0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.03	% Command    : run_vampire %s %d THM
0.07/0.34	% Computer   : n010.cluster.edu
0.07/0.34	% Model      : x86_64 x86_64
0.07/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.07/0.34	% Memory     : 8046.5625MB
0.07/0.34	% OS         : Linux 6.8.0-71-generic
0.07/0.34	% CPULimit   : 1440
0.07/0.34	% WCLimit    : 180
0.07/0.34	% DateTime   : Mon Jul 27 09:50:49 UTC 2026
0.07/0.34	% CPUTime    : 
0.13/0.37	This is a THF_ problem
0.13/0.37	Running higher-order theorem proving
0.13/0.39	Running /export/starexec/sandbox2/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/sandbox2/tmp/tmp.5WNS1tjDqG/E---3.1_963930.p -m 16384 -t 180
0.13/0.41	% (963978)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_963930 for (1799ds/2Mi)
0.13/0.41	% (963978)Instruction limit reached!
0.13/0.41	% (963978)------------------------------
0.13/0.41	% (963978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.41	% (963978)Termination reason: Unknown
0.13/0.41	% (963978)Termination phase: Saturation
0.13/0.41	
0.13/0.41	% (963978)Memory used [KB]: 5500
0.13/0.41	% (963978)Time elapsed: 0.003 s
0.13/0.41	% (963978)Instructions burned: 3 (million)
0.13/0.41	% (963978)------------------------------
0.13/0.41	% (963978)------------------------------
0.13/0.42	% (963974)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_963930 for (1799ds/183Mi)
0.13/0.42	% (963975)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_963930 for (1799ds/4Mi)
0.13/0.42	% (963976)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_963930 for (1799ds/27Mi)
0.13/0.42	% (963977)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_963930 for (1799ds/2Mi)
0.13/0.42	% (963979)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_963930 for (1799ds/275Mi)
0.13/0.42	% (963980)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_963930 for (1799ds/18Mi)
0.13/0.42	% (963977)Instruction limit reached!
0.13/0.42	% (963977)------------------------------
0.13/0.42	% (963977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.42	% (963977)Termination reason: Unknown
0.13/0.42	% (963977)Termination phase: Saturation
0.13/0.42	
0.13/0.42	% (963977)Memory used [KB]: 5500
0.13/0.42	% (963977)Time elapsed: 0.004 s
0.13/0.42	% (963977)Instructions burned: 2 (million)
0.13/0.42	% (963977)------------------------------
0.13/0.42	% (963977)------------------------------
0.13/0.42	% (963975)Instruction limit reached!
0.13/0.42	% (963975)------------------------------
0.13/0.42	% (963975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.42	% (963975)Termination reason: Unknown
0.13/0.42	% (963975)Termination phase: Saturation
0.13/0.42	
0.13/0.42	% (963975)Memory used [KB]: 5500
0.13/0.42	% (963975)Time elapsed: 0.005 s
0.13/0.42	% (963975)Instructions burned: 4 (million)
0.13/0.42	% (963975)------------------------------
0.13/0.42	% (963975)------------------------------
0.13/0.42	% (963981)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_963930 for (1799ds/3Mi)
0.13/0.42	% (963981)Instruction limit reached!
0.13/0.42	% (963981)------------------------------
0.13/0.42	% (963981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.42	% (963981)Termination reason: Unknown
0.13/0.42	% (963981)Termination phase: Saturation
0.13/0.42	
0.13/0.42	% (963981)Memory used [KB]: 5500
0.13/0.42	% (963981)Time elapsed: 0.002 s
0.13/0.42	% (963981)Instructions burned: 3 (million)
0.13/0.42	% (963981)------------------------------
0.13/0.42	% (963981)------------------------------
0.13/0.43	% (963980)Instruction limit reached!
