0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : run_vampire %s %d THM 0.11/0.33 % Computer : n028.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 07:36:39 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.5Zki7DWx3W/E---3.1_8583.p -m 16384 -t 180 0.11/0.38 % (8699)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_8583 for (1799ds/18Mi) 0.11/0.38 % (8698)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_8583 for (1799ds/275Mi) 0.11/0.38 % (8695)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_8583 for (1799ds/27Mi) 0.11/0.38 % (8696)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_8583 for (1799ds/2Mi) 0.11/0.38 % (8694)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_8583 for (1799ds/4Mi) 0.11/0.38 % (8697)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_8583 for (1799ds/2Mi) 0.11/0.38 % (8696)Instruction limit reached! 0.11/0.38 % (8696)------------------------------ 0.11/0.38 % (8696)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (8696)Termination reason: Unknown 0.11/0.38 % (8696)Termination phase: Property scanning 0.11/0.38 0.11/0.38 % (8696)Memory used [KB]: 1023 0.11/0.38 % (8696)Time elapsed: 0.003 s 0.11/0.38 % (8697)Instruction limit reached! 0.11/0.38 % (8697)------------------------------ 0.11/0.38 % (8697)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (8697)Termination reason: Unknown 0.11/0.38 % (8697)Termination phase: shuffling 0.11/0.38 0.11/0.38 % (8697)Memory used [KB]: 1023 0.11/0.38 % (8697)Time elapsed: 0.003 s 0.11/0.38 % (8697)Instructions burned: 2 (million) 0.11/0.38 % (8697)------------------------------ 0.11/0.38 % (8697)------------------------------ 0.11/0.38 % (8696)Instructions burned: 3 (million) 0.11/0.38 % (8696)------------------------------ 0.11/0.38 % (8696)------------------------------ 0.11/0.38 % (8694)Instruction limit reached! 0.11/0.38 % (8694)------------------------------ 0.11/0.38 % (8694)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (8694)Termination reason: Unknown 0.11/0.38 % (8694)Termination phase: Property scanning 0.11/0.38 0.11/0.38 % (8694)Memory used [KB]: 1023 0.11/0.38 % (8694)Time elapsed: 0.004 s 0.11/0.38 % (8694)Instructions burned: 4 (million) 0.11/0.38 % (8694)------------------------------ 0.11/0.38 % (8694)------------------------------ 0.11/0.38 % (8692)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_8583 for (1799ds/183Mi) 0.11/0.38 % (8698)Refutation not found, incomplete strategy 0.11/0.38 % (8698)------------------------------ 0.11/0.38 % (8698)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.38 % (8698)Termination reason: Refutation not found, incomplete strategy 0.11/0.38 0.11/0.38 0.11/0.38 % (8698)Memory used [KB]: 5628 0.11/0.38 % (8698)Time elapsed: 0.006 s 0.11/0.38 % (8698)Instructions burned: 6 (million) 0.11/0.38 % (8698)------------------------------ 0.11/0.38 % (8698)------------------------------ 0.11/0.39 % (8699)Instruction limit reached! 0.11/0.39 % (8699)------------------------------ 0.11/0.39 % (8699)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.39 % (8699)Termination reason: Unknown 0.11/0.39 % (8699)Termination phase: Saturation 0.11/0.39 0.11/0.39 % (8699)Memory used [KB]: 5756 0.11/0.39 % (8699)Time elapsed: 0.011 s 0.11/0.39 % (8699)Instructions burned: 18 (million) 0.11/0.39 % (8699)------------------------------ 0.11/0.39 % (8699)------------------------------ 0.11/0.39 % (8695)Instruction limit reached! 0.11/0.39 % (8695)------------------------------ 0.11/0.39 % (8695)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.39 % (8695)Termination reason: Unknown 0.11/0.39 % (8695)Termination phase: Saturation 0.11/0.39 0.11/0.39 % (8695)Memory used [KB]: 5756 0.11/0.39 % (8695)Time elapsed: 0.016 s 0.11/0.39 % (8695)Instructions burned: 28 (million) 0.11/0.39 % (8695)------------------------------ 0.11/0.39 % (8695)------------------------------ 0.11/0.40 % (8700)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_8583 for (1799ds/3Mi) 0.11/0.40 % (8701)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_8583 for (1799ds/37Mi) 0.11/0.40 % (8700)Instruction limit reached! 