0.10/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.11 % Command : run_vampire %s %d THM 0.11/0.33 % Computer : n016.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1440 0.11/0.33 % WCLimit : 180 0.11/0.33 % DateTime : Thu Jul 4 07:54:24 EDT 2024 0.11/0.33 % CPUTime : 0.11/0.35 This is a THF_ problem 0.11/0.35 Running higher-order theorem proving 0.11/0.36 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.URgehPM934/E---3.1_28510.p -m 16384 -t 180 0.11/0.38 % (28621)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_28510 for (1799ds/4Mi) 0.11/0.38 % (28622)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_28510 for (1799ds/27Mi) 0.11/0.38 % (28625)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_28510 for (1799ds/275Mi) 0.11/0.38 % (28624)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_28510 for (1799ds/2Mi) 0.11/0.38 % (28623)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_28510 for (1799ds/2Mi) 0.11/0.38 % (28626)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_28510 for (1799ds/18Mi) 0.11/0.38 % (28623)Instruction limit reached! 0.11/0.38 % (28623)------------------------------ 0.11/0.38 % (28623)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (28623)Termination reason: Unknown 0.11/0.38 % (28623)Termination phase: shuffling 0.11/0.38 0.11/0.38 % (28624)Instruction limit reached! 0.11/0.38 % (28624)------------------------------ 0.11/0.38 % (28624)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (28624)Termination reason: Unknown 0.11/0.38 % (28624)Termination phase: Property scanning 0.11/0.38 0.11/0.38 % (28624)Memory used [KB]: 1023 0.11/0.38 % (28624)Time elapsed: 0.003 s 0.11/0.38 % (28624)Instructions burned: 2 (million) 0.11/0.38 % (28624)------------------------------ 0.11/0.38 % (28624)------------------------------ 0.11/0.38 % (28623)Memory used [KB]: 1023 0.11/0.38 % (28623)Time elapsed: 0.003 s 0.11/0.38 % (28623)Instructions burned: 2 (million) 0.11/0.38 % (28623)------------------------------ 0.11/0.38 % (28623)------------------------------ 0.11/0.38 % (28621)Instruction limit reached! 0.11/0.38 % (28621)------------------------------ 0.11/0.38 % (28621)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (28621)Termination reason: Unknown 0.11/0.38 % (28621)Termination phase: Function definition elimination 0.11/0.38 0.11/0.38 % (28621)Memory used [KB]: 1023 0.11/0.38 % (28621)Time elapsed: 0.004 s 0.11/0.38 % (28621)Instructions burned: 4 (million) 0.11/0.38 % (28621)------------------------------ 0.11/0.38 % (28621)------------------------------ 0.11/0.38 % (28619)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_28510 for (1799ds/183Mi) 0.11/0.38 % (28625)Refutation not found, incomplete strategy 0.11/0.38 % (28625)------------------------------ 0.11/0.38 % (28625)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (28625)Termination reason: Refutation not found, incomplete strategy 0.11/0.38 0.11/0.38 0.11/0.38 % (28625)Memory used [KB]: 5500 0.11/0.38 % (28625)Time elapsed: 0.005 s 0.11/0.38 % (28625)Instructions burned: 6 (million) 0.11/0.38 % (28625)------------------------------ 0.11/0.38 % (28625)------------------------------ 0.11/0.39 % (28622)Refutation not found, incomplete strategy 0.11/0.39 % (28622)------------------------------ 0.11/0.39 % (28622)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.39 % (28622)Termination reason: Refutation not found, incomplete strategy 0.11/0.39 0.11/0.39 0.11/0.39 % (28622)Memory used [KB]: 5628 0.11/0.39 % (28622)Time elapsed: 0.007 s 0.11/0.39 % (28622)Instructions burned: 7 (million) 0.11/0.39 % (28622)------------------------------ 0.11/0.39 % (28622)------------------------------ 0.11/0.39 % (28626)Instruction limit reached! 