0.03/0.10	% Problem    : Vampire---4.8_20489 : TPTP v0.0.0. Released v0.0.0.
0.03/0.11	% Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
0.11/0.31	% Computer : n012.cluster.edu
0.11/0.31	% Model    : x86_64 x86_64
0.11/0.31	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.31	% Memory   : 8042.1875MB
0.11/0.31	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.31	% CPULimit   : 1440
0.11/0.31	% WCLimit    : 180
0.11/0.31	% DateTime   : Mon Jul  3 13:04:22 EDT 2023
0.11/0.31	% CPUTime    : 
0.11/0.32	This is a THF_ problem
0.11/0.32	Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.CC7u0Zxb1z/Vampire---4.8_20489 -m 12000  -t 180
0.11/0.33	% (20599)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1800ds/36Mi)
0.11/0.33	% (20601)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1800ds/385Mi)
0.11/0.33	% (20603)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on Vampire---4 for (1800ds/74Mi)
0.11/0.33	% (20605)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1800ds/915Mi)
0.11/0.33	% (20604)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1800ds/4Mi)
0.11/0.33	% (20598)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1800ds/96Mi)
0.11/0.33	% (20602)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1800ds/17Mi)
0.11/0.33	% (20600)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1800ds/34Mi)
0.11/0.33	% (20605)Refutation not found, incomplete strategy
0.11/0.33	% (20605)------------------------------
0.11/0.33	% (20605)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.11/0.33	% (20605)Termination reason: Refutation not found, incomplete strategy
0.11/0.33	
0.11/0.33	
0.11/0.33	% (20605)Memory used [KB]: 5500
0.11/0.33	% (20605)Time elapsed: 0.002 s
0.11/0.33	% (20605)Instructions burned: 2 (million)
0.11/0.33	% (20605)------------------------------
0.11/0.33	% (20605)------------------------------
0.11/0.33	% (20604)Instruction limit reached!
0.11/0.33	% (20604)------------------------------
0.11/0.33	% (20604)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.11/0.33	% (20604)Termination reason: Unknown
0.11/0.34	% (20604)Termination phase: Saturation
0.11/0.34	
0.11/0.34	% (20604)Memory used [KB]: 5500
0.11/0.34	% (20604)Time elapsed: 0.003 s
0.11/0.34	% (20604)Instructions burned: 4 (million)
0.11/0.34	% (20604)------------------------------
0.11/0.34	% (20604)------------------------------
0.11/0.34	% (20599)Refutation not found, incomplete strategy
0.11/0.34	% (20599)------------------------------
0.11/0.34	% (20599)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.11/0.34	% (20599)Termination reason: Refutation not found, incomplete strategy
0.11/0.34	
0.11/0.34	
0.11/0.34	% (20599)Memory used [KB]: 5500
0.11/0.34	% (20599)Time elapsed: 0.005 s
0.11/0.34	% (20599)Instructions burned: 5 (million)
0.11/0.34	% (20599)------------------------------
0.11/0.34	% (20599)------------------------------
0.11/0.34	% (20602)Instruction limit reached!
0.11/0.34	% (20602)------------------------------
0.11/0.34	% (20602)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.11/0.34	% (20602)Termination reason: Unknown
0.11/0.34	% (20602)Termination phase: Saturation
0.11/0.34	
0.11/0.34	% (20602)Memory used [KB]: 5628
0.11/0.34	% (20602)Time elapsed: 0.010 s
0.11/0.34	% (20602)Instructions burned: 17 (million)
0.11/0.34	% (20602)------------------------------
0.11/0.34	% (20602)------------------------------
0.17/0.35	% (20601)First to succeed.
0.17/0.35	% (20606)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (1799ds/21Mi)
0.17/0.35	% (20607)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi)
0.17/0.35	% (20608)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (1799ds/1021Mi)
0.17/0.35	% (20601)Refutation found. Thanks to Tanya!
0.17/0.35	% SZS status Theorem for Vampire---4
0.17/0.35	% SZS output start Proof for Vampire---4
0.17/0.35	thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
0.17/0.35	thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
0.17/0.35	thf(func_def_2, type, cZERO: ($i > $o) > $o).
0.17/0.35	thf(func_def_16, type, sK0: ($i > $o) > $o).
0.17/0.35	thf(func_def_18, type, sK2: (($i > $o) > $o) > $o).
0.17/0.35	thf(func_def_19, type, sK3: ((($i > $o) > $o) > $o) > ($i > $o) > $o).
0.17/0.35	thf(func_def_20, type, ph4: !>[X0: $tType]:(X0)).
0.17/0.35	thf(func_def_21, type, sK5: ($i > $o) > $i).