0.13/0.43	% (963980)------------------------------
0.13/0.43	% (963980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.43	% (963980)Termination reason: Unknown
0.13/0.43	% (963980)Termination phase: Saturation
0.13/0.43	
0.13/0.43	% (963980)Memory used [KB]: 5628
0.13/0.43	% (963980)Time elapsed: 0.014 s
0.13/0.43	% (963980)Instructions burned: 19 (million)
0.13/0.43	% (963980)------------------------------
0.13/0.43	% (963980)------------------------------
0.13/0.43	% (963984)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_963930 for (1799ds/3Mi)
0.13/0.43	% (963984)Instruction limit reached!
0.13/0.43	% (963984)------------------------------
0.13/0.43	% (963984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.43	% (963984)Termination reason: Unknown
0.13/0.43	% (963984)Termination phase: Saturation
0.13/0.43	
0.13/0.43	% (963984)Memory used [KB]: 5500
0.13/0.43	% (963984)Time elapsed: 0.002 s
0.13/0.43	% (963984)Instructions burned: 3 (million)
0.13/0.43	% (963984)------------------------------
0.13/0.43	% (963984)------------------------------
0.13/0.44	% (963976)Instruction limit reached!
0.13/0.44	% (963976)------------------------------
0.13/0.44	% (963976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.44	% (963976)Termination reason: Unknown
0.13/0.44	% (963976)Termination phase: Saturation
0.13/0.44	
0.13/0.44	% (963976)Memory used [KB]: 5628
0.13/0.44	% (963976)Time elapsed: 0.020 s
0.13/0.44	% (963976)Instructions burned: 28 (million)
0.13/0.44	% (963976)------------------------------
0.13/0.44	% (963976)------------------------------
0.13/0.44	% (963982)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_963930 for (1799ds/37Mi)
0.13/0.44	% (963983)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_963930 for (1799ds/15Mi)
0.13/0.44	% (963986)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_963930 for (1799ds/7Mi)
0.13/0.45	% (963974)First to succeed.
0.13/0.45	% (963986)Instruction limit reached!
0.13/0.45	% (963986)------------------------------
0.13/0.45	% (963986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.45	% (963986)Termination reason: Unknown
0.13/0.45	% (963986)Termination phase: Saturation
0.13/0.45	
0.13/0.45	% (963986)Memory used [KB]: 1023
0.13/0.45	% (963986)Time elapsed: 0.004 s
0.13/0.45	% (963986)Instructions burned: 8 (million)
0.13/0.45	% (963986)------------------------------
0.13/0.45	% (963986)------------------------------
0.13/0.45	% (963983)Instruction limit reached!
0.13/0.45	% (963983)------------------------------
0.13/0.45	% (963983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.45	% (963983)Termination reason: Unknown
0.13/0.45	% (963983)Termination phase: Saturation
0.13/0.45	% (963985)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_963930 for (1799ds/1041Mi)
0.13/0.45	
0.13/0.45	% (963983)Memory used [KB]: 5628
0.13/0.45	% (963983)Time elapsed: 0.012 s
0.13/0.45	% (963983)Instructions burned: 15 (million)
0.13/0.45	% (963983)------------------------------
0.13/0.45	% (963983)------------------------------
0.13/0.45	% (963974)Refutation found. Thanks to Tanya!
0.13/0.45	% SZS status Theorem for E---3.1_963930
0.13/0.45	% SZS output start Proof for E---3.1_963930
0.13/0.45	thf(func_def_0, type, cHALF: $i > $i > $o).
0.13/0.45	thf(func_def_1, type, cDOUBLE: $i > $i > $o).
0.13/0.45	thf(func_def_2, type, cS: $i > $i).
0.13/0.45	thf(func_def_7, type, sK0: ($i > $i > $o) > $i).
0.13/0.45	thf(func_def_8, type, sK1: ($i > $i > $o) > $i).
0.13/0.45	thf(func_def_13, type, ph5: !>[X0: $tType]:(X0)).
0.13/0.45	thf(f239,plain,(
0.13/0.45	  $false),
0.13/0.45	  inference(avatar_sat_refutation,[status(thm)],[f129,f219,f236])).
