(thm)],[f97,f55])). 0.22/0.40 thf(f55,plain,( 0.22/0.40 ((func @ sK10 @ sK11 @ sK9) = $true)), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f97,plain,( 0.22/0.40 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ sK11)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ($true != (in @ X0 @ sK10)) | ((func @ sK10 @ sK11 @ sK9) != $true) | ($true = (in @ (kpair @ X0 @ X1) @ sK9))) )), 0.22/0.40 inference(duplicate_literal_removal,[status(thm)],[f95])). 0.22/0.40 thf(f95,plain,( 0.22/0.40 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ sK10)) | ($true != (in @ X1 @ sK11)) | ($true = (in @ (kpair @ X0 @ X1) @ sK9)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ($true != (in @ X0 @ sK10)) | ((func @ sK10 @ sK11 @ sK9) != $true)) )), 0.22/0.40 inference(superposition,[status(thm)],[f75,f89])). 0.22/0.40 thf(f89,plain,( 0.22/0.40 ( ! [X0 : $i,X1 : $i] : (((ap @ sK10 @ sK11 @ sK9 @ X0) = X1) | ($true != (in @ X0 @ sK10)) | ($true != (in @ X1 @ sK11)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12))) )), 0.22/0.40 inference(subsumption_resolution,[status(thm)],[f88,f56])). 0.22/0.40 thf(f56,plain,( 0.22/0.40 ($true = (func @ sK10 @ sK11 @ sK12))), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f88,plain,( 0.22/0.40 ( ! [X0 : $i,X1 : $i] : (($true != (func @ sK10 @ sK11 @ sK12)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ($true != (in @ X0 @ sK10)) | ((ap @ sK10 @ sK11 @ sK9 @ X0) = X1) | ($true != (in @ X1 @ sK11))) )), 0.22/0.40 inference(duplicate_literal_removal,[status(thm)],[f79])). 0.22/0.40 thf(f79,plain,( 0.22/0.40 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ sK11)) | ((ap @ sK10 @ sK11 @ sK9 @ X0) = X1) | ($true != (in @ X0 @ sK10)) | ($true != (func @ sK10 @ sK11 @ sK12)) | ($true != (in @ (kpair @ X0 @ X1) @ sK12)) | ($true != (in @ X0 @ sK10))) )), 0.22/0.40 inference(superposition,[status(thm)],[f74,f61])). 0.22/0.40 thf(f61,plain,( 0.22/0.40 ( ! [X4 : $i] : (((ap @ sK10 @ sK11 @ sK9 @ X4) = (ap @ sK10 @ sK11 @ sK12 @ X4)) | ((in @ X4 @ sK10) != $true)) )), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f74,plain,( 0.22/0.40 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) = X9) | ($true != (in @ (kpair @ X8 @ X9) @ X5)) | ($true != (func @ X6 @ X7 @ X5)) | ($true != (in @ X8 @ X6)) | ($true != (in @ X9 @ X7))) )), 0.22/0.40 inference(trivial_inequality_removal,[status(thm)],[f69])). 0.22/0.40 thf(f69,plain,( 0.22/0.40 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ X5)) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ($true != (func @ X6 @ X7 @ X5)) | ($true != (in @ X8 @ X6)) | ($true != (in @ X9 @ X7)) | ($true != $true)) )), 0.22/0.40 inference(definition_unfolding,[status(thm)],[f45,f63])). 0.22/0.40 thf(f63,plain,( 0.22/0.40 (funcGraphProp2 = $true)), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f45,plain,( 0.22/0.40 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != (func @ X6 @ X7 @ X5)) | ($true != (in @ X8 @ X6)) | ((ap @ X6 @ X7 @ X5 @ X8) = X9) | ($true != (in @ (kpair @ X8 @ X9) @ X5)) | ($true != (in @ X9 @ X7)) | (funcGraphProp2 != $true)) )), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f34])). 0.22/0.40 thf(f34,plain,( 0.22/0.40 ((funcGraphProp2 = $true) | (($true = (func @ sK1 @ sK2 @ sK0)) & (($true = (in @ sK3 @ sK1)) & (((ap @ sK1 @ sK2 @ sK0 @ sK3) != sK4) & ($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) & ($true = (in @ sK4 @ sK2)))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (($true != (func @ X6 @ X7 @ X5)) | ! [X8 : $i] : (($true != (in @ X8 @ X6)) | ! [X9 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) = X9) | ($true != (in @ (kpair @ X8 @ X9) @ X5)) | ($true != (in @ X9 @ X7))))) | (funcGraphProp2 != $true))), 0.22/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f30,f33,f32,f31])). 