0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.37	% Computer : n016.cluster.edu
0.11/0.37	% Model    : x86_64 x86_64
0.11/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.37	% Memory   : 8046.5625MB
0.11/0.37	% OS       : Linux 6.8.0-71-generic
0.11/0.37	% CPULimit : 1440
0.11/0.37	% WCLimit  : 180
0.11/0.37	% DateTime : Mon Jul 27 09:56:37 UTC 2026
0.11/0.38	% CPUTime  : 
0.11/0.38	Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.11/0.41	Running higher-order theorem proving
0.11/0.42	Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p
0.21/0.47	% (1129681)Detected a higher-order problem, will run a greedy HOL sequence.
0.21/0.47	% (1129687)lrs+10_16_si=on:nwc=1.5:random_seed=1147421733:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi)
0.21/0.47	% (1129686)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=283214583:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.21/0.47	% (1129686)Refutation not found, incomplete strategy
0.21/0.47	% (1129686)------------------------------
0.21/0.47	% (1129686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.21/0.47	% (1129686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.21/0.47	% (1129686)CaDiCaL version: 2.1.3
0.21/0.47	% (1129686)Termination reason: Refutation not found, incomplete strategy
0.21/0.47	% (1129686)Time elapsed: 0.002 s
0.21/0.47	% (1129686)Peak memory usage: 12 MB
0.21/0.47	% (1129686)Instructions burned: 1 (million)
0.21/0.47	% (1129687) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1129681-1129687"...
0.21/0.47	% (1129686)------------------------------
0.21/0.47	% (1129686)------------------------------
0.21/0.47	% (1129687)...printing done.
0.21/0.47	% (1129687)Refutation found. Thanks to Tanya!
0.21/0.47	% SZS status Theorem for theBenchmark
0.21/0.47	% SZS output start Proof for theBenchmark
0.21/0.47	thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
0.21/0.47	thf(func_def_0, type, cN: ($i > $i)).
0.21/0.47	thf(func_def_1, type, cM: ($i > $i)).
0.21/0.47	thf(func_def_3, type, sK0: (($i > $i) > $o)).
0.21/0.47	thf(func_def_6, type, vNOT: ($o > $o)).
0.21/0.47	thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.21/0.47	thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
0.21/0.47	thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.21/0.47	thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
0.21/0.47	thf(f1,conjecture,(
0.21/0.47	  ! [X1 : ($i > $o),X0 : $i] : ((X1 @ (cN @ X0)) <=> (X1 @ (cM @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ cN) <=> (X2 @ cM))),
0.21/0.47	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEXT_A_LEIB2)).
0.21/0.47	thf(f2,negated_conjecture,(
0.21/0.47	  ~(! [X1 : ($i > $o),X0 : $i] : ((X1 @ (cN @ X0)) <=> (X1 @ (cM @ X0))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ cN) <=> (X2 @ cM)))),
0.21/0.47	  inference(negated_conjecture,[status(cth)],[f1])).
0.21/0.47	thf(f3,plain,(
0.21/0.47	  ~(! [X0 : ($i > $o),X1 : $i] : ((X0 @ (cN @ X1)) <=> (X0 @ (cM @ X1))) => ! [X2 : (($i > $i) > $o)] : ((X2 @ cN) <=> (X2 @ cM)))),
0.21/0.47	  inference(rectify,[],[f2])).
0.21/0.47	thf(f4,plain,(
0.21/0.47	  ~(! [X1 : $i,X0 : ($i > $o)] : (((X0 @ (cN @ X1))) = ((X0 @ (cM @ X1)))) => ! [X2 : (($i > $i) > $o)] : (((X2 @ cN)) = ((X2 @ cM))))),
0.21/0.47	  inference(fool_elimination,[],[f3])).
0.21/0.47	thf(f5,plain,(
0.21/0.47	  ? [X2 : (($i > $i) > $o)] : (((X2 @ cN)) != ((X2 @ cM))) & ! [X1 : $i,X0 : ($i > $o)] : (((X0 @ (cN @ X1))) = ((X0 @ (cM @ X1))))),
0.21/0.47	  inference(ennf_transformation,[],[f4])).
0.21/0.47	thf(f6,plain,(
0.21/0.47	  ? [X0 : (($i > $i) > $o)] : (((X0 @ cM)) != ((X0 @ cN))) & ! [X1 : $i,X2 : ($i > $o)] : (((X2 @ (cM @ X1))) = ((X2 @ (cN @ X1))))),
0.21/0.47	  inference(rectify,[],[f5])).
0.21/0.47	thf(f7,plain,(
0.21/0.47	  (((sK0 @ cN)) != ((sK0 @ cM))) & ! [X1 : $i,X2 : ($i > $o)] : (((X2 @ (cM @ X1))) = ((X2 @ (cN @ X1))))),
0.21/0.47	  inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6])).
