0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.09/0.36	% Computer : n017.cluster.edu
0.09/0.36	% Model    : x86_64 x86_64
0.09/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.36	% Memory   : 8046.5625MB
0.09/0.36	% OS       : Linux 6.8.0-71-generic
0.09/0.36	% CPULimit : 1440
0.09/0.36	% WCLimit  : 180
0.09/0.36	% DateTime : Mon Jul 27 11:17:07 UTC 2026
0.09/0.36	% CPUTime  : 
0.09/0.37	Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.09/0.39	Running higher-order theorem proving
0.09/0.41	Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox2/benchmark/theBenchmark.p
0.09/0.45	% (1301996)Detected a higher-order problem, will run a greedy HOL sequence.
0.09/0.45	% (1302001)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1571494121:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.09/0.45	% (1302001) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1301996-1302001"...
0.09/0.45	% (1302001)...printing done.
0.09/0.45	% (1302001)Refutation found. Thanks to Tanya!
0.09/0.45	% SZS status Theorem for theBenchmark
0.09/0.45	% SZS output start Proof for theBenchmark
0.09/0.45	thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
0.09/0.45	thf(func_def_0, type, in: ($i > ($i > $o) > $o)).
0.09/0.45	thf(func_def_2, type, is_a: ($i > ($i > $o) > $o)).
0.09/0.45	thf(func_def_3, type, emptyset: ($i > $o)).
0.09/0.45	thf(func_def_4, type, unord_pair: ($i > $i > $i > $o)).
0.09/0.45	thf(func_def_5, type, singleton: ($i > $i > $o)).
0.09/0.45	thf(func_def_6, type, union: (($i > $o) > ($i > $o) > $i > $o)).
0.09/0.45	thf(func_def_7, type, excl_union: (($i > $o) > ($i > $o) > $i > $o)).
0.09/0.45	thf(func_def_8, type, intersection: (($i > $o) > ($i > $o) > $i > $o)).
0.09/0.45	thf(func_def_9, type, setminus: (($i > $o) > ($i > $o) > $i > $o)).
0.09/0.45	thf(func_def_10, type, complement: (($i > $o) > $i > $o)).
0.09/0.45	thf(func_def_11, type, disjoint: (($i > $o) > ($i > $o) > $o)).
0.09/0.45	thf(func_def_12, type, subset: (($i > $o) > ($i > $o) > $o)).
0.09/0.45	thf(func_def_13, type, meets: (($i > $o) > ($i > $o) > $o)).
0.09/0.45	thf(func_def_14, type, misses: (($i > $o) > ($i > $o) > $o)).
0.09/0.45	thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.09/0.45	thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
0.09/0.45	thf(func_def_19, type, db0: !>[X0: $tType]:(X0)).
0.09/0.45	thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.09/0.45	thf(func_def_21, type, vOR: ($o > $o > $o)).
0.09/0.45	thf(func_def_22, type, vAND: ($o > $o > $o)).
0.09/0.45	thf(func_def_23, type, db2: !>[X0: $tType]:(X0)).
0.09/0.45	thf(func_def_24, type, vNOT: ($o > $o)).
0.09/0.45	thf(func_def_25, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
0.09/0.45	thf(func_def_26, type, vIMP: ($o > $o > $o)).
0.09/0.45	thf(func_def_27, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
0.09/0.45	thf(func_def_28, type, sK0: ($i > $o)).
0.09/0.45	thf(func_def_29, type, sK1: ($i > $o)).
0.09/0.45	thf(func_def_30, type, sK2: ($i > $o)).
0.09/0.45	thf(f6,axiom,(
0.09/0.45	  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = union)),
0.09/0.45	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',union)).
0.09/0.45	thf(f9,axiom,(
0.09/0.45	  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : (~(X1 @ X2) & (X0 @ X2))) = setminus)),
0.09/0.45	  file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',setminus)).