0.11/0.39 % (28626)------------------------------ 0.11/0.39 % (28626)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.39 % (28626)Termination reason: Unknown 0.11/0.39 % (28626)Termination phase: Saturation 0.11/0.39 0.11/0.39 % (28626)Memory used [KB]: 5628 0.11/0.39 % (28626)Time elapsed: 0.011 s 0.11/0.39 % (28626)Instructions burned: 18 (million) 0.11/0.39 % (28626)------------------------------ 0.11/0.39 % (28626)------------------------------ 0.11/0.40 % (28627)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_28510 for (1799ds/3Mi) 0.11/0.40 % (28628)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_28510 for (1799ds/37Mi) 0.11/0.40 % (28629)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_28510 for (1799ds/15Mi) 0.11/0.40 % (28627)Instruction limit reached! 0.11/0.40 % (28627)------------------------------ 0.11/0.40 % (28627)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.40 % (28627)Termination reason: Unknown 0.11/0.40 % (28627)Termination phase: Property scanning 0.11/0.40 0.11/0.40 % (28627)Memory used [KB]: 1023 0.11/0.40 % (28627)Time elapsed: 0.003 s 0.11/0.40 % (28627)Instructions burned: 3 (million) 0.11/0.40 % (28627)------------------------------ 0.11/0.40 % (28627)------------------------------ 0.11/0.40 % (28630)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_28510 for (1799ds/3Mi) 0.11/0.40 % (28630)Instruction limit reached! 0.11/0.40 % (28630)------------------------------ 0.11/0.40 % (28630)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.40 % (28630)Termination reason: Unknown 0.11/0.40 % (28630)Termination phase: Property scanning 0.11/0.40 0.11/0.40 % (28630)Memory used [KB]: 1023 0.11/0.40 % (28630)Time elapsed: 0.003 s 0.11/0.40 % (28630)Instructions burned: 3 (million) 0.11/0.40 % (28630)------------------------------ 0.11/0.40 % (28630)------------------------------ 0.11/0.40 % (28629)Refutation not found, incomplete strategy 0.11/0.40 % (28629)------------------------------ 0.11/0.40 % (28629)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.40 % (28629)Termination reason: Refutation not found, incomplete strategy 0.11/0.40 0.11/0.40 0.11/0.40 % (28629)Memory used [KB]: 5628 0.11/0.40 % (28629)Time elapsed: 0.007 s 0.11/0.40 % (28629)Instructions burned: 11 (million) 0.11/0.40 % (28629)------------------------------ 0.11/0.40 % (28629)------------------------------ 0.20/0.40 % (28632)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_28510 for (1799ds/7Mi) 0.20/0.41 % (28631)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_28510 for (1799ds/1041Mi) 0.20/0.41 % (28632)Instruction limit reached! 0.20/0.41 % (28632)------------------------------ 0.20/0.41 % (28632)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.41 % (28632)Termination reason: Unknown 0.20/0.41 % (28632)Termination phase: Saturation 0.20/0.41 0.20/0.41 % (28632)Memory used [KB]: 1023 0.20/0.41 % (28632)Time elapsed: 0.005 s 0.20/0.41 % (28632)Instructions burned: 7 (million) 0.20/0.41 % (28632)------------------------------ 0.20/0.41 % (28632)------------------------------ 0.20/0.41 % (28633)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_28510 for (1799ds/16Mi) 0.20/0.41 % (28631)First to succeed. 0.20/0.41 % (28628)Instruction limit reached! 0.20/0.41 % (28628)------------------------------ 0.20/0.41 % (28628)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.41 % (28628)Termination reason: Unknown 0.20/0.41 % (28628)Termination phase: Saturation 0.20/0.41 0.20/0.41 % (28628)Memory used [KB]: 5884 0.20/0.41 % (28628)Time elapsed: 0.020 s 0.20/0.41 % (28628)Instructions burned: 38 (million) 0.20/0.41 % (28628)------------------------------ 0.20/0.41 % (28628)------------------------------ 0.20/0.41 % (28631)Refutation found. Thanks to Tanya! 0.20/0.41 % SZS status Theorem for E---3.1_28510 0.20/0.41 % SZS output start Proof for E---3.1_28510 0.20/0.41 thf(type_def_5, type, mu: $tType). 0.20/0.41 thf(func_def_0, type, mu: $tType). 0.20/0.41 thf(func_def_1, type, meq_ind: mu > mu > $i > $o). 0.20/0.41 thf(func_def_2, type, mtrue: $i > $o). 0.20/0.41 thf(func_def_3, type, mfalse: $i > $o). 