0.21/0.47	thf(f8,plain,(
0.21/0.47	  ( ! [X2 : ($i > $o),X1 : $i] : ((((X2 @ (cM @ X1))) = ((X2 @ (cN @ X1))))) )),
0.21/0.47	  inference(cnf_transformation,[],[f7])).
0.21/0.47	thf(f9,plain,(
0.21/0.47	  (((sK0 @ cN)) != ((sK0 @ cM)))),
0.21/0.47	  inference(cnf_transformation,[],[f7])).
0.21/0.47	thf(f12,plain,(
0.21/0.47	  (((sK0 @ cM)) = $true) | (((sK0 @ cN)) = $true)),
0.21/0.47	  inference(xor_proxy_clausification,[],[f9])).
0.21/0.47	thf(f13,plain,(
0.21/0.47	  (((sK0 @ cN)) = $false) | (((sK0 @ cM)) = $false)),
0.21/0.47	  inference(xor_proxy_clausification,[],[f9])).
0.21/0.47	thf(f14,plain,(
0.21/0.47	  ( ! [X2 : ($i > $o),X1 : $i] : ((((X2 @ (cM @ X1))) = $true) | (((X2 @ (cN @ X1))) = $false)) )),
0.21/0.47	  inference(iff_proxy_clausification,[],[f8])).
0.21/0.47	thf(f17,definition,(
0.21/0.47	  spl1_1 <=> (((sK0 @ cM)) = $false)),
0.21/0.47	  introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
0.21/0.47	thf(f19,plain,(
0.21/0.47	  (((sK0 @ cM)) = $false) | ~spl1_1),
0.21/0.47	  inference(avatar_component_clause,[],[f17])).
0.21/0.47	thf(f21,definition,(
0.21/0.47	  spl1_2 <=> (((sK0 @ cN)) = $false)),
0.21/0.47	  introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
0.21/0.47	thf(f23,plain,(
0.21/0.47	  (((sK0 @ cN)) = $false) | ~spl1_2),
0.21/0.47	  inference(avatar_component_clause,[],[f21])).
0.21/0.47	thf(f24,plain,(
0.21/0.47	  spl1_1 | spl1_2),
0.21/0.47	  inference(avatar_split_clause,[],[f13,f21,f17])).
0.21/0.47	thf(f26,definition,(
0.21/0.47	  spl1_3 <=> (((sK0 @ cN)) = $true)),
0.21/0.47	  introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
0.21/0.47	thf(f28,plain,(
0.21/0.47	  (((sK0 @ cN)) = $true) | ~spl1_3),
0.21/0.47	  inference(avatar_component_clause,[],[f26])).
0.21/0.47	thf(f30,definition,(
0.21/0.47	  spl1_4 <=> (((sK0 @ cM)) = $true)),
0.21/0.47	  introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
0.21/0.47	thf(f32,plain,(
0.21/0.47	  (((sK0 @ cM)) = $true) | ~spl1_4),
0.21/0.47	  inference(avatar_component_clause,[],[f30])).
0.21/0.47	thf(f33,plain,(
0.21/0.47	  spl1_3 | spl1_4),
0.21/0.47	  inference(avatar_split_clause,[],[f12,f30,f26])).
0.21/0.47	thf(f34,plain,(
0.21/0.47	  ($false = $true) | (~spl1_2 | ~spl1_3)),
0.21/0.47	  inference(constrained_superposition,[],[f28,f23])).
0.21/0.47	thf(f38,plain,(
0.21/0.47	  $false | (~spl1_2 | ~spl1_3)),
0.21/0.47	  inference(trivial_inequality_removal,[],[f34])).
0.21/0.47	thf(f39,plain,(
0.21/0.47	  ~spl1_2 | ~spl1_3),
0.21/0.47	  inference(avatar_contradiction_clause,[],[f38])).
0.21/0.47	thf(f42,plain,(
0.21/0.47	  (cN != cM) | ($false = $true) | (~spl1_1 | ~spl1_3)),
0.21/0.47	  inference(constrained_superposition,[],[f28,f19])).
0.21/0.47	thf(f43,plain,(
0.21/0.47	  (cN != cM) | (~spl1_1 | ~spl1_3)),
0.21/0.47	  inference(trivial_inequality_removal,[],[f42])).
0.21/0.47	thf(f45,plain,(
0.21/0.47	  (((cM @ sK2)) != ((cN @ sK2))) | (~spl1_1 | ~spl1_3)),
0.21/0.47	  inference(negative_extensionality,[],[f43])).