0.11/0.40 % (8700)------------------------------ 0.11/0.40 % (8700)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.40 % (8702)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_8583 for (1799ds/15Mi) 0.11/0.40 % (8700)Termination reason: Unknown 0.11/0.40 % (8700)Termination phase: Property scanning 0.11/0.40 0.11/0.40 % (8700)Memory used [KB]: 1023 0.11/0.40 % (8700)Time elapsed: 0.003 s 0.11/0.40 % (8700)Instructions burned: 3 (million) 0.11/0.40 % (8700)------------------------------ 0.11/0.40 % (8700)------------------------------ 0.11/0.40 % (8703)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_8583 for (1799ds/3Mi) 0.11/0.40 % (8703)Instruction limit reached! 0.11/0.40 % (8703)------------------------------ 0.11/0.40 % (8703)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.40 % (8703)Termination reason: Unknown 0.11/0.40 % (8703)Termination phase: Property scanning 0.11/0.40 0.11/0.40 % (8703)Memory used [KB]: 1023 0.11/0.40 % (8703)Time elapsed: 0.003 s 0.11/0.40 % (8703)Instructions burned: 3 (million) 0.11/0.40 % (8703)------------------------------ 0.11/0.40 % (8703)------------------------------ 0.11/0.40 % (8704)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_8583 for (1799ds/1041Mi) 0.11/0.40 % (8702)Instruction limit reached! 0.11/0.40 % (8702)------------------------------ 0.11/0.40 % (8702)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.40 % (8702)Termination reason: Unknown 0.11/0.40 % (8702)Termination phase: Saturation 0.11/0.40 0.11/0.40 % (8702)Memory used [KB]: 5628 0.11/0.40 % (8702)Time elapsed: 0.009 s 0.11/0.40 % (8702)Instructions burned: 15 (million) 0.11/0.40 % (8702)------------------------------ 0.11/0.40 % (8702)------------------------------ 0.11/0.41 % (8705)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_8583 for (1799ds/7Mi) 0.11/0.41 % (8706)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_8583 for (1799ds/16Mi) 0.11/0.41 % (8707)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on E---3.1_8583 for (1799ds/3Mi) 0.11/0.41 % (8705)Instruction limit reached! 0.11/0.41 % (8705)------------------------------ 0.11/0.41 % (8705)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.41 % (8705)Termination reason: Unknown 0.11/0.41 % (8705)Termination phase: Saturation 0.11/0.41 0.11/0.41 % (8705)Memory used [KB]: 1023 0.11/0.41 % (8705)Time elapsed: 0.005 s 0.11/0.41 % (8705)Instructions burned: 7 (million) 0.11/0.41 % (8705)------------------------------ 0.11/0.41 % (8705)------------------------------ 0.11/0.41 % (8707)Instruction limit reached! 0.11/0.41 % (8707)------------------------------ 0.11/0.41 % (8707)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.11/0.41 % (8707)Termination reason: Unknown 0.11/0.41 % (8707)Termination phase: Property scanning 0.11/0.41 0.11/0.41 % (8707)Memory used [KB]: 1023 0.11/0.41 % (8707)Time elapsed: 0.003 s 0.11/0.41 % (8707)Instructions burned: 3 (million) 0.11/0.41 % (8707)------------------------------ 0.11/0.41 % (8707)------------------------------ 0.20/0.41 % (8701)Instruction limit reached! 0.20/0.41 % (8701)------------------------------ 0.20/0.41 % (8701)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.41 % (8701)Termination reason: Unknown 0.20/0.41 % (8701)Termination phase: Saturation 0.20/0.41 0.20/0.41 % (8701)Memory used [KB]: 6140 0.20/0.41 % (8701)Time elapsed: 0.021 s 0.20/0.41 % (8701)Instructions burned: 38 (million) 0.20/0.41 % (8701)------------------------------ 0.20/0.41 % (8701)------------------------------ 0.20/0.42 % (8706)Instruction limit reached! 0.20/0.42 % (8706)------------------------------ 0.20/0.42 % (8706)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.42 % (8706)Termination reason: Unknown 0.20/0.42 % (8706)Termination phase: Saturation 0.20/0.42 0.20/0.42 % (8706)Memory used [KB]: 5756 0.20/0.42 % (8706)Time elapsed: 0.009 s 0.20/0.42 % (8706)Instructions burned: 16 (million) 0.20/0.42 % (8706)------------------------------ 0.20/0.42 % (8706)------------------------------ 0.20/0.42 % (8704)First to succeed. 