0.13/0.45	thf(f236,plain,(
0.13/0.45	  ~spl4_5),
0.13/0.45	  inference(avatar_contradiction_clause,[status(thm)],[f235])).
0.13/0.45	thf(f235,plain,(
0.13/0.45	  $false | ~spl4_5),
0.13/0.45	  inference(subsumption_resolution,[status(thm)],[f231,f15])).
0.13/0.45	thf(f15,plain,(
0.13/0.45	  ((cDOUBLE @ sK2 @ sK3) = $true)),
0.13/0.45	  inference(cnf_transformation,[status(thm)],[f11])).
0.13/0.45	thf(f11,plain,(
0.13/0.45	  ! [X0 : $i,X1 : $i > $i > $o,X2 : $i] : (((X1 @ c0 @ c0) != $true) | ((X1 @ X0 @ X2) = $true) | ((cDOUBLE @ X0 @ X2) != $true) | (((X1 @ (sK1 @ X1) @ (sK0 @ X1)) = $true) & ((X1 @ (cS @ (sK1 @ X1)) @ (cS @ (cS @ (sK0 @ X1)))) != $true))) & (((cHALF @ sK3 @ sK2) != $true) & ((cDOUBLE @ sK2 @ sK3) = $true)) & ((cHALF @ c0 @ c0) = $true) & ! [X7 : $i,X8 : $i] : (((cHALF @ (cS @ (cS @ X8)) @ (cS @ X7)) = $true) | ((cHALF @ X8 @ X7) != $true)) & ((cHALF @ (cS @ c0) @ c0) = $true)),
0.13/0.45	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f10,f9])).
0.13/0.45	thf(f9,plain,(
0.13/0.45	  ! [X1 : $i > $i > $o] : (? [X3 : $i,X4 : $i] : (((X1 @ X4 @ X3) = $true) & ((X1 @ (cS @ X4) @ (cS @ (cS @ X3))) != $true)) => (((X1 @ (sK1 @ X1) @ (sK0 @ X1)) = $true) & ((X1 @ (cS @ (sK1 @ X1)) @ (cS @ (cS @ (sK0 @ X1)))) != $true)))),
0.13/0.45	  introduced(definition,[],[choice_axiom])).
0.13/0.45	thf(f10,plain,(
0.13/0.45	  ? [X5 : $i,X6 : $i] : (((cHALF @ X6 @ X5) != $true) & ((cDOUBLE @ X5 @ X6) = $true)) => (((cHALF @ sK3 @ sK2) != $true) & ((cDOUBLE @ sK2 @ sK3) = $true))),
0.13/0.45	  introduced(definition,[],[choice_axiom])).
0.13/0.45	thf(f8,plain,(
0.13/0.45	  ! [X0 : $i,X1 : $i > $i > $o,X2 : $i] : (((X1 @ c0 @ c0) != $true) | ((X1 @ X0 @ X2) = $true) | ((cDOUBLE @ X0 @ X2) != $true) | ? [X3 : $i,X4 : $i] : (((X1 @ X4 @ X3) = $true) & ((X1 @ (cS @ X4) @ (cS @ (cS @ X3))) != $true))) & ? [X5 : $i,X6 : $i] : (((cHALF @ X6 @ X5) != $true) & ((cDOUBLE @ X5 @ X6) = $true)) & ((cHALF @ c0 @ c0) = $true) & ! [X7 : $i,X8 : $i] : (((cHALF @ (cS @ (cS @ X8)) @ (cS @ X7)) = $true) | ((cHALF @ X8 @ X7) != $true)) & ((cHALF @ (cS @ c0) @ c0) = $true)),
0.13/0.45	  inference(rectify,[status(thm)],[f7])).