0.22/0.40 thf(f31,plain,( 0.22/0.40 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ (kpair @ X3 @ X4) @ X0)) & ($true = (in @ X4 @ X2))))) => (($true = (func @ sK1 @ sK2 @ sK0)) & ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X3) != X4) & ($true = (in @ (kpair @ X3 @ X4) @ sK0)) & ($true = (in @ X4 @ sK2)))))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f32,plain,( 0.22/0.40 ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ X3) != X4) & ($true = (in @ (kpair @ X3 @ X4) @ sK0)) & ($true = (in @ X4 @ sK2)))) => (($true = (in @ sK3 @ sK1)) & ? [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ sK3) != X4) & ((in @ (kpair @ sK3 @ X4) @ sK0) = $true) & ($true = (in @ X4 @ sK2))))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f33,plain,( 0.22/0.40 ? [X4 : $i] : (((ap @ sK1 @ sK2 @ sK0 @ sK3) != X4) & ((in @ (kpair @ sK3 @ X4) @ sK0) = $true) & ($true = (in @ X4 @ sK2))) => (((ap @ sK1 @ sK2 @ sK0 @ sK3) != sK4) & ($true = (in @ (kpair @ sK3 @ sK4) @ sK0)) & ($true = (in @ sK4 @ sK2)))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f30,plain,( 0.22/0.40 ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ (kpair @ X3 @ X4) @ X0)) & ($true = (in @ X4 @ X2)))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (($true != (func @ X6 @ X7 @ X5)) | ! [X8 : $i] : (($true != (in @ X8 @ X6)) | ! [X9 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) = X9) | ($true != (in @ (kpair @ X8 @ X9) @ X5)) | ($true != (in @ X9 @ X7))))) | (funcGraphProp2 != $true))), 0.22/0.40 inference(rectify,[status(thm)],[f29])). 0.22/0.40 thf(f29,plain,( 0.22/0.40 ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ (kpair @ X3 @ X4) @ X0)) & ($true = (in @ X4 @ X2)))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X1 @ X2 @ X0)) | ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ (kpair @ X3 @ X4) @ X0)) | ($true != (in @ X4 @ X2))))) | (funcGraphProp2 != $true))), 0.22/0.40 inference(nnf_transformation,[status(thm)],[f27])). 0.22/0.40 thf(f27,plain,( 0.22/0.40 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X1 @ X2 @ X0)) | ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ (kpair @ X3 @ X4) @ X0)) | ($true != (in @ X4 @ X2)))))), 0.22/0.40 inference(flattening,[status(thm)],[f26])). 0.22/0.40 thf(f26,plain,( 0.22/0.40 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ (kpair @ X3 @ X4) @ X0))) | ($true != (in @ X4 @ X2))) | ($true != (in @ X3 @ X1))) | ($true != (func @ X1 @ X2 @ X0)))), 0.22/0.40 inference(ennf_transformation,[status(thm)],[f23])). 0.22/0.40 thf(f23,plain,( 0.22/0.40 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ! [X4 : $i] : (($true = (in @ X4 @ X2)) => (($true = (in @ (kpair @ X3 @ X4) @ X0)) => ((ap @ X1 @ X2 @ X0 @ X3) = X4)))))), 0.22/0.40 inference(fool_elimination,[status(thm)],[f22])). 0.22/0.40 thf(f22,plain,( 0.22/0.40 (funcGraphProp2 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))))), 0.22/0.40 inference(rectify,[status(thm)],[f6])). 0.22/0.40 thf(f6,axiom,( 0.22/0.40 (funcGraphProp2 = ! [X7 : $i,X0 : $i,X3 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => ! [X6 : $i] : ((in @ X6 @ X3) => ((in @ (kpair @ X1 @ X6) @ X7) => ((ap @ X0 @ X3 @ X7 @ X1) = X6))))))), 0.22/0.40 file('/export/starexec/sandbox/tmp/tmp.ayrFukndGU/E---3.1_20509.p',funcGraphProp2)). 0.22/0.40 thf(f75,plain,( 0.22/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X0)) | ($true != (func @ X0 @ X1 @ X2))) )), 0.22/0.40 inference(trivial_inequality_removal,[status(thm)],[f70])). 0.22/0.40 thf(f70,plain,( 0.22/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (func @ X0 @ X1 @ X2)) | ($true != $true) | ($true != (in @ X3 @ X0)) | ($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))) )), 0.22/0.40 inference(definition_unfolding,[status(thm)],[f54,f62])). 