0.09/0.45	thf(f15,conjecture,(
0.09/0.45	  ! [X0 : ($i > $o),X2 : ($i > $o),X1 : ($i > $o)] : (((setminus @ (union @ X0 @ X1) @ X2)) = ((union @ (setminus @ X0 @ X2) @ (setminus @ X1 @ X2))))),
0.09/0.45	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
0.09/0.45	thf(f16,negated_conjecture,(
0.09/0.45	  ~ ! [X0 : ($i > $o),X2 : ($i > $o),X1 : ($i > $o)] : (((setminus @ (union @ X0 @ X1) @ X2)) = ((union @ (setminus @ X0 @ X2) @ (setminus @ X1 @ X2))))),
0.09/0.45	  inference(negated_conjecture,[status(cth)],[f15])).
0.09/0.45	thf(f21,plain,(
0.09/0.45	  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = union)),
0.09/0.45	  inference(rectify,[],[f6])).
0.09/0.45	thf(f22,plain,(
0.09/0.45	  (union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
0.09/0.45	  inference(fool_elimination,[],[f21])).
0.09/0.45	thf(f36,plain,(
0.09/0.45	  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : (~(X1 @ X2) & (X0 @ X2))) = setminus)),
0.09/0.45	  inference(rectify,[],[f9])).
0.09/0.45	thf(f37,plain,(
0.09/0.45	  (setminus = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 @ Y2)))))))))),
0.09/0.45	  inference(fool_elimination,[],[f36])).
0.09/0.45	thf(f39,plain,(
0.09/0.45	  ~ ! [X2 : ($i > $o),X1 : ($i > $o),X0 : ($i > $o)] : (((union @ (setminus @ X0 @ X1) @ (setminus @ X2 @ X1))) = ((setminus @ (union @ X0 @ X2) @ X1)))),
0.09/0.45	  inference(rectify,[],[f16])).
0.09/0.45	thf(f40,plain,(
0.09/0.45	  ? [X1 : ($i > $o),X0 : ($i > $o),X2 : ($i > $o)] : (((union @ (setminus @ X0 @ X1) @ (setminus @ X2 @ X1))) != ((setminus @ (union @ X0 @ X2) @ X1)))),
0.09/0.45	  inference(ennf_transformation,[],[f39])).
0.09/0.45	thf(f41,plain,(
0.09/0.45	  ? [X0 : ($i > $o),X1 : ($i > $o),X2 : ($i > $o)] : (((union @ (setminus @ X1 @ X0) @ (setminus @ X2 @ X0))) != ((setminus @ (union @ X1 @ X2) @ X0)))),
0.09/0.45	  inference(rectify,[],[f40])).
0.09/0.45	thf(f42,plain,(
0.09/0.45	  (((setminus @ (union @ sK1 @ sK2) @ sK0)) != ((union @ (setminus @ sK1 @ sK0) @ (setminus @ sK2 @ sK0))))),
0.09/0.45	  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f41])).
0.09/0.45	thf(f49,plain,(
0.09/0.45	  (((setminus @ (union @ sK1 @ sK2) @ sK0)) != ((union @ (setminus @ sK1 @ sK0) @ (setminus @ sK2 @ sK0))))),
0.09/0.45	  inference(cnf_transformation,[],[f42])).
0.09/0.45	thf(f53,plain,(
0.09/0.45	  (union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
0.09/0.45	  inference(cnf_transformation,[],[f22])).
0.09/0.45	thf(f57,plain,(
0.09/0.45	  (setminus = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 @ Y2)))))))))),
0.09/0.45	  inference(cnf_transformation,[],[f37])).
0.09/0.45	thf(f61,plain,(
0.09/0.45	  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 @ Y2)))))))) @ sK1 @ sK0) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 @ Y2)))))))) @ sK2 @ sK0))) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ sK1 @ sK2) @ sK0)))),
0.09/0.45	  inference(definition_unfolding,[],[f49,f57,f53,f53,f57,f57])).
0.09/0.45	thf(f62,plain,(
0.09/0.45	  ((^[Y0 : $i]: (((sK2 @ Y0) | (sK1 @ Y0)) & (~ (sK0 @ Y0)))) != (^[Y0 : $i]: (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))))),
0.09/0.45	  inference(beta-eta_normalization,[],[f61])).
0.09/0.45	thf(f63,plain,(
0.09/0.45	  ((((^[Y0 : $i]: (((sK2 @ Y0) | (sK1 @ Y0)) & (~ (sK0 @ Y0)))) @ sK3)) != (((^[Y0 : $i]: (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) @ sK3)))),
0.09/0.45	  inference(negative_extensionality,[],[f62])).