0.13/0.45	thf(f7,plain,(
0.13/0.45	  ! [X3 : $i,X2 : $i > $i > $o,X4 : $i] : (($true != (X2 @ c0 @ c0)) | ((X2 @ X3 @ X4) = $true) | ((cDOUBLE @ X3 @ X4) != $true) | ? [X6 : $i,X5 : $i] : (((X2 @ X5 @ X6) = $true) & ((X2 @ (cS @ X5) @ (cS @ (cS @ X6))) != $true))) & ? [X8 : $i,X7 : $i] : (((cHALF @ X7 @ X8) != $true) & ((cDOUBLE @ X8 @ X7) = $true)) & ((cHALF @ c0 @ c0) = $true) & ! [X0 : $i,X1 : $i] : (((cHALF @ (cS @ (cS @ X1)) @ (cS @ X0)) = $true) | ((cHALF @ X1 @ X0) != $true)) & ((cHALF @ (cS @ c0) @ c0) = $true)),
0.13/0.45	  inference(flattening,[status(thm)],[f6])).
0.13/0.45	thf(f6,plain,(
0.13/0.45	  ? [X8 : $i,X7 : $i] : (((cHALF @ X7 @ X8) != $true) & ((cDOUBLE @ X8 @ X7) = $true)) & (! [X0 : $i,X1 : $i] : (((cHALF @ (cS @ (cS @ X1)) @ (cS @ X0)) = $true) | ((cHALF @ X1 @ X0) != $true)) & ((cHALF @ (cS @ c0) @ c0) = $true) & ((cHALF @ c0 @ c0) = $true) & ! [X3 : $i,X4 : $i,X2 : $i > $i > $o] : (((X2 @ X3 @ X4) = $true) | (($true != (X2 @ c0 @ c0)) | ((cDOUBLE @ X3 @ X4) != $true) | ? [X6 : $i,X5 : $i] : (((X2 @ X5 @ X6) = $true) & ((X2 @ (cS @ X5) @ (cS @ (cS @ X6))) != $true)))))),
0.13/0.45	  inference(ennf_transformation,[status(thm)],[f5])).
0.13/0.45	thf(f5,plain,(
0.13/0.45	  ~((! [X1 : $i,X0 : $i] : (((cHALF @ X1 @ X0) = $true) => ((cHALF @ (cS @ (cS @ X1)) @ (cS @ X0)) = $true)) & ((cHALF @ (cS @ c0) @ c0) = $true) & ((cHALF @ c0 @ c0) = $true) & ! [X3 : $i,X4 : $i,X2 : $i > $i > $o] : ((($true = (X2 @ c0 @ c0)) & ((cDOUBLE @ X3 @ X4) = $true) & ! [X5 : $i,X6 : $i] : (((X2 @ X5 @ X6) = $true) => ((X2 @ (cS @ X5) @ (cS @ (cS @ X6))) = $true))) => ((X2 @ X3 @ X4) = $true))) => ! [X8 : $i,X7 : $i] : (((cDOUBLE @ X8 @ X7) = $true) => ((cHALF @ X7 @ X8) = $true)))),
0.13/0.45	  inference(fool_elimination,[status(thm)],[f4])).
0.13/0.45	thf(f4,plain,(
0.13/0.45	  ~((! [X0 : $i,X1 : $i] : ((cHALF @ X1 @ X0) => (cHALF @ (cS @ (cS @ X1)) @ (cS @ X0))) & (cHALF @ c0 @ c0) & ! [X2 : $i > $i > $o,X3 : $i,X4 : $i] : (((X2 @ c0 @ c0) & ! [X5 : $i,X6 : $i] : ((X2 @ X5 @ X6) => (X2 @ (cS @ X5) @ (cS @ (cS @ X6)))) & (cDOUBLE @ X3 @ X4)) => (X2 @ X3 @ X4)) & (cHALF @ (cS @ c0) @ c0)) => ! [X7 : $i,X8 : $i] : ((cDOUBLE @ X8 @ X7) => (cHALF @ X7 @ X8)))),
0.13/0.45	  inference(rectify,[status(thm)],[f2])).
