0.00/0.02	% 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
0.12/0.37	% Computer : n008.cluster.edu
0.12/0.37	% Model    : x86_64 x86_64
0.12/0.37	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.37	% Memory   : 8046.5625MB
0.12/0.37	% OS       : Linux 6.8.0-71-generic
0.12/0.37	% CPULimit : 1440
0.12/0.37	% WCLimit  : 180
0.12/0.37	% DateTime : Mon Jul 27 12:10:43 UTC 2026
0.12/0.37	% CPUTime  : 
0.12/0.37	Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 180 THM
0.12/0.41	Running higher-order theorem proving
0.12/0.42	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
0.19/0.46	% (1099130)Detected a higher-order problem, will run a greedy HOL sequence.
0.19/0.46	% (1099135)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=550711313:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.19/0.46	% (1099135) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1099130-1099135"...
0.19/0.46	% (1099135)...printing done.
0.19/0.46	% (1099135)Refutation found. Thanks to Tanya!
0.19/0.46	% SZS status Theorem for theBenchmark
0.19/0.46	% SZS output start Proof for theBenchmark
0.19/0.46	thf(type_def_5, type, nat: $tType).
0.19/0.46	thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
0.19/0.46	thf(func_def_0, type, x: nat).
0.19/0.46	thf(func_def_1, type, y: nat).
0.19/0.46	thf(func_def_2, type, pl: (nat > nat > nat)).
0.19/0.46	thf(func_def_6, type, sK0: nat).
0.19/0.46	thf(func_def_7, type, sK1: nat).
0.19/0.46	thf(func_def_8, type, sK2: nat).
0.19/0.46	thf(func_def_9, type, sK3: nat).
0.19/0.46	thf(func_def_10, type, vNOT: ($o > $o)).
0.19/0.46	thf(f2,conjecture,(
0.19/0.46	  ~(((x = y) => ~ ~ ! [X0 : nat] : (x != ((pl @ y @ X0)))) => ~ ~((~ ! [X0 : nat] : (x != ((pl @ y @ X0))) => ~ ~ ! [X0 : nat] : (y != ((pl @ x @ X0)))) => ~(~ ! [X0 : nat] : (y != ((pl @ x @ X0))) => (x != y))))),
0.19/0.46	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz9b)).
0.19/0.46	thf(f3,negated_conjecture,(
0.19/0.46	  ~ ~(((x = y) => ~ ~ ! [X0 : nat] : (x != ((pl @ y @ X0)))) => ~ ~((~ ! [X0 : nat] : (x != ((pl @ y @ X0))) => ~ ~ ! [X0 : nat] : (y != ((pl @ x @ X0)))) => ~(~ ! [X0 : nat] : (y != ((pl @ x @ X0))) => (x != y))))),
0.19/0.46	  inference(negated_conjecture,[status(cth)],[f2])).
0.19/0.46	thf(f4,axiom,(
0.19/0.46	  ! [X1 : nat,X0 : nat] : (((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))),
0.19/0.46	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz6)).
0.19/0.46	thf(f5,axiom,(
0.19/0.46	  ! [X0 : nat,X1 : nat] : (X1 != ((pl @ X0 @ X1)))),
0.19/0.46	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz7)).
0.19/0.46	thf(f6,axiom,(
0.19/0.46	  ! [X2 : nat,X1 : nat,X0 : nat] : (((pl @ (pl @ X0 @ X1) @ X2)) = ((pl @ X0 @ (pl @ X1 @ X2))))),
0.19/0.46	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz5)).
0.19/0.46	thf(f10,plain,(
0.19/0.46	  ! [X0 : nat,X1 : nat,X2 : nat] : (((pl @ (pl @ X2 @ X1) @ X0)) = ((pl @ X2 @ (pl @ X1 @ X0))))),
0.19/0.46	  inference(rectify,[],[f6])).
0.19/0.46	thf(f11,plain,(
0.19/0.46	  ~ ~(((x = y) => ~ ~ ! [X0 : nat] : (x != ((pl @ y @ X0)))) => ~ ~((~ ! [X1 : nat] : (x != ((pl @ y @ X1))) => ~ ~ ! [X2 : nat] : (y != ((pl @ x @ X2)))) => ~(~ ! [X3 : nat] : (y != ((pl @ x @ X3))) => (x != y))))),
0.19/0.46	  inference(rectify,[],[f3])).
0.19/0.46	thf(f12,plain,(
0.19/0.46	  ((x = y) => ! [X0 : nat] : (x != ((pl @ y @ X0)))) => ((~ ! [X1 : nat] : (x != ((pl @ y @ X1))) => ! [X2 : nat] : (y != ((pl @ x @ X2)))) => ~(~ ! [X3 : nat] : (y != ((pl @ x @ X3))) => (x != y)))),
0.19/0.46	  inference(flattening,[],[f11])).