0.20/0.41 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_6, type, mor: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_7, type, mand: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_8, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_9, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_10, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_11, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_12, type, mforall_ind: (mu > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_13, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_14, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_15, type, mexists_ind: (mu > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_16, type, mexists_indset: ((mu > $i > $o) > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_17, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_18, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_19, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_20, type, rel: $i > $i > $o). 0.20/0.41 thf(func_def_21, type, mbox: ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_22, type, mdia: ($i > $o) > $i > $o). 0.20/0.41 thf(func_def_23, type, mvalid: ($i > $o) > $o). 0.20/0.41 thf(func_def_24, type, minvalid: ($i > $o) > $o). 0.20/0.41 thf(func_def_25, type, positive: (mu > $i > $o) > $i > $o). 0.20/0.41 thf(func_def_26, type, god: mu > $i > $o). 0.20/0.41 thf(func_def_44, type, ph1: !>[X0: $tType]:(X0)). 0.20/0.41 thf(func_def_45, type, sK2: $i > $i). 0.20/0.41 thf(f136,plain,( 0.20/0.41 $false), 0.20/0.41 inference(trivial_inequality_removal,[],[f134])). 0.20/0.41 thf(f134,plain,( 0.20/0.41 ($false = $true)), 0.20/0.41 inference(superposition,[],[f132,f121])). 0.20/0.41 thf(f121,plain,( 0.20/0.41 ( ! [X0 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ X0 @ Y0)))) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f120])). 0.20/0.42 thf(f120,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ X0 @ Y0))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f119])). 0.20/0.42 thf(f119,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: ((^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))) & (rel @ X0 @ Y0))))) = $true)) )), 0.20/0.42 inference(superposition,[],[f117,f113])). 0.20/0.42 thf(f113,plain,( 0.20/0.42 ( ! [X1 : $i] : (((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f112])). 0.20/0.42 thf(f112,plain,( 0.20/0.42 ((!! @ $i @ (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f108])). 0.20/0.42 thf(f108,plain,( 0.20/0.42 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ (positive @ (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (positive @ Y1) @ (Y1 @ Y0))))))) = $true)), 0.20/0.42 inference(definition_unfolding,[],[f91,f79,f106])). 0.20/0.42 thf(f106,plain,( 0.20/0.42 (god = (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (positive @ Y1) @ (Y1 @ Y0))))))), 0.20/0.42 inference(definition_unfolding,[],[f80,f101,f90])). 0.20/0.42 thf(f90,plain,( 0.20/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))), 0.20/0.42 inference(cnf_transformation,[],[f67])). 0.20/0.42 thf(f67,plain,( 0.20/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))), 0.20/0.42 inference(fool_elimination,[],[f66])). 0.20/0.42 thf(f66,plain,( 0.20/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) => (X1 @ X2))) = mimplies)), 0.20/0.42 inference(rectify,[],[f7])). 0.20/0.42 thf(f7,axiom,( 0.20/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) => (X4 @ X2))) = mimplies)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',mimplies)). 0.20/0.42 thf(f101,plain,( 0.20/0.42 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))), 0.20/0.42 inference(cnf_transformation,[],[f61])). 0.20/0.42 thf(f61,plain,( 0.20/0.42 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))), 0.20/0.42 inference(fool_elimination,[],[f60])). 0.20/0.42 thf(f60,plain,( 0.20/0.42 ((^[X0 : (mu > $i > $o) > $i > $o, X1 : $i] : (! [X2 : mu > $i > $o] : (X0 @ X2 @ X1))) = mforall_indset)), 0.20/0.42 inference(rectify,[],[f12])). 0.20/0.42 thf(f12,axiom,( 0.20/0.42 ((^[X3 : (mu > $i > $o) > $i > $o, X2 : $i] : (! [X0 : mu > $i > $o] : (X3 @ X0 @ X2))) = mforall_indset)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',mforall_indset)). 