0.09/0.45	thf(f64,plain,(
0.09/0.45	  ((((^[Y0 : $i]: (((sK2 @ Y0) | (sK1 @ Y0)) & (~ (sK0 @ Y0)))) @ sK3)) = $true) | ((((^[Y0 : $i]: (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) @ sK3)) = $true)),
0.09/0.45	  inference(xor_proxy_clausification,[],[f63])).
0.09/0.45	thf(f65,plain,(
0.09/0.45	  ($false = (((^[Y0 : $i]: (((sK2 @ Y0) & (~ (sK0 @ Y0))) | ((sK1 @ Y0) & (~ (sK0 @ Y0))))) @ sK3))) | ((((^[Y0 : $i]: (((sK2 @ Y0) | (sK1 @ Y0)) & (~ (sK0 @ Y0)))) @ sK3)) = $false)),
0.09/0.45	  inference(xor_proxy_clausification,[],[f63])).
0.09/0.45	thf(f66,plain,(
0.09/0.45	  ($false = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3))))) | (((((sK2 @ sK3) & (~ (sK0 @ sK3))) | ((sK1 @ sK3) & (~ (sK0 @ sK3))))) = $false)),
0.09/0.45	  inference(beta-eta_normalization,[],[f65])).
0.09/0.45	thf(f67,plain,(
0.09/0.45	  ((((sK2 @ sK3) | (sK1 @ sK3))) = $false) | (((((sK2 @ sK3) & (~ (sK0 @ sK3))) | ((sK1 @ sK3) & (~ (sK0 @ sK3))))) = $false) | ($false = ((~ (sK0 @ sK3))))),
0.09/0.45	  inference(and_proxy_clausification,[],[f66])).
0.09/0.45	thf(f68,plain,(
0.09/0.45	  (((((sK2 @ sK3) & (~ (sK0 @ sK3))) | ((sK1 @ sK3) & (~ (sK0 @ sK3))))) = $false) | ($false = ((~ (sK0 @ sK3)))) | ($false = ((sK1 @ sK3)))),
0.09/0.45	  inference(or_proxy_clausification,[],[f67])).
0.09/0.45	thf(f69,plain,(
0.09/0.45	  (((((sK2 @ sK3) & (~ (sK0 @ sK3))) | ((sK1 @ sK3) & (~ (sK0 @ sK3))))) = $false) | ($false = ((sK2 @ sK3))) | ($false = ((~ (sK0 @ sK3))))),
0.09/0.45	  inference(or_proxy_clausification,[],[f67])).
0.09/0.45	thf(f71,plain,(
0.09/0.45	  ($false = ((~ (sK0 @ sK3)))) | ($false = ((sK2 @ sK3))) | ((((sK2 @ sK3) & (~ (sK0 @ sK3)))) = $false)),
0.09/0.45	  inference(or_proxy_clausification,[],[f69])).
0.09/0.45	thf(f72,plain,(
0.09/0.45	  ($true = ((sK0 @ sK3))) | ($false = ((sK2 @ sK3))) | ((((sK2 @ sK3) & (~ (sK0 @ sK3)))) = $false)),
0.09/0.45	  inference(not_proxy_clausification,[],[f71])).
0.09/0.45	thf(f73,plain,(
0.09/0.45	  ($false = ((~ (sK0 @ sK3)))) | ($true = ((sK0 @ sK3))) | ($false = ((sK2 @ sK3))) | ($false = ((sK2 @ sK3)))),
0.09/0.45	  inference(and_proxy_clausification,[],[f72])).
0.09/0.45	thf(f74,plain,(
0.09/0.45	  ($false = ((sK2 @ sK3))) | ($true = ((sK0 @ sK3))) | ($false = ((sK2 @ sK3))) | ($true = ((sK0 @ sK3)))),
0.09/0.45	  inference(not_proxy_clausification,[],[f73])).
0.09/0.45	thf(f75,plain,(
0.09/0.45	  ($true = ((sK0 @ sK3))) | ($false = ((sK2 @ sK3)))),
0.09/0.45	  inference(duplicate_literal_removal,[],[f74])).