0.21/0.47	thf(f47,plain,(
0.21/0.47	  ( ! [X0 : $i] : ((((cN @ X0)) = ((cM @ X0)))) )),
0.21/0.47	  inference(leibniz_equality_elimination,[],[f14])).
0.21/0.47	thf(f74,plain,(
0.21/0.47	  (((cN @ sK2)) != ((cN @ sK2))) | (~spl1_1 | ~spl1_3)),
0.21/0.47	  inference(constrained_superposition,[],[f45,f47])).
0.21/0.47	thf(f76,plain,(
0.21/0.47	  $false | (~spl1_1 | ~spl1_3)),
0.21/0.47	  inference(trivial_inequality_removal,[],[f74])).
0.21/0.47	thf(f77,plain,(
0.21/0.47	  ~spl1_1 | ~spl1_3),
0.21/0.47	  inference(avatar_contradiction_clause,[],[f76])).
0.21/0.47	thf(f85,plain,(
0.21/0.47	  ($false = $true) | (cN != cM) | (~spl1_2 | ~spl1_4)),
0.21/0.47	  inference(constrained_superposition,[],[f32,f23])).
0.21/0.47	thf(f87,plain,(
0.21/0.47	  (cN != cM) | (~spl1_2 | ~spl1_4)),
0.21/0.47	  inference(trivial_inequality_removal,[],[f85])).
0.21/0.47	thf(f89,plain,(
0.21/0.47	  (((cM @ sK3)) != ((cN @ sK3))) | (~spl1_2 | ~spl1_4)),
0.21/0.47	  inference(negative_extensionality,[],[f87])).
0.21/0.47	thf(f90,plain,(
0.21/0.47	  $false | (~spl1_2 | ~spl1_4)),
0.21/0.47	  inference(forward_subsumption_resolution,[],[f89,f47])).
0.21/0.47	thf(f91,plain,(
0.21/0.47	  ~spl1_2 | ~spl1_4),
0.21/0.47	  inference(avatar_contradiction_clause,[],[f90])).
0.21/0.47	thf(f94,plain,(
0.21/0.47	  ($false = $true) | (~spl1_1 | ~spl1_4)),
0.21/0.47	  inference(constrained_superposition,[],[f19,f32])).
0.21/0.47	thf(f108,plain,(
0.21/0.47	  $false | (~spl1_1 | ~spl1_4)),
0.21/0.47	  inference(trivial_inequality_removal,[],[f94])).
0.21/0.47	thf(f109,plain,(
0.21/0.47	  ~spl1_1 | ~spl1_4),
0.21/0.47	  inference(avatar_contradiction_clause,[],[f108])).
0.21/0.47	cnf(s1, plain, spl1_1 | spl1_2, inference(sat_conversion,[],[f24])).
0.21/0.47	cnf(s2, plain, spl1_3 | spl1_4, inference(sat_conversion,[],[f33])).
0.21/0.47	cnf(s4, plain, ~spl1_2 | ~spl1_3, inference(sat_conversion,[],[f39])).
0.21/0.47	cnf(s5, plain, ~spl1_1 | ~spl1_3, inference(sat_conversion,[],[f77])).
0.21/0.47	cnf(s6, plain, ~spl1_2 | ~spl1_4, inference(sat_conversion,[],[f91])).
0.21/0.47	cnf(s8, plain, ~spl1_1 | ~spl1_4, inference(sat_conversion,[],[f109])).
0.21/0.47	cnf(s9, plain, ~spl1_2, inference(rat,[],[s2,s4,s6])).
0.21/0.47	cnf(s10, plain, spl1_1, inference(rat,[],[s1,s9])).
0.21/0.47	cnf(s11, plain, ~spl1_4, inference(rat,[],[s8,s10])).
0.21/0.47	cnf(s12, plain, ~spl1_3, inference(rat,[],[s5,s10])).
0.21/0.47	cnf(s13, plain, $false, inference(rat,[],[s2,s11,s12])).
0.21/0.47	thf(f110,plain,(
0.21/0.47	  $false),
0.21/0.47	  inference(avatar_sat_refutation,[],[s13])).
0.21/0.47	% SZS output end Proof for theBenchmark
0.21/0.47	% (1129687)------------------------------
0.21/0.47	% (1129687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.21/0.47	% (1129687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.21/0.47	% (1129687)CaDiCaL version: 2.1.3
0.21/0.47	% (1129687)Termination reason: Refutation
0.21/0.47	% (1129687)Time elapsed: 0.004 s
0.21/0.47	% (1129687)Peak memory usage: 13 MB
0.21/0.47	% (1129687)Instructions burned: 6 (million)
0.21/0.47	% (1129681)Success in time 0.038 s
0.21/0.47	% Vampire exiting
0.21/0.48	EOF