0.20/0.42 % (8704)Refutation found. Thanks to Tanya! 0.20/0.42 % SZS status Theorem for E---3.1_8583 0.20/0.42 % SZS output start Proof for E---3.1_8583 0.20/0.42 thf(type_def_5, type, mu: $tType). 0.20/0.42 thf(func_def_0, type, mu: $tType). 0.20/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o). 0.20/0.42 thf(func_def_2, type, mtrue: $i > $o). 0.20/0.42 thf(func_def_3, type, mfalse: $i > $o). 0.20/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_6, type, mor: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_7, type, mand: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_8, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_9, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_10, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_11, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_12, type, mforall_ind: (mu > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_13, type, mforall_indset: ((mu > $i > $o) > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_14, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_15, type, mexists_ind: (mu > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_16, type, mexists_indset: ((mu > $i > $o) > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_17, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_18, type, mbox_generic: ($i > $i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_19, type, mdia_generic: ($i > $i > $o) > ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_20, type, rel: $i > $i > $o). 0.20/0.42 thf(func_def_21, type, mbox: ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_22, type, mdia: ($i > $o) > $i > $o). 0.20/0.42 thf(func_def_23, type, mvalid: ($i > $o) > $o). 0.20/0.42 thf(func_def_24, type, minvalid: ($i > $o) > $o). 0.20/0.42 thf(func_def_25, type, msymmetric: ($i > $i > $o) > $o). 0.20/0.42 thf(func_def_26, type, positive: (mu > $i > $o) > $i > $o). 0.20/0.42 thf(func_def_27, type, god: mu > $i > $o). 0.20/0.42 thf(func_def_28, type, essence: (mu > $i > $o) > mu > $i > $o). 0.20/0.42 thf(func_def_29, type, necessary_existence: mu > $i > $o). 0.20/0.42 thf(func_def_47, type, ph1: !>[X0: $tType]:(X0)). 0.20/0.42 thf(func_def_48, type, sK2: $i > $i). 0.20/0.42 thf(func_def_49, type, sK3: $i > mu). 0.20/0.42 thf(func_def_52, type, sK6: mu > mu > $i > $o). 0.20/0.42 thf(f231,plain,( 0.20/0.42 $false), 0.20/0.42 inference(trivial_inequality_removal,[],[f230])). 0.20/0.42 thf(f230,plain,( 0.20/0.42 ($false = $true)), 0.20/0.42 inference(boolean_simplification,[],[f229])). 0.20/0.42 thf(f229,plain,( 0.20/0.42 ((~ $true) = $true)), 0.20/0.42 inference(superposition,[],[f225,f152])). 0.20/0.42 thf(f152,plain,( 0.20/0.42 ( ! [X0 : $i] : (((rel @ (sK2 @ X0) @ X0) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f149])). 0.20/0.42 thf(f149,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (rel @ (sK2 @ X0) @ X0)) = $true)) )), 0.20/0.42 inference(superposition,[],[f137,f143])). 0.20/0.42 thf(f143,plain,( 0.20/0.42 ( ! [X1 : $i] : (((rel @ X1 @ (sK2 @ X1)) = $true)) )), 0.20/0.42 inference(binary_proxy_clausification,[],[f142])). 0.20/0.42 thf(f142,plain,( 0.20/0.42 ( ! [X1 : $i] : ((((?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1))))))) & (rel @ X1 @ (sK2 @ X1))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f141])). 0.20/0.42 thf(f141,plain,( 0.20/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ X1 @ Y0))) @ (sK2 @ X1)))) )), 0.20/0.42 inference(sigma_clausification,[],[f140])). 0.20/0.42 thf(f140,plain,( 0.20/0.42 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))) & (rel @ X1 @ Y0)))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f139])). 0.20/0.42 thf(f139,plain,( 0.20/0.42 ( ! [X1 : $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))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f130])). 0.20/0.42 thf(f130,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,[],[f125])). 0.20/0.42 thf(f125,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,[],[f95,f115,f121,f97,f122])). 