0.17/0.35	thf(func_def_22, type, sK6: $i > $o).
0.17/0.35	thf(f303,plain,(
0.17/0.35	  $false),
0.17/0.35	  inference(avatar_sat_refutation,[],[f89,f251,f302])).
0.17/0.35	thf(f302,plain,(
0.17/0.35	  ~spl1_5),
0.17/0.35	  inference(avatar_contradiction_clause,[],[f301])).
0.17/0.35	thf(f301,plain,(
0.17/0.35	  $false | ~spl1_5),
0.17/0.35	  inference(trivial_inequality_removal,[],[f300])).
0.17/0.35	thf(f300,plain,(
0.17/0.35	  ($false = $true) | ~spl1_5),
0.17/0.35	  inference(backward_demodulation,[],[f31,f299])).
0.17/0.35	thf(f299,plain,(
0.17/0.35	  ($false = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl1_5),
0.17/0.35	  inference(trivial_inequality_removal,[],[f298])).
0.17/0.35	thf(f298,plain,(
0.17/0.35	  ($false = $true) | ($false = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl1_5),
0.17/0.35	  inference(forward_demodulation,[],[f297,f87])).
0.17/0.35	thf(f87,plain,(
0.17/0.35	  ((sK2 @ (sK3 @ sK2)) = $true) | ~spl1_5),
0.17/0.35	  inference(avatar_component_clause,[],[f85])).
0.17/0.35	thf(f85,plain,(
0.17/0.35	  spl1_5 <=> ((sK2 @ (sK3 @ sK2)) = $true)),
0.17/0.35	  introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
0.17/0.35	thf(f297,plain,(
0.17/0.35	  ($false = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($false = (sK2 @ (sK3 @ sK2)))),
0.17/0.35	  inference(trivial_inequality_removal,[],[f296])).
0.17/0.35	thf(f296,plain,(
0.17/0.35	  ($false = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($false = $true) | ($false = (sK2 @ (sK3 @ sK2)))),
0.17/0.35	  inference(forward_demodulation,[],[f284,f247])).
0.17/0.35	thf(f247,plain,(
0.17/0.35	  ($false = (sK2 @ sK0))),
0.17/0.35	  inference(trivial_inequality_removal,[],[f241])).
0.17/0.35	thf(f241,plain,(
0.17/0.35	  ($false = $true) | ($false = (sK2 @ sK0))),
0.17/0.35	  inference(superposition,[],[f35,f29])).
0.17/0.35	thf(f29,plain,(
0.17/0.35	  ((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))) = $false)),
0.17/0.35	  inference(binary_proxy_clausification,[],[f28])).
0.17/0.35	thf(f28,plain,(
0.17/0.35	  ($false = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))))),
0.17/0.35	  inference(beta_eta_normalization,[],[f27])).
0.17/0.35	thf(f27,plain,(
0.17/0.35	  ($false = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ sK2))),
0.17/0.35	  inference(sigma_clausification,[],[f26])).
0.17/0.35	thf(f26,plain,(
0.17/0.35	  ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) != $true)),
0.17/0.35	  inference(beta_eta_normalization,[],[f24])).
0.17/0.35	thf(f24,plain,(
0.17/0.35	  (((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))) @ sK0)) != $true)),
0.17/0.35	  inference(definition_unfolding,[],[f21,f23,f19])).
0.17/0.35	thf(f19,plain,(
0.17/0.35	  (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
0.17/0.35	  inference(cnf_transformation,[],[f14])).
0.17/0.35	thf(f14,plain,(
0.17/0.35	  (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))),
0.17/0.35	  inference(fool_elimination,[],[f13])).
0.17/0.35	thf(f13,plain,(
0.17/0.35	  ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3)))) & (X1 @ X2)))) = cSUCC)),
0.17/0.35	  inference(rectify,[],[f2])).
0.17/0.35	thf(f2,axiom,(
0.17/0.35	  ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3)))) & (X0 @ X1)))) = cSUCC)),
0.17/0.35	  file('/export/starexec/sandbox/tmp/tmp.CC7u0Zxb1z/Vampire---4.8_20489',cSUCC_def)).
0.17/0.35	thf(f23,plain,(
0.17/0.35	  (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
0.17/0.35	  inference(definition_unfolding,[],[f22,f19,f18])).
0.17/0.35	thf(f18,plain,(
0.17/0.35	  (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
0.17/0.35	  inference(cnf_transformation,[],[f12])).
0.17/0.35	thf(f12,plain,(
0.17/0.35	  (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
0.17/0.35	  inference(fool_elimination,[],[f11])).
0.17/0.35	thf(f11,plain,(
0.17/0.35	  ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
0.17/0.35	  inference(rectify,[],[f1])).