0.09/0.45	thf(f80,plain,(
0.09/0.45	  ($false = ((sK1 @ sK3))) | ($false = ((~ (sK0 @ sK3)))) | ($false = (((sK1 @ sK3) & (~ (sK0 @ sK3)))))),
0.09/0.45	  inference(or_proxy_clausification,[],[f68])).
0.09/0.45	thf(f86,plain,(
0.09/0.45	  ($false = (((sK1 @ sK3) & (~ (sK0 @ sK3))))) | ($true = ((sK0 @ sK3))) | ($false = ((sK1 @ sK3)))),
0.09/0.45	  inference(not_proxy_clausification,[],[f80])).
0.09/0.45	thf(f87,plain,(
0.09/0.45	  ($true = ((sK0 @ sK3))) | ($false = ((~ (sK0 @ sK3)))) | ($false = ((sK1 @ sK3))) | ($false = ((sK1 @ sK3)))),
0.09/0.45	  inference(and_proxy_clausification,[],[f86])).
0.09/0.45	thf(f88,plain,(
0.09/0.45	  ($false = ((sK1 @ sK3))) | ($true = ((sK0 @ sK3))) | ($true = ((sK0 @ sK3))) | ($false = ((sK1 @ sK3)))),
0.09/0.45	  inference(not_proxy_clausification,[],[f87])).
0.09/0.45	thf(f89,plain,(
0.09/0.45	  ($false = ((sK1 @ sK3))) | ($true = ((sK0 @ sK3)))),
0.09/0.45	  inference(duplicate_literal_removal,[],[f88])).
0.09/0.45	thf(f90,plain,(
0.09/0.45	  (((((sK2 @ sK3) & (~ (sK0 @ sK3))) | ((sK1 @ sK3) & (~ (sK0 @ sK3))))) = $true) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3)))))),
0.09/0.45	  inference(beta-eta_normalization,[],[f64])).
0.09/0.45	thf(f91,plain,(
0.09/0.45	  ((((sK2 @ sK3) & (~ (sK0 @ sK3)))) = $true) | ((((sK1 @ sK3) & (~ (sK0 @ sK3)))) = $true) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3)))))),
0.09/0.45	  inference(or_proxy_clausification,[],[f90])).
0.09/0.45	thf(f92,plain,(
0.09/0.45	  ($true = ((~ (sK0 @ sK3)))) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3))))) | ((((sK1 @ sK3) & (~ (sK0 @ sK3)))) = $true)),
0.09/0.45	  inference(and_proxy_clausification,[],[f91])).
0.09/0.45	thf(f93,plain,(
0.09/0.45	  ((((sK1 @ sK3) & (~ (sK0 @ sK3)))) = $true) | ($true = ((sK2 @ sK3))) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3)))))),
0.09/0.45	  inference(and_proxy_clausification,[],[f91])).
0.09/0.45	thf(f95,plain,(
0.09/0.45	  ($true = ((sK2 @ sK3))) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3))))) | (((sK1 @ sK3)) = $true)),
0.09/0.45	  inference(and_proxy_clausification,[],[f93])).
0.09/0.45	thf(f97,plain,(
0.09/0.45	  (((sK1 @ sK3)) = $true) | ((((sK2 @ sK3) | (sK1 @ sK3))) = $true) | ($true = ((sK2 @ sK3)))),
0.09/0.45	  inference(and_proxy_clausification,[],[f95])).
0.09/0.45	thf(f98,plain,(
0.09/0.45	  ($true = ((sK2 @ sK3))) | (((sK1 @ sK3)) = $true) | (((sK1 @ sK3)) = $true) | ($true = ((sK2 @ sK3)))),
0.09/0.45	  inference(or_proxy_clausification,[],[f97])).
0.09/0.45	thf(f99,plain,(
0.09/0.45	  (((sK1 @ sK3)) = $true) | ($true = ((sK2 @ sK3)))),
0.09/0.45	  inference(duplicate_literal_removal,[],[f98])).
0.09/0.45	thf(f108,plain,(
0.09/0.45	  ((((sK1 @ sK3) & (~ (sK0 @ sK3)))) = $true) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3))))) | ($false = ((sK0 @ sK3)))),
0.09/0.45	  inference(not_proxy_clausification,[],[f92])).