0.20/0.42 thf(f122,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,[],[f117,f113,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,[],[f89])). 0.20/0.42 thf(f89,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,[],[f88])). 0.20/0.42 thf(f88,plain,( 0.20/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) => (X1 @ X2))))), 0.20/0.42 inference(rectify,[],[f7])). 0.20/0.42 thf(f7,axiom,( 0.20/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) => (X4 @ X2))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',mimplies)). 0.20/0.42 thf(f113,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,[],[f74])). 0.20/0.42 thf(f74,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,[],[f73])). 0.20/0.42 thf(f73,plain,( 0.20/0.42 (mforall_indset = (^[X0 : (mu > $i > $o) > $i > $o, X1 : $i] : (! [X2 : mu > $i > $o] : (X0 @ X2 @ X1))))), 0.20/0.42 inference(rectify,[],[f12])). 0.20/0.42 thf(f12,axiom,( 0.20/0.42 (mforall_indset = (^[X3 : (mu > $i > $o) > $i > $o, X2 : $i] : (! [X0 : mu > $i > $o] : (X3 @ X0 @ X2))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',mforall_indset)). 0.20/0.42 thf(f117,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,[],[f68])). 0.20/0.42 thf(f68,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,[],[f67])). 0.20/0.42 thf(f67,plain,( 0.20/0.42 (god = (^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (positive @ X1) @ (X1 @ X0))))))), 0.20/0.42 inference(rectify,[],[f25])). 0.20/0.42 thf(f25,axiom,( 0.20/0.42 (god = (^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (positive @ X3) @ (X3 @ X0))))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',defD1)). 0.20/0.42 thf(f97,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,[],[f77])). 0.20/0.42 thf(f77,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,[],[f76])). 0.20/0.42 thf(f76,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.5Zki7DWx3W/E---3.1_8583.p',mexists_ind)). 0.20/0.42 thf(f121,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,[],[f109,f116])). 0.20/0.42 thf(f116,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,[],[f40])). 0.20/0.42 thf(f40,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,[],[f39])). 0.20/0.42 thf(f39,plain,( 0.20/0.42 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X0 @ X2 @ X3) & (X1 @ X3)))) = mdia_generic)), 0.20/0.42 inference(rectify,[],[f18])). 0.20/0.42 thf(f18,axiom,( 0.20/0.42 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (? [X7] : ((X6 @ X2 @ X7) & (X3 @ X7)))) = mdia_generic)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',mdia_generic)). 0.20/0.42 thf(f109,plain,( 0.20/0.42 (mdia = (mdia_generic @ rel))), 0.20/0.42 inference(cnf_transformation,[],[f33])). 0.20/0.42 thf(f33,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.5Zki7DWx3W/E---3.1_8583.p',mdia)). 0.20/0.42 thf(f115,plain,( 0.20/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 0.20/0.42 inference(cnf_transformation,[],[f81])). 0.20/0.42 thf(f81,plain,( 0.20/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 0.20/0.42 inference(fool_elimination,[],[f80])). 0.20/0.42 thf(f80,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.5Zki7DWx3W/E---3.1_8583.p',mvalid)). 0.20/0.42 thf(f95,plain,( 0.20/0.42 ((mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0))))) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f54])). 0.20/0.42 thf(f54,plain,( 0.20/0.42 ((mvalid @ (mdia @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0))))) = $true)), 0.20/0.42 inference(fool_elimination,[],[f53])). 0.20/0.42 thf(f53,plain,( 0.20/0.42 (mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 inference(rectify,[],[f29])). 0.20/0.42 thf(f29,axiom,( 0.20/0.42 (mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',corC)). 0.20/0.42 thf(f137,plain,( 0.20/0.42 ( ! [X2 : $i,X1 : $i] : ((((rel @ X1 @ X2) => (rel @ X2 @ X1)) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f136])). 0.20/0.42 thf(f136,plain,( 0.20/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel @ X1 @ Y0) => (rel @ Y0 @ X1))) @ X2) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f135])). 