0.17/0.35	thf(f1,axiom,(
0.17/0.35	  ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
0.17/0.35	  file('/export/starexec/sandbox/tmp/tmp.CC7u0Zxb1z/Vampire---4.8_20489',cZERO_def)).
0.17/0.35	thf(f22,plain,(
0.17/0.35	  (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
0.17/0.35	  inference(cnf_transformation,[],[f10])).
0.17/0.35	thf(f10,plain,(
0.17/0.35	  (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
0.17/0.35	  inference(fool_elimination,[],[f9])).
0.17/0.35	thf(f9,plain,(
0.17/0.35	  ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))) = cNAT)),
0.17/0.35	  inference(rectify,[],[f3])).
0.17/0.35	thf(f3,axiom,(
0.17/0.35	  ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))) = cNAT)),
0.17/0.35	  file('/export/starexec/sandbox/tmp/tmp.CC7u0Zxb1z/Vampire---4.8_20489',cNAT_def)).
0.17/0.35	thf(f21,plain,(
0.17/0.35	  ((cNAT @ (cSUCC @ sK0)) != $true)),
0.17/0.35	  inference(cnf_transformation,[],[f17])).
0.17/0.35	thf(f17,plain,(
0.17/0.35	  ((cNAT @ (cSUCC @ sK0)) != $true) & ((cNAT @ sK0) = $true)),
0.17/0.35	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16])).
0.17/0.35	thf(f16,plain,(
0.17/0.35	  ? [X0 : ($i > $o) > $o] : (((cNAT @ (cSUCC @ X0)) != $true) & ((cNAT @ X0) = $true)) => (((cNAT @ (cSUCC @ sK0)) != $true) & ((cNAT @ sK0) = $true))),
0.17/0.35	  introduced(choice_axiom,[])).
0.17/0.35	thf(f15,plain,(
0.17/0.35	  ? [X0 : ($i > $o) > $o] : (((cNAT @ (cSUCC @ X0)) != $true) & ((cNAT @ X0) = $true))),
0.17/0.35	  inference(ennf_transformation,[],[f8])).
0.17/0.35	thf(f8,plain,(
0.17/0.35	  ~! [X0 : ($i > $o) > $o] : (((cNAT @ X0) = $true) => ((cNAT @ (cSUCC @ X0)) = $true))),
0.17/0.35	  inference(fool_elimination,[],[f7])).
0.17/0.35	thf(f7,plain,(
0.17/0.35	  ~! [X0 : ($i > $o) > $o] : ((cNAT @ X0) => (cNAT @ (cSUCC @ X0)))),
0.17/0.35	  inference(rectify,[],[f5])).
0.17/0.35	thf(f5,negated_conjecture,(
0.17/0.35	  ~! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
0.17/0.35	  inference(negated_conjecture,[],[f4])).
0.17/0.35	thf(f4,conjecture,(
0.17/0.35	  ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
0.17/0.35	  file('/export/starexec/sandbox/tmp/tmp.CC7u0Zxb1z/Vampire---4.8_20489',cTTTP6101)).
0.17/0.35	thf(f35,plain,(
0.17/0.35	  ( ! [X1 : ($i > $o) > $o] : (((sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))) = $true) | ((sK2 @ X1) = $false)) )),
0.17/0.35	  inference(binary_proxy_clausification,[],[f34])).
0.17/0.35	thf(f34,plain,(
0.17/0.35	  ( ! [X1 : ($i > $o) > $o] : (($true = ((sK2 @ X1) => (sK2 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))))))))))) )),
0.17/0.35	  inference(beta_eta_normalization,[],[f33])).
0.17/0.35	thf(f33,plain,(
0.17/0.35	  ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ X1))) )),
0.17/0.35	  inference(pi_clausification,[],[f32])).
0.17/0.35	thf(f32,plain,(
0.17/0.35	  ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $true)),
0.17/0.35	  inference(binary_proxy_clausification,[],[f30])).
0.17/0.35	thf(f30,plain,(
0.17/0.35	  (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK2 @ Y0) => (sK2 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) = $true)),
0.17/0.35	  inference(binary_proxy_clausification,[],[f28])).
0.17/0.35	thf(f284,plain,(
0.17/0.35	  ((sK2 @ sK0) = $true) | ($false = (sK2 @ (sK3 @ sK2))) | ($false = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
0.17/0.35	  inference(trivial_inequality_removal,[],[f282])).
0.17/0.35	thf(f282,plain,(
0.17/0.35	  ($false = (sK2 @ (sK3 @ sK2))) | ($false = $true) | ((sK2 @ sK0) = $true) | ($false = (sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
0.17/0.35	  inference(superposition,[],[f35,f43])).