0.13/0.45	thf(f2,negated_conjecture,(
0.13/0.45	  ~((! [X3 : $i,X2 : $i] : ((cHALF @ X2 @ X3) => (cHALF @ (cS @ (cS @ X2)) @ (cS @ X3))) & (cHALF @ c0 @ c0) & ! [X4 : $i > $i > $o,X0 : $i,X1 : $i] : (((X4 @ c0 @ c0) & ! [X2 : $i,X3 : $i] : ((X4 @ X2 @ X3) => (X4 @ (cS @ X2) @ (cS @ (cS @ X3)))) & (cDOUBLE @ X0 @ X1)) => (X4 @ X0 @ X1)) & (cHALF @ (cS @ c0) @ c0)) => ! [X1 : $i,X0 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0)))),
0.13/0.45	  inference(negated_conjecture,[status(cth)],[f1])).
0.13/0.45	thf(f1,conjecture,(
0.13/0.45	  (! [X3 : $i,X2 : $i] : ((cHALF @ X2 @ X3) => (cHALF @ (cS @ (cS @ X2)) @ (cS @ X3))) & (cHALF @ c0 @ c0) & ! [X4 : $i > $i > $o,X0 : $i,X1 : $i] : (((X4 @ c0 @ c0) & ! [X2 : $i,X3 : $i] : ((X4 @ X2 @ X3) => (X4 @ (cS @ X2) @ (cS @ (cS @ X3)))) & (cDOUBLE @ X0 @ X1)) => (X4 @ X0 @ X1)) & (cHALF @ (cS @ c0) @ c0)) => ! [X1 : $i,X0 : $i] : ((cDOUBLE @ X0 @ X1) => (cHALF @ X1 @ X0))),
0.13/0.45	  file('/export/starexec/sandbox2/tmp/tmp.5WNS1tjDqG/E---3.1_963930.p',cTHM301)).
0.13/0.45	thf(f231,plain,(
0.13/0.45	  ((cDOUBLE @ sK2 @ sK3) != $true) | ~spl4_5),
0.13/0.45	  inference(trivial_inequality_removal,[status(thm)],[f223])).
0.13/0.45	thf(f223,plain,(
0.13/0.45	  ((cDOUBLE @ sK2 @ sK3) != $true) | ($true != $true) | ~spl4_5),
0.13/0.45	  inference(superposition,[status(thm)],[f16,f124])).
0.13/0.45	thf(f124,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) = $true) | ((cDOUBLE @ X0 @ X1) != $true)) ) | ~spl4_5),
0.13/0.45	  inference(avatar_component_clause,[status(thm)],[f123])).
0.13/0.45	thf(f123,definition,(
0.13/0.45	  spl4_5 <=> ! [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) = $true) | ((cDOUBLE @ X0 @ X1) != $true))),
0.13/0.45	  introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
0.13/0.45	thf(f16,plain,(
0.13/0.45	  ((cHALF @ sK3 @ sK2) != $true)),
0.13/0.45	  inference(cnf_transformation,[status(thm)],[f11])).
0.13/0.45	thf(f219,plain,(
0.13/0.45	  spl4_5 | spl4_6),
0.13/0.45	  inference(avatar_split_clause,[status(thm)],[f218,f126,f123])).
0.13/0.45	thf(f126,definition,(
0.13/0.45	  spl4_6 <=> ((cHALF @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) = $true)),
0.13/0.45	  introduced(definition,[new_symbols(naming,[spl4_6])],[avatar_definition])).
0.13/0.45	thf(f218,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ X1 @ X0) = $true)) ) | spl4_6),
0.13/0.45	  inference(subsumption_resolution,[status(thm)],[f216,f14])).
0.13/0.45	thf(f14,plain,(
0.13/0.45	  ((cHALF @ c0 @ c0) = $true)),
0.13/0.45	  inference(cnf_transformation,[status(thm)],[f11])).
0.13/0.45	thf(f216,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ X1 @ X0) = $true) | ((cHALF @ c0 @ c0) != $true)) ) | spl4_6),
0.13/0.45	  inference(beta_eta_normalization,[status(thm)],[f215])).
0.13/0.45	thf(f215,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ((cDOUBLE @ X0 @ X1) != $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) ) | spl4_6),
0.13/0.45	  inference(trivial_inequality_removal,[status(thm)],[f214])).