0.20/0.42 thf(f135,plain,( 0.20/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel @ X1 @ Y0) => (rel @ Y0 @ X1)))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f134])). 0.20/0.42 thf(f134,plain,( 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel @ Y0 @ Y1) => (rel @ Y1 @ Y0))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f132])). 0.20/0.42 thf(f132,plain,( 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel @ Y0 @ Y1) => (rel @ Y1 @ Y0)))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f127])). 0.20/0.42 thf(f127,plain,( 0.20/0.42 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel) = $true)), 0.20/0.42 inference(definition_unfolding,[],[f108,f99])). 0.20/0.42 thf(f99,plain,( 0.20/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))), 0.20/0.42 inference(cnf_transformation,[],[f50])). 0.20/0.42 thf(f50,plain,( 0.20/0.42 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))), 0.20/0.42 inference(fool_elimination,[],[f49])). 0.20/0.42 thf(f49,plain,( 0.20/0.42 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))), 0.20/0.42 inference(rectify,[],[f23])). 0.20/0.42 thf(f23,axiom,( 0.20/0.42 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',msymmetric)). 0.20/0.42 thf(f108,plain,( 0.20/0.42 ((msymmetric @ rel) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f70])). 0.20/0.42 thf(f70,plain,( 0.20/0.42 ((msymmetric @ rel) = $true)), 0.20/0.42 inference(fool_elimination,[],[f69])). 0.20/0.42 thf(f69,plain,( 0.20/0.42 (msymmetric @ rel)), 0.20/0.42 inference(rectify,[],[f24])). 0.20/0.42 thf(f24,axiom,( 0.20/0.42 (msymmetric @ rel)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',sym)). 0.20/0.42 thf(f225,plain,( 0.20/0.42 ( ! [X0 : $i] : (((~ (rel @ (sK2 @ X0) @ sK5)) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f216])). 0.20/0.42 thf(f216,plain,( 0.20/0.42 ( ! [X0 : $i] : ((((~ (rel @ (sK2 @ X0) @ sK5)) | $false) = $true)) )), 0.20/0.42 inference(superposition,[],[f214,f170])). 0.20/0.42 thf(f170,plain,( 0.20/0.42 ((?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5)))))) = $false)), 0.20/0.42 inference(boolean_simplification,[],[f169])). 0.20/0.42 thf(f169,plain,( 0.20/0.42 ($false = ($false | (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))))))), 0.20/0.42 inference(backward_demodulation,[],[f166,f168])). 0.20/0.42 thf(f168,plain,( 0.20/0.42 ((~ (rel @ sK4 @ sK5)) = $false)), 0.20/0.42 inference(binary_proxy_clausification,[],[f166])). 0.20/0.42 thf(f166,plain,( 0.20/0.42 ($false = ((~ (rel @ sK4 @ sK5)) | (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ sK5) => (Y1 @ Y0 @ sK5))))))))), 0.20/0.42 inference(beta_eta_normalization,[],[f165])). 0.20/0.42 thf(f165,plain,( 0.20/0.42 (((^[Y0 : $i]: ((~ (rel @ sK4 @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))) @ sK5) = $false)), 0.20/0.42 inference(sigma_clausification,[],[f164])). 0.20/0.42 thf(f164,plain,( 0.20/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ sK4 @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))))), 0.20/0.42 inference(beta_eta_normalization,[],[f163])). 0.20/0.42 thf(f163,plain,( 0.20/0.42 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ Y0 @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))))))) @ sK4) = $false)), 0.20/0.42 inference(sigma_clausification,[],[f160])). 0.20/0.42 thf(f160,plain,( 0.20/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ Y0 @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1))))))))))))), 0.20/0.42 inference(not_proxy_clausification,[],[f129])). 0.20/0.42 thf(f129,plain,( 0.20/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ Y0 @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y1) => (Y3 @ Y2 @ Y1)))))))))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f124])). 0.20/0.42 thf(f124,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]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ 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,[],[f94,f115,f120,f97,f122])). 0.20/0.42 thf(f120,plain,( 0.20/0.42 (mbox = ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ rel))), 0.20/0.42 inference(definition_unfolding,[],[f106,f98])). 