0.09/0.45	thf(f109,plain,(
0.09/0.45	  ($true = ((~ (sK0 @ sK3)))) | ($false = ((sK0 @ sK3))) | ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3)))))),
0.09/0.45	  inference(and_proxy_clausification,[],[f108])).
0.09/0.45	thf(f117,plain,(
0.09/0.45	  ($true = ((((sK2 @ sK3) | (sK1 @ sK3)) & (~ (sK0 @ sK3))))) | ($false = ((sK0 @ sK3))) | ($false = ((sK0 @ sK3)))),
0.09/0.45	  inference(not_proxy_clausification,[],[f109])).
0.09/0.45	thf(f118,plain,(
0.09/0.45	  ($false = ((sK0 @ sK3))) | ($false = ((sK0 @ sK3))) | ($true = ((~ (sK0 @ sK3))))),
0.09/0.45	  inference(and_proxy_clausification,[],[f117])).
0.09/0.45	thf(f122,plain,(
0.09/0.45	  ($false = ((sK0 @ sK3))) | ($false = ((sK0 @ sK3))) | ($false = ((sK0 @ sK3)))),
0.09/0.45	  inference(not_proxy_clausification,[],[f118])).
0.09/0.45	thf(f123,plain,(
0.09/0.45	  ($false = ((sK0 @ sK3)))),
0.09/0.45	  inference(duplicate_literal_removal,[],[f122])).
0.09/0.45	thf(f125,definition,(
0.09/0.45	  spl4_1 <=> ($true = ((sK0 @ sK3)))),
0.09/0.45	  introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
0.09/0.45	thf(f127,plain,(
0.09/0.45	  ($true = ((sK0 @ sK3))) | ~spl4_1),
0.09/0.45	  inference(avatar_component_clause,[],[f125])).
0.09/0.45	thf(f129,definition,(
0.09/0.45	  spl4_2 <=> ($false = ((sK2 @ sK3)))),
0.09/0.45	  introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
0.09/0.45	thf(f131,plain,(
0.09/0.45	  ($false = ((sK2 @ sK3))) | ~spl4_2),
0.09/0.45	  inference(avatar_component_clause,[],[f129])).
0.09/0.45	thf(f132,plain,(
0.09/0.45	  spl4_1 | spl4_2),
0.09/0.45	  inference(avatar_split_clause,[],[f75,f129,f125])).
0.09/0.45	thf(f134,definition,(
0.09/0.45	  spl4_3 <=> ($false = ((sK1 @ sK3)))),
0.09/0.45	  introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
0.09/0.45	thf(f136,plain,(
0.09/0.45	  ($false = ((sK1 @ sK3))) | ~spl4_3),
0.09/0.45	  inference(avatar_component_clause,[],[f134])).
0.09/0.45	thf(f139,plain,(
0.09/0.45	  spl4_3 | spl4_1),
0.09/0.45	  inference(avatar_split_clause,[],[f89,f125,f134])).
0.09/0.45	thf(f141,definition,(
0.09/0.45	  spl4_4 <=> ($true = ((sK2 @ sK3)))),
0.09/0.45	  introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
0.09/0.45	thf(f143,plain,(
0.09/0.45	  ($true = ((sK2 @ sK3))) | ~spl4_4),
0.09/0.45	  inference(avatar_component_clause,[],[f141])).
0.09/0.45	thf(f145,definition,(
0.09/0.45	  spl4_5 <=> (((sK1 @ sK3)) = $true)),
0.09/0.45	  introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
0.09/0.45	thf(f147,plain,(
0.09/0.45	  (((sK1 @ sK3)) = $true) | ~spl4_5),
0.09/0.45	  inference(avatar_component_clause,[],[f145])).
0.09/0.45	thf(f148,plain,(
0.09/0.45	  spl4_4 | spl4_5),
0.09/0.45	  inference(avatar_split_clause,[],[f99,f145,f141])).
0.09/0.45	thf(f150,definition,(
0.09/0.45	  spl4_6 <=> ($false = ((sK0 @ sK3)))),
0.09/0.45	  introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition])).
0.09/0.45	thf(f152,plain,(
0.09/0.45	  ($false = ((sK0 @ sK3))) | ~spl4_6),
0.09/0.45	  inference(avatar_component_clause,[],[f150])).