0.13/0.45	thf(f214,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (((cDOUBLE @ X0 @ X1) != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0))) ) | spl4_6),
0.13/0.45	  inference(superposition,[status(thm)],[f128,f18])).
0.13/0.45	thf(f18,plain,(
0.13/0.45	  ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (((X1 @ (sK1 @ X1) @ (sK0 @ X1)) = $true) | ((X1 @ X0 @ X2) = $true) | ((X1 @ c0 @ c0) != $true) | ((cDOUBLE @ X0 @ X2) != $true)) )),
0.13/0.45	  inference(cnf_transformation,[status(thm)],[f11])).
0.13/0.45	thf(f128,plain,(
0.13/0.45	  ((cHALF @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) != $true) | spl4_6),
0.13/0.45	  inference(avatar_component_clause,[status(thm)],[f126])).
0.13/0.45	thf(f129,plain,(
0.13/0.45	  spl4_5 | ~spl4_6),
0.13/0.45	  inference(avatar_split_clause,[status(thm)],[f121,f126,f123])).
0.13/0.45	thf(f121,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (((cHALF @ X1 @ X0) = $true) | ((cHALF @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) != $true) | ((cDOUBLE @ X0 @ X1) != $true)) )),
0.13/0.45	  inference(subsumption_resolution,[status(thm)],[f87,f14])).
0.13/0.45	thf(f87,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (((cHALF @ c0 @ c0) != $true) | ((cHALF @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ Y1 @ Y0)))))) != $true) | ((cHALF @ X1 @ X0) = $true) | ((cDOUBLE @ X0 @ X1) != $true)) )),
0.13/0.45	  inference(beta_eta_normalization,[status(thm)],[f86])).
0.13/0.45	thf(f86,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0)) | ((cDOUBLE @ X0 @ X1) != $true) | ((cHALF @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) != $true)) )),
0.13/0.45	  inference(trivial_inequality_removal,[status(thm)],[f78])).
0.13/0.45	thf(f78,plain,(
0.13/0.45	  ( ! [X0 : $i,X1 : $i] : (($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ c0 @ c0)) | ((cDOUBLE @ X0 @ X1) != $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))) @ X0 @ X1) = $true) | ($true != $true) | ((cHALF @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1)))))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (cHALF @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))) @ Y0 @ Y1))))))) != $true)) )),
0.13/0.45	  inference(superposition,[status(thm)],[f17,f13])).
0.13/0.45	thf(f13,plain,(
0.13/0.45	  ( ! [X8 : $i,X7 : $i] : (((cHALF @ (cS @ (cS @ X8)) @ (cS @ X7)) = $true) | ((cHALF @ X8 @ X7) != $true)) )),
0.13/0.45	  inference(cnf_transformation,[status(thm)],[f11])).
0.13/0.45	thf(f17,plain,(
0.13/0.45	  ( ! [X2 : $i,X0 : $i,X1 : $i > $i > $o] : (((X1 @ (cS @ (sK1 @ X1)) @ (cS @ (cS @ (sK0 @ X1)))) != $true) | ((X1 @ X0 @ X2) = $true) | ((X1 @ c0 @ c0) != $true) | ((cDOUBLE @ X0 @ X2) != $true)) )),
0.13/0.45	  inference(cnf_transformation,[status(thm)],[f11])).
0.13/0.45	% SZS output end Proof for E---3.1_963930
0.13/0.45	% (963974)------------------------------
0.13/0.45	% (963974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.45	% (963974)Termination reason: Refutation
0.13/0.45	
0.13/0.45	% (963974)Memory used [KB]: 5756
0.13/0.45	% (963974)Time elapsed: 0.032 s
0.13/0.45	% (963974)Instructions burned: 44 (million)
0.13/0.45	% (963974)------------------------------
0.13/0.45	% (963974)------------------------------
0.13/0.45	% (963973)Success in time 0.042 s
0.13/0.45	EOF