0.20/0.42 thf(f98,plain,( 0.20/0.42 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))), 0.20/0.42 inference(cnf_transformation,[],[f85])). 0.20/0.42 thf(f85,plain,( 0.20/0.42 (mbox_generic = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))), 0.20/0.42 inference(fool_elimination,[],[f84])). 0.20/0.42 thf(f84,plain,( 0.20/0.42 (mbox_generic = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))), 0.20/0.42 inference(rectify,[],[f17])). 0.20/0.42 thf(f17,axiom,( 0.20/0.42 (mbox_generic = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',mbox_generic)). 0.20/0.42 thf(f106,plain,( 0.20/0.42 (mbox = (mbox_generic @ rel))), 0.20/0.42 inference(cnf_transformation,[],[f75])). 0.20/0.42 thf(f75,plain,( 0.20/0.42 (mbox = (mbox_generic @ rel))), 0.20/0.42 inference(fool_elimination,[],[f19])). 0.20/0.42 thf(f19,axiom,( 0.20/0.42 (mbox = (mbox_generic @ rel))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',mbox)). 0.20/0.42 thf(f94,plain,( 0.20/0.42 ((~ (mvalid @ (mbox @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f64])). 0.20/0.42 thf(f64,plain,( 0.20/0.42 ((~ (mvalid @ (mbox @ (mexists_ind @ (^[Y0 : mu]: (god @ Y0)))))) = $true)), 0.20/0.42 inference(fool_elimination,[],[f63])). 0.20/0.42 thf(f63,plain,( 0.20/0.42 ~(mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 inference(rectify,[],[f28])). 0.20/0.42 thf(f28,negated_conjecture,( 0.20/0.42 ~(mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 inference(negated_conjecture,[],[f27])). 0.20/0.42 thf(f27,conjecture,( 0.20/0.42 (mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : (god @ X0)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',thmT3)). 0.20/0.42 thf(f214,plain,( 0.20/0.42 ( ! [X0 : $i,X1 : $i] : ((((~ (rel @ (sK2 @ X0) @ X1)) | (?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ X1) => (Y1 @ Y0 @ X1))))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f213])). 0.20/0.42 thf(f213,plain,( 0.20/0.42 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f212])). 0.20/0.42 thf(f212,plain,( 0.20/0.42 ( ! [X0 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0))))))))) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f211])). 0.20/0.42 thf(f211,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))))))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f206])). 0.20/0.42 thf(f206,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: ((^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))))))) = $true)) )), 0.20/0.42 inference(superposition,[],[f195,f204])). 0.20/0.42 thf(f204,plain,( 0.20/0.42 ( ! [X0 : $i] : (((essence @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ (sK3 @ X0) @ (sK2 @ X0)) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f203])). 0.20/0.42 thf(f203,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (essence @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ (sK3 @ X0) @ (sK2 @ X0))) = $true)) )), 0.20/0.42 inference(superposition,[],[f200,f148])). 0.20/0.42 thf(f148,plain,( 0.20/0.42 ( ! [X1 : $i] : (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ (sK2 @ X1)) => (Y0 @ (sK3 @ X1) @ (sK2 @ X1))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f147])). 0.20/0.42 thf(f147,plain,( 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1)))))) @ (sK3 @ X1)) = $true)) )), 0.20/0.42 inference(sigma_clausification,[],[f146])). 0.20/0.42 thf(f146,plain,( 0.20/0.42 ( ! [X1 : $i] : (((?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1))))))) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f145])). 0.20/0.42 thf(f145,plain,( 0.20/0.42 ( ! [X1 : $i] : ((((?? @ mu @ (^[Y0 : mu]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ (sK2 @ X1)) => (Y1 @ Y0 @ (sK2 @ X1))))))) & $true) = $true)) )), 0.20/0.42 inference(backward_demodulation,[],[f142,f143])). 0.20/0.42 thf(f200,plain,( 0.20/0.42 ( ! [X2 : mu,X1 : $i] : ((((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (Y0 @ X2 @ X1)))) => (essence @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y1) => (Y2 @ Y0 @ Y1))))))) @ X2 @ X1)) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f199])). 