0.20/0.42 thf(f80,plain,( 0.20/0.42 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))), 0.20/0.42 inference(cnf_transformation,[],[f51])). 0.20/0.42 thf(f51,plain,( 0.20/0.42 (god = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (positive @ Y1) @ (Y1 @ Y0))))))), 0.20/0.42 inference(fool_elimination,[],[f50])). 0.20/0.42 thf(f50,plain,( 0.20/0.42 ((^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (positive @ X1) @ (X1 @ X0))))) = god)), 0.20/0.42 inference(rectify,[],[f23])). 0.20/0.42 thf(f23,axiom,( 0.20/0.42 ((^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (X3 @ X0))))) = god)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',defD1)). 0.20/0.42 thf(f79,plain,( 0.20/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 0.20/0.42 inference(cnf_transformation,[],[f42])). 0.20/0.42 thf(f42,plain,( 0.20/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 0.20/0.42 inference(fool_elimination,[],[f41])). 0.20/0.42 thf(f41,plain,( 0.20/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))), 0.20/0.42 inference(rectify,[],[f21])). 0.20/0.42 thf(f21,axiom,( 0.20/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',mvalid)). 0.20/0.42 thf(f91,plain,( 0.20/0.42 ((mvalid @ (positive @ god)) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f57])). 0.20/0.42 thf(f57,plain,( 0.20/0.42 ((mvalid @ (positive @ god)) = $true)), 0.20/0.42 inference(fool_elimination,[],[f56])). 0.20/0.42 thf(f56,plain,( 0.20/0.42 (mvalid @ (positive @ god))), 0.20/0.42 inference(rectify,[],[f27])). 0.20/0.42 thf(f27,axiom,( 0.20/0.42 (mvalid @ (positive @ god))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',axA3)). 0.20/0.42 thf(f117,plain,( 0.20/0.42 ( ! [X2 : mu > $i > $o,X1 : $i] : ((((positive @ X2 @ X1) => (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (X2 @ Y1 @ Y0))) & (rel @ X1 @ Y0))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f116])). 0.20/0.42 thf(f116,plain,( 0.20/0.42 ( ! [X2 : mu > $i > $o,X1 : $i] : ((((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))) & (rel @ X1 @ Y1)))))) @ X2) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f115])). 0.20/0.42 thf(f115,plain,( 0.20/0.42 ( ! [X1 : $i] : (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))) & (rel @ X1 @ Y1))))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f114])). 0.20/0.42 thf(f114,plain,( 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2))) & (rel @ Y0 @ Y2)))))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f111])). 0.20/0.42 thf(f111,plain,( 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2))) & (rel @ Y0 @ Y2))))))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f109])). 0.20/0.42 thf(f109,plain,( 0.20/0.42 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ (positive @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) & (Y1 @ Y3 @ Y4))))))))) @ rel @ ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (?? @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: (Y0 @ Y1)))))))) = $true)), 0.20/0.42 inference(definition_unfolding,[],[f99,f79,f101,f90,f105,f95])). 0.20/0.42 thf(f95,plain,( 0.20/0.42 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))), 0.20/0.42 inference(cnf_transformation,[],[f55])). 0.20/0.42 thf(f55,plain,( 0.20/0.42 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))), 0.20/0.42 inference(fool_elimination,[],[f54])). 0.20/0.42 thf(f54,plain,( 0.20/0.42 (mexists_ind = (^[X0 : mu > $i > $o, X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))), 0.20/0.42 inference(rectify,[],[f14])). 0.20/0.42 thf(f14,axiom,( 0.20/0.42 (mexists_ind = (^[X3 : mu > $i > $o, X2 : $i] : (? [X0 : mu] : (X3 @ X0 @ X2))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',mexists_ind)). 0.20/0.42 thf(f105,plain,( 0.20/0.42 (mdia = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))) @ rel))), 0.20/0.42 inference(definition_unfolding,[],[f89,f102])). 