0.17/0.35	thf(f43,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK3 @ X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))) = $false) | ((X1 @ sK0) = $true) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
0.17/0.35	  inference(binary_proxy_clausification,[],[f42])).
0.17/0.35	thf(f42,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : (($false = ((X1 @ (sK3 @ X1)) => (X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK3 @ X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2)))))))))))) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ((X1 @ sK0) = $true)) )),
0.17/0.35	  inference(beta_eta_normalization,[],[f41])).
0.17/0.35	thf(f41,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : ((((^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3)))))))))))) @ (sK3 @ X1)) = $false) | ((X1 @ sK0) = $true) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
0.17/0.35	  inference(sigma_clausification,[],[f40])).
0.17/0.35	thf(f40,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ sK0) = $true) | ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) = $false) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
0.17/0.35	  inference(binary_proxy_clausification,[],[f39])).
0.17/0.35	thf(f39,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : (($false = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ((X1 @ sK0) = $true)) )),
0.17/0.35	  inference(binary_proxy_clausification,[],[f38])).
0.17/0.35	thf(f38,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : (((((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK0)) = $true)) )),
0.17/0.35	  inference(beta_eta_normalization,[],[f37])).
0.17/0.35	thf(f37,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : ((((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK0))) @ X1) = $true)) )),
0.17/0.35	  inference(pi_clausification,[],[f36])).
0.17/0.35	thf(f36,plain,(
0.17/0.35	  ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK0)))) = $true)),
0.17/0.35	  inference(beta_eta_normalization,[],[f25])).
0.17/0.35	thf(f25,plain,(
0.17/0.35	  (((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ sK0) = $true)),
0.17/0.35	  inference(definition_unfolding,[],[f20,f23])).
0.17/0.35	thf(f20,plain,(
0.17/0.35	  ((cNAT @ sK0) = $true)),
0.17/0.35	  inference(cnf_transformation,[],[f17])).
0.17/0.35	thf(f31,plain,(
0.17/0.35	  ((sK2 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $true)),
0.17/0.35	  inference(binary_proxy_clausification,[],[f30])).
0.17/0.35	thf(f251,plain,(
0.17/0.35	  ~spl1_4),
0.17/0.35	  inference(avatar_contradiction_clause,[],[f250])).
0.17/0.35	thf(f250,plain,(
0.17/0.35	  $false | ~spl1_4),
0.17/0.35	  inference(trivial_inequality_removal,[],[f249])).
0.17/0.35	thf(f249,plain,(
0.17/0.35	  ($false = $true) | ~spl1_4),
0.17/0.35	  inference(backward_demodulation,[],[f83,f247])).
0.17/0.35	thf(f83,plain,(
0.17/0.35	  ((sK2 @ sK0) = $true) | ~spl1_4),
0.17/0.35	  inference(avatar_component_clause,[],[f81])).
0.17/0.35	thf(f81,plain,(
0.17/0.35	  spl1_4 <=> ((sK2 @ sK0) = $true)),
0.17/0.35	  introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
0.17/0.35	thf(f89,plain,(
0.17/0.35	  spl1_5 | spl1_4),
0.17/0.35	  inference(avatar_split_clause,[],[f78,f81,f85])).
0.17/0.35	thf(f78,plain,(
0.17/0.35	  ((sK2 @ sK0) = $true) | ((sK2 @ (sK3 @ sK2)) = $true)),
0.17/0.35	  inference(trivial_inequality_removal,[],[f77])).
0.17/0.35	thf(f77,plain,(
0.17/0.35	  ($false = $true) | ((sK2 @ sK0) = $true) | ((sK2 @ (sK3 @ sK2)) = $true)),
0.17/0.35	  inference(superposition,[],[f44,f31])).
0.17/0.35	thf(f44,plain,(
0.17/0.35	  ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ((X1 @ sK0) = $true) | ((X1 @ (sK3 @ X1)) = $true)) )),
0.17/0.35	  inference(binary_proxy_clausification,[],[f42])).
0.17/0.35	% SZS output end Proof for Vampire---4
0.17/0.35	% (20601)------------------------------
0.17/0.35	% (20601)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100)
0.17/0.35	% (20601)Termination reason: Refutation
0.17/0.35	
0.17/0.35	% (20601)Memory used [KB]: 5628
0.17/0.35	% (20601)Time elapsed: 0.018 s
0.17/0.35	% (20601)Instructions burned: 26 (million)
0.17/0.35	% (20601)------------------------------
0.17/0.35	% (20601)------------------------------
0.17/0.35	% (20597)Success in time 0.028 s
0.17/0.35	% Vampire---4.8 exiting
0.17/0.35	EOF