0.20/0.42 thf(f199,plain,( 0.20/0.42 ( ! [X2 : mu,X1 : $i] : ((((^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ X1) => (Y1 @ Y0 @ X1)))) => (essence @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y2) => (Y3 @ Y1 @ Y2))))))) @ Y0 @ X1))) @ X2) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f197])). 0.20/0.42 thf(f197,plain,( 0.20/0.42 ( ! [X1 : $i] : (((!! @ mu @ (^[Y0 : mu]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ X1) => (Y1 @ Y0 @ X1)))) => (essence @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((positive @ Y3 @ Y2) => (Y3 @ Y1 @ Y2))))))) @ Y0 @ X1)))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f196])). 0.20/0.42 thf(f196,plain,( 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (essence @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f133])). 0.20/0.42 thf(f133,plain,( 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((positive @ Y2 @ Y0) => (Y2 @ Y1 @ Y0)))) => (essence @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((positive @ Y4 @ Y3) => (Y4 @ Y2 @ Y3))))))) @ Y1 @ Y0)))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f128])). 0.20/0.42 thf(f128,plain,( 0.20/0.42 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ ((^[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) @ (essence @ (^[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))))))), 0.20/0.42 inference(definition_unfolding,[],[f119,f115,f112,f90,f122,f122])). 0.20/0.42 thf(f112,plain,( 0.20/0.42 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))), 0.20/0.42 inference(cnf_transformation,[],[f42])). 0.20/0.42 thf(f42,plain,( 0.20/0.42 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))), 0.20/0.42 inference(fool_elimination,[],[f41])). 0.20/0.42 thf(f41,plain,( 0.20/0.42 ((^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))) = mforall_ind)), 0.20/0.42 inference(rectify,[],[f11])). 0.20/0.42 thf(f11,axiom,( 0.20/0.42 ((^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))) = mforall_ind)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',mforall_ind)). 0.20/0.42 thf(f119,plain,( 0.20/0.42 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (god @ Y0) @ (essence @ god @ Y0))))) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f62])). 0.20/0.42 thf(f62,plain,( 0.20/0.42 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mimplies @ (god @ Y0) @ (essence @ god @ Y0))))) = $true)), 0.20/0.42 inference(fool_elimination,[],[f61])). 0.20/0.42 thf(f61,plain,( 0.20/0.42 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))), 0.20/0.42 inference(rectify,[],[f30])). 0.20/0.42 thf(f30,axiom,( 0.20/0.42 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mimplies @ (god @ X0) @ (essence @ god @ X0)))))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',thmT2)). 0.20/0.42 thf(f195,plain,( 0.20/0.42 ( ! [X0 : $i,X1 : mu > $i > $o] : ((((essence @ X1 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((~ (rel @ (sK2 @ X0) @ Y0)) | (?? @ mu @ (^[Y1 : mu]: (X1 @ Y1 @ Y0))))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f194])). 0.20/0.42 thf(f194,plain,( 0.20/0.42 ( ! [X0 : $i,X1 : mu > $i > $o] : ((((^[Y0 : mu > $i > $o]: ((essence @ Y0 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ (sK2 @ X0) @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f193])). 0.20/0.42 thf(f193,plain,( 0.20/0.42 ( ! [X0 : $i] : (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((essence @ Y0 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ (sK2 @ X0) @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))))) = $true)) )), 0.20/0.42 inference(boolean_simplification,[],[f192])). 0.20/0.42 thf(f192,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => (!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((essence @ Y0 @ (sK3 @ X0) @ (sK2 @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((~ (rel @ (sK2 @ X0) @ Y1)) | (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f191])). 