0.20/0.42 thf(f102,plain,( 0.20/0.42 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))))), 0.20/0.42 inference(cnf_transformation,[],[f47])). 0.20/0.42 thf(f47,plain,( 0.20/0.42 (mdia_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))))), 0.20/0.42 inference(fool_elimination,[],[f46])). 0.20/0.42 thf(f46,plain,( 0.20/0.42 (mdia_generic = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X0 @ X2 @ X3) & (X1 @ X3)))))), 0.20/0.42 inference(rectify,[],[f18])). 0.20/0.42 thf(f18,axiom,( 0.20/0.42 (mdia_generic = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (? [X7] : ((X6 @ X2 @ X7) & (X3 @ X7)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',mdia_generic)). 0.20/0.42 thf(f89,plain,( 0.20/0.42 (mdia = (mdia_generic @ rel))), 0.20/0.42 inference(cnf_transformation,[],[f45])). 0.20/0.42 thf(f45,plain,( 0.20/0.42 (mdia = (mdia_generic @ rel))), 0.20/0.42 inference(fool_elimination,[],[f20])). 0.20/0.42 thf(f20,axiom,( 0.20/0.42 (mdia = (mdia_generic @ rel))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',mdia)). 0.20/0.42 thf(f99,plain,( 0.20/0.42 ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1)))))))) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f72])). 0.20/0.42 thf(f72,plain,( 0.20/0.42 ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mdia @ (mexists_ind @ (^[Y1 : mu]: (Y0 @ Y1)))))))) = $true)), 0.20/0.42 inference(fool_elimination,[],[f71])). 0.20/0.42 thf(f71,plain,( 0.20/0.42 (mvalid @ (mforall_indset @ (^[X0 : mu > $i > $o] : (mimplies @ (positive @ X0) @ (mdia @ (mexists_ind @ (^[X1 : mu] : (X0 @ X1))))))))), 0.20/0.42 inference(rectify,[],[f26])). 0.20/0.42 thf(f26,axiom,( 0.20/0.42 (mvalid @ (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (mdia @ (mexists_ind @ (^[X0 : mu] : (X3 @ X0))))))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',thmT1)). 0.20/0.42 thf(f132,plain,( 0.20/0.42 ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ sK3 @ Y0)))))), 0.20/0.42 inference(beta_eta_normalization,[],[f131])). 0.20/0.42 thf(f131,plain,( 0.20/0.42 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))) & (rel @ Y0 @ Y1))))) @ sK3) = $false)), 0.20/0.42 inference(sigma_clausification,[],[f124])). 0.20/0.42 thf(f124,plain,( 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))) & (rel @ Y0 @ Y1)))))) = $false)), 0.20/0.42 inference(not_proxy_clausification,[],[f110])). 0.20/0.42 thf(f110,plain,( 0.20/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))) & (rel @ Y0 @ Y1))))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f107])). 0.20/0.42 thf(f107,plain,( 0.20/0.42 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & (Y0 @ Y2 @ Y3))))))))) @ rel @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (positive @ Y2) @ (Y2 @ Y1))))) @ Y0)))))) = $true)), 0.20/0.42 inference(definition_unfolding,[],[f86,f79,f105,f95,f106])). 0.20/0.42 thf(f86,plain,( 0.20/0.42 ((~ (mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f59])). 0.20/0.42 thf(f59,plain,( 0.20/0.42 ((~ (mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))) = $true)), 0.20/0.42 inference(fool_elimination,[],[f58])). 0.20/0.42 thf(f58,plain,( 0.20/0.42 ~(mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 inference(rectify,[],[f25])). 0.20/0.42 thf(f25,negated_conjecture,( 0.20/0.42 ~(mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 inference(negated_conjecture,[],[f24])). 0.20/0.42 thf(f24,conjecture,( 0.20/0.42 (mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.URgehPM934/E---3.1_28510.p',corC)). 0.20/0.42 % SZS output end Proof for E---3.1_28510 0.20/0.42 % (28631)------------------------------ 0.20/0.42 % (28631)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.42 % (28631)Termination reason: Refutation 0.20/0.42 0.20/0.42 % (28631)Memory used [KB]: 5628 0.20/0.42 % (28631)Time elapsed: 0.010 s 0.20/0.42 % (28631)Instructions burned: 11 (million) 0.20/0.42 % (28631)------------------------------ 0.20/0.42 % (28631)------------------------------ 0.20/0.42 % (28618)Success in time 0.045 s 0.20/0.42 EOF