0.19/0.46	thf(f13,plain,(
0.19/0.46	  (((x = y) & ? [X3 : nat] : (y = ((pl @ x @ X3)))) | (? [X2 : nat] : (y = ((pl @ x @ X2))) & ? [X1 : nat] : (x = ((pl @ y @ X1))))) | ((x = y) & ? [X0 : nat] : (x = ((pl @ y @ X0))))),
0.19/0.46	  inference(ennf_transformation,[],[f12])).
0.19/0.46	thf(f14,plain,(
0.19/0.46	  ((x = y) & ? [X3 : nat] : (y = ((pl @ x @ X3)))) | ((x = y) & ? [X0 : nat] : (x = ((pl @ y @ X0)))) | (? [X2 : nat] : (y = ((pl @ x @ X2))) & ? [X1 : nat] : (x = ((pl @ y @ X1))))),
0.19/0.46	  inference(flattening,[],[f13])).
0.19/0.46	thf(f16,plain,(
0.19/0.46	  ((x = y) & ? [X0 : nat] : (y = ((pl @ x @ X0)))) | ((x = y) & ? [X1 : nat] : (x = ((pl @ y @ X1)))) | (? [X2 : nat] : (y = ((pl @ x @ X2))) & ? [X3 : nat] : (x = ((pl @ y @ X3))))),
0.19/0.46	  inference(rectify,[],[f14])).
0.19/0.46	thf(f17,plain,(
0.19/0.46	  ((x = y) & (y = ((pl @ x @ sK0)))) | ((x = y) & (x = ((pl @ y @ sK1)))) | ((y = ((pl @ x @ sK2))) & (x = ((pl @ y @ sK3))))),
0.19/0.46	  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f16])).
0.19/0.46	thf(f18,plain,(
0.19/0.46	  ! [X0 : nat,X1 : nat] : (((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))),
0.19/0.46	  inference(rectify,[],[f4])).
0.19/0.46	thf(f19,plain,(
0.19/0.46	  ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ X1)) != X1)) )),
0.19/0.46	  inference(cnf_transformation,[],[f5])).
0.19/0.46	thf(f21,plain,(
0.19/0.46	  (y = ((pl @ x @ sK2))) | (y = ((pl @ x @ sK0))) | (x = ((pl @ y @ sK1)))),
0.19/0.46	  inference(cnf_transformation,[],[f17])).
0.19/0.46	thf(f26,plain,(
0.19/0.46	  (x = y) | (x = ((pl @ y @ sK3))) | (x = y)),
0.19/0.46	  inference(cnf_transformation,[],[f17])).
0.19/0.46	thf(f27,plain,(
0.19/0.46	  (x = y) | (x = y) | (y = ((pl @ x @ sK2)))),
0.19/0.46	  inference(cnf_transformation,[],[f17])).
0.19/0.46	thf(f28,plain,(
0.19/0.46	  ( ! [X2 : nat,X0 : nat,X1 : nat] : ((((pl @ (pl @ X2 @ X1) @ X0)) = ((pl @ X2 @ (pl @ X1 @ X0))))) )),
0.19/0.46	  inference(cnf_transformation,[],[f10])).
0.19/0.46	thf(f29,plain,(
0.19/0.46	  ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ X1)) = ((pl @ X1 @ X0)))) )),
0.19/0.46	  inference(cnf_transformation,[],[f18])).
0.19/0.46	thf(f34,plain,(
0.19/0.46	  (y = ((pl @ x @ sK2))) | (x = y)),
0.19/0.46	  inference(duplicate_literal_removal,[],[f27])).
0.19/0.46	thf(f35,plain,(
0.19/0.46	  (x = y) | (x = ((pl @ y @ sK3)))),
0.19/0.46	  inference(duplicate_literal_removal,[],[f26])).
0.19/0.46	thf(f37,definition,(
0.19/0.46	  spl4_1 <=> (x = y)),
0.19/0.46	  introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
0.19/0.46	thf(f39,plain,(
0.19/0.46	  (x = y) | ~spl4_1),
0.19/0.46	  inference(avatar_component_clause,[],[f37])).
0.19/0.46	thf(f41,definition,(
0.19/0.46	  spl4_2 <=> (x = ((pl @ y @ sK3)))),
0.19/0.46	  introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
0.19/0.46	thf(f43,plain,(
0.19/0.46	  (x = ((pl @ y @ sK3))) | ~spl4_2),
0.19/0.46	  inference(avatar_component_clause,[],[f41])).
0.19/0.46	thf(f45,definition,(
0.19/0.46	  spl4_3 <=> (y = ((pl @ x @ sK0)))),
0.19/0.46	  introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
0.19/0.46	thf(f47,plain,(
0.19/0.46	  (y = ((pl @ x @ sK0))) | ~spl4_3),
0.19/0.46	  inference(avatar_component_clause,[],[f45])).