0.20/0.42 thf(f191,plain,( 0.20/0.42 ( ! [X0 : $i] : ((($true => ((^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((essence @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y1 @ Y3)) | (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ (sK3 @ X0) @ (sK2 @ X0))) = $true)) )), 0.20/0.42 inference(superposition,[],[f154,f190])). 0.20/0.42 thf(f190,plain,( 0.20/0.42 ( ! [X1 : $i] : (((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((essence @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y1 @ Y3)) | (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ X1) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f131])). 0.20/0.42 thf(f131,plain,( 0.20/0.42 ((!! @ $i @ (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((essence @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((~ (rel @ Y1 @ Y3)) | (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))))) = $true)), 0.20/0.42 inference(beta_eta_normalization,[],[f126])). 0.20/0.42 thf(f126,plain,( 0.20/0.42 ($true = ((^[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))))))) @ (essence @ Y1 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ rel @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: (Y1 @ Y2)))))))))))), 0.20/0.42 inference(definition_unfolding,[],[f104,f115,f123])). 0.20/0.42 thf(f123,plain,( 0.20/0.42 (necessary_existence = (^[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))))))) @ (essence @ Y1 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ rel @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: (Y1 @ Y2)))))))))), 0.20/0.42 inference(definition_unfolding,[],[f118,f113,f90,f120,f97])). 0.20/0.42 thf(f118,plain,( 0.20/0.42 (necessary_existence = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (essence @ Y1 @ Y0) @ (mbox @ (mexists_ind @ (^[Y2 : mu]: (Y1 @ Y2)))))))))), 0.20/0.42 inference(cnf_transformation,[],[f66])). 0.20/0.42 thf(f66,plain,( 0.20/0.42 (necessary_existence = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (essence @ Y1 @ Y0) @ (mbox @ (mexists_ind @ (^[Y2 : mu]: (Y1 @ Y2)))))))))), 0.20/0.42 inference(fool_elimination,[],[f65])). 0.20/0.42 thf(f65,plain,( 0.20/0.42 ((^[X0 : mu] : (mforall_indset @ (^[X1 : mu > $i > $o] : (mimplies @ (essence @ X1 @ X0) @ (mbox @ (mexists_ind @ (^[X2 : mu] : (X1 @ X2)))))))) = necessary_existence)), 0.20/0.42 inference(rectify,[],[f26])). 0.20/0.42 thf(f26,axiom,( 0.20/0.42 ((^[X0 : mu] : (mforall_indset @ (^[X3 : mu > $i > $o] : (mimplies @ (essence @ X3 @ X0) @ (mbox @ (mexists_ind @ (^[X1 : mu] : (X3 @ X1)))))))) = necessary_existence)), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',defD3)). 0.20/0.42 thf(f104,plain,( 0.20/0.42 ((mvalid @ (positive @ necessary_existence)) = $true)), 0.20/0.42 inference(cnf_transformation,[],[f48])). 0.20/0.42 thf(f48,plain,( 0.20/0.42 ((mvalid @ (positive @ necessary_existence)) = $true)), 0.20/0.42 inference(fool_elimination,[],[f47])). 0.20/0.42 thf(f47,plain,( 0.20/0.42 (mvalid @ (positive @ necessary_existence))), 0.20/0.42 inference(rectify,[],[f31])). 0.20/0.42 thf(f31,axiom,( 0.20/0.42 (mvalid @ (positive @ necessary_existence))), 0.20/0.42 file('/export/starexec/sandbox/tmp/tmp.5Zki7DWx3W/E---3.1_8583.p',axA5)). 0.20/0.42 thf(f154,plain,( 0.20/0.42 ( ! [X2 : mu > $i > $o,X1 : $i] : ((((positive @ X2 @ (sK2 @ X1)) => (X2 @ (sK3 @ X1) @ (sK2 @ X1))) = $true)) )), 0.20/0.42 inference(beta_eta_normalization,[],[f153])). 0.20/0.42 thf(f153,plain,( 0.20/0.42 ( ! [X2 : mu > $i > $o,X1 : $i] : ((((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ (sK2 @ X1)) => (Y0 @ (sK3 @ X1) @ (sK2 @ X1)))) @ X2) = $true)) )), 0.20/0.42 inference(pi_clausification,[],[f148])). 0.20/0.42 % SZS output end Proof for E---3.1_8583 0.20/0.42 % (8704)------------------------------ 0.20/0.42 % (8704)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.20/0.42 % (8704)Termination reason: Refutation 0.20/0.42 0.20/0.42 % (8704)Memory used [KB]: 5884 0.20/0.42 % (8704)Time elapsed: 0.021 s 0.20/0.42 % (8704)Instructions burned: 30 (million) 0.20/0.42 % (8704)------------------------------ 0.20/0.42 % (8704)------------------------------ 0.20/0.42 % (8691)Success in time 0.052 s 0.20/0.42 EOF