0.09/0.45	thf(f159,plain,(
0.09/0.45	  spl4_6),
0.09/0.45	  inference(avatar_split_clause,[],[f123,f150])).
0.09/0.45	thf(f160,plain,(
0.09/0.45	  ($false = $true) | (~spl4_2 | ~spl4_4)),
0.09/0.45	  inference(forward_demodulation,[],[f131,f143])).
0.09/0.45	thf(f161,plain,(
0.09/0.45	  $false | (~spl4_2 | ~spl4_4)),
0.09/0.45	  inference(trivial_inequality_removal,[],[f160])).
0.09/0.45	thf(f162,plain,(
0.09/0.45	  ~spl4_2 | ~spl4_4),
0.09/0.45	  inference(avatar_contradiction_clause,[],[f161])).
0.09/0.45	thf(f163,plain,(
0.09/0.45	  ($false = $true) | (~spl4_1 | ~spl4_6)),
0.09/0.45	  inference(forward_demodulation,[],[f127,f152])).
0.09/0.45	thf(f164,plain,(
0.09/0.45	  $false | (~spl4_1 | ~spl4_6)),
0.09/0.45	  inference(trivial_inequality_removal,[],[f163])).
0.09/0.45	thf(f165,plain,(
0.09/0.45	  ~spl4_1 | ~spl4_6),
0.09/0.45	  inference(avatar_contradiction_clause,[],[f164])).
0.09/0.45	thf(f168,plain,(
0.09/0.45	  ($false = $true) | (~spl4_3 | ~spl4_5)),
0.09/0.45	  inference(forward_demodulation,[],[f147,f136])).
0.09/0.45	thf(f169,plain,(
0.09/0.45	  $false | (~spl4_3 | ~spl4_5)),
0.09/0.45	  inference(trivial_inequality_removal,[],[f168])).
0.09/0.45	thf(f170,plain,(
0.09/0.45	  ~spl4_3 | ~spl4_5),
0.09/0.45	  inference(avatar_contradiction_clause,[],[f169])).
0.09/0.45	cnf(s1, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f132])).
0.09/0.45	cnf(s4, plain, spl4_1 | spl4_3, inference(sat_conversion,[],[f139])).
0.09/0.45	cnf(s5, plain, spl4_4 | spl4_5, inference(sat_conversion,[],[f148])).
0.09/0.45	cnf(s12, plain, spl4_6, inference(sat_conversion,[],[f159])).
0.09/0.45	cnf(s13, plain, ~spl4_2 | ~spl4_4, inference(sat_conversion,[],[f162])).
0.09/0.45	cnf(s14, plain, ~spl4_1 | ~spl4_6, inference(sat_conversion,[],[f165])).
0.09/0.45	cnf(s15, plain, ~spl4_3 | ~spl4_5, inference(sat_conversion,[],[f170])).
0.09/0.45	cnf(s16, plain, ~spl4_1, inference(rat,[],[s14,s12])).
0.09/0.45	cnf(s17, plain, spl4_3, inference(rat,[],[s4,s16])).
0.09/0.45	cnf(s18, plain, ~spl4_5, inference(rat,[],[s15,s17])).
0.09/0.45	cnf(s19, plain, spl4_4, inference(rat,[],[s5,s18])).
0.09/0.45	cnf(s20, plain, ~spl4_2, inference(rat,[],[s13,s19])).
0.09/0.45	cnf(s21, plain, $false, inference(rat,[],[s1,s20,s16])).
0.09/0.45	thf(f172,plain,(
0.09/0.45	  $false),
0.09/0.45	  inference(avatar_sat_refutation,[],[s21])).
0.09/0.45	% SZS output end Proof for theBenchmark
0.09/0.45	% (1302001)------------------------------
0.09/0.45	% (1302001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.09/0.45	% (1302001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.09/0.45	% (1302001)CaDiCaL version: 2.1.3
0.09/0.45	% (1302001)Termination reason: Refutation
0.09/0.45	% (1302001)Time elapsed: 0.003 s
0.09/0.45	% (1302001)Peak memory usage: 13 MB
0.09/0.45	% (1302001)Instructions burned: 8 (million)
0.09/0.45	% (1301996)Success in time 0.027 s
0.09/0.45	% Vampire exiting
0.09/0.45	EOF