0.22/0.40 thf(f62,plain,( 0.22/0.40 (funcGraphProp1 = $true)), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 thf(f54,plain,( 0.22/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (func @ X0 @ X1 @ X2)) | ($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X0)) | (funcGraphProp1 != $true)) )), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f39])). 0.22/0.40 thf(f39,plain,( 0.22/0.40 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X1 @ X2)) | ! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X0)))) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | (($true = (func @ sK5 @ sK6 @ sK7)) & (($true != (in @ (kpair @ sK8 @ (ap @ sK5 @ sK6 @ sK7 @ sK8)) @ sK7)) & ($true = (in @ sK8 @ sK5)))))), 0.22/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f36,f38,f37])). 0.22/0.40 thf(f37,plain,( 0.22/0.40 ? [X4 : $i,X5 : $i,X6 : $i] : (($true = (func @ X4 @ X5 @ X6)) & ? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ X4 @ X5 @ X6 @ X7)) @ X6)) & ($true = (in @ X7 @ X4)))) => (($true = (func @ sK5 @ sK6 @ sK7)) & ? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ sK5 @ sK6 @ sK7 @ X7)) @ sK7)) & ($true = (in @ X7 @ sK5))))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f38,plain,( 0.22/0.40 ? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ sK5 @ sK6 @ sK7 @ X7)) @ sK7)) & ($true = (in @ X7 @ sK5))) => (($true != (in @ (kpair @ sK8 @ (ap @ sK5 @ sK6 @ sK7 @ sK8)) @ sK7)) & ($true = (in @ sK8 @ sK5)))), 0.22/0.40 introduced(definition,[],[choice_axiom])). 0.22/0.40 thf(f36,plain,( 0.22/0.40 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X1 @ X2)) | ! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X0)))) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (($true = (func @ X4 @ X5 @ X6)) & ? [X7 : $i] : (($true != (in @ (kpair @ X7 @ (ap @ X4 @ X5 @ X6 @ X7)) @ X6)) & ($true = (in @ X7 @ X4)))))), 0.22/0.40 inference(rectify,[status(thm)],[f35])). 0.22/0.40 thf(f35,plain,( 0.22/0.40 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X1 @ X2)) | ! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X0)))) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X1 @ X2)) & ? [X3 : $i] : (($true != (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) & ($true = (in @ X3 @ X0)))))), 0.22/0.40 inference(nnf_transformation,[status(thm)],[f28])). 0.22/0.40 thf(f28,plain,( 0.22/0.40 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X0 @ X1 @ X2)) | ! [X3 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) | ($true != (in @ X3 @ X0)))) <=> (funcGraphProp1 = $true)), 0.22/0.40 inference(ennf_transformation,[status(thm)],[f11])). 0.22/0.40 thf(f11,plain,( 0.22/0.40 (funcGraphProp1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X0 @ X1 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X0)) => ($true = (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))))), 0.22/0.40 inference(fool_elimination,[status(thm)],[f10])). 0.22/0.40 thf(f10,plain,( 0.22/0.40 (funcGraphProp1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))))), 0.22/0.40 inference(rectify,[status(thm)],[f5])). 0.22/0.40 thf(f5,axiom,( 0.22/0.40 (funcGraphProp1 = ! [X0 : $i,X3 : $i,X7 : $i] : ((func @ X0 @ X3 @ X7) => ! [X1 : $i] : ((in @ X1 @ X0) => (in @ (kpair @ X1 @ (ap @ X0 @ X3 @ X7 @ X1)) @ X7))))), 0.22/0.40 file('/export/starexec/sandbox/tmp/tmp.ayrFukndGU/E---3.1_20509.p',funcGraphProp1)). 0.22/0.40 thf(f58,plain,( 0.22/0.40 ($true != (in @ (kpair @ sK13 @ sK14) @ sK9))), 0.22/0.40 inference(cnf_transformation,[status(thm)],[f44])). 0.22/0.40 % SZS output end Proof for E---3.1_20509 0.22/0.40 % (20621)------------------------------ 0.22/0.40 % (20621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.40 % (20621)Termination reason: Refutation 0.22/0.40 0.22/0.40 % (20621)Memory used [KB]: 5628 0.22/0.40 % (20621)Time elapsed: 0.016 s 0.22/0.40 % (20621)Instructions burned: 17 (million) 0.22/0.40 % (20621)------------------------------ 0.22/0.40 % (20621)------------------------------ 0.22/0.40 % (20615)Success in time 0.021 s 0.22/0.40 EOF