0.19/0.46	thf(f50,definition,(
0.19/0.46	  spl4_4 <=> (y = ((pl @ x @ sK2)))),
0.19/0.46	  introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
0.19/0.46	thf(f52,plain,(
0.19/0.46	  (y = ((pl @ x @ sK2))) | ~spl4_4),
0.19/0.46	  inference(avatar_component_clause,[],[f50])).
0.19/0.46	thf(f53,plain,(
0.19/0.46	  spl4_1 | spl4_4),
0.19/0.46	  inference(avatar_split_clause,[],[f34,f50,f37])).
0.19/0.46	thf(f54,plain,(
0.19/0.46	  spl4_2 | spl4_1),
0.19/0.46	  inference(avatar_split_clause,[],[f35,f37,f41])).
0.19/0.46	thf(f56,definition,(
0.19/0.46	  spl4_5 <=> (x = ((pl @ y @ sK1)))),
0.19/0.46	  introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
0.19/0.46	thf(f58,plain,(
0.19/0.46	  (x = ((pl @ y @ sK1))) | ~spl4_5),
0.19/0.46	  inference(avatar_component_clause,[],[f56])).
0.19/0.46	thf(f61,plain,(
0.19/0.46	  spl4_5 | spl4_4 | spl4_3),
0.19/0.46	  inference(avatar_split_clause,[],[f21,f45,f50,f56])).
0.19/0.46	thf(f67,plain,(
0.19/0.46	  ( ! [X0 : nat,X1 : nat] : ((((pl @ X0 @ X1)) != X0)) )),
0.19/0.46	  inference(constrained_superposition,[],[f19,f29])).
0.19/0.46	thf(f71,plain,(
0.19/0.46	  (x != y) | ~spl4_4),
0.19/0.46	  inference(constrained_superposition,[],[f67,f52])).
0.19/0.46	thf(f75,plain,(
0.19/0.46	  ~spl4_1 | ~spl4_4),
0.19/0.46	  inference(avatar_split_clause,[],[f71,f50,f37])).
0.19/0.46	thf(f78,plain,(
0.19/0.46	  ( ! [X0 : nat] : ((((pl @ y @ X0)) = ((pl @ x @ (pl @ sK2 @ X0))))) ) | ~spl4_4),
0.19/0.46	  inference(constrained_superposition,[],[f28,f52])).
0.19/0.46	thf(f94,plain,(
0.19/0.46	  ( ! [X0 : nat] : ((x != ((pl @ y @ X0)))) ) | ~spl4_4),
0.19/0.46	  inference(constrained_superposition,[],[f67,f78])).
0.19/0.46	thf(f100,plain,(
0.19/0.46	  (x != x) | (~spl4_2 | ~spl4_4)),
0.19/0.46	  inference(constrained_superposition,[],[f94,f43])).
0.19/0.46	thf(f101,plain,(
0.19/0.46	  $false | (~spl4_2 | ~spl4_4)),
0.19/0.46	  inference(trivial_inequality_removal,[],[f100])).
0.19/0.46	thf(f102,plain,(
0.19/0.46	  ~spl4_2 | ~spl4_4),
0.19/0.46	  inference(avatar_contradiction_clause,[],[f101])).
0.19/0.46	thf(f103,plain,(
0.19/0.46	  (x = ((pl @ x @ sK0))) | (~spl4_1 | ~spl4_3)),
0.19/0.46	  inference(forward_demodulation,[],[f47,f39])).
0.19/0.46	thf(f106,plain,(
0.19/0.46	  $false | (~spl4_1 | ~spl4_3)),
0.19/0.46	  inference(forward_subsumption_resolution,[],[f103,f67])).
0.19/0.46	thf(f107,plain,(
0.19/0.46	  ~spl4_1 | ~spl4_3),
0.19/0.46	  inference(avatar_contradiction_clause,[],[f106])).
0.19/0.46	thf(f108,plain,(
0.19/0.46	  (x = ((pl @ x @ sK1))) | (~spl4_1 | ~spl4_5)),
0.19/0.46	  inference(forward_demodulation,[],[f58,f39])).
0.19/0.46	thf(f110,plain,(
0.19/0.46	  $false | (~spl4_1 | ~spl4_5)),
0.19/0.46	  inference(forward_subsumption_resolution,[],[f108,f67])).
0.19/0.46	thf(f111,plain,(
0.19/0.46	  ~spl4_1 | ~spl4_5),
0.19/0.46	  inference(avatar_contradiction_clause,[],[f110])).
0.19/0.46	cnf(s2, plain, spl4_1 | spl4_4, inference(sat_conversion,[],[f53])).
0.19/0.46	cnf(s3, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f54])).
0.19/0.46	cnf(s6, plain, spl4_3 | spl4_4 | spl4_5, inference(sat_conversion,[],[f61])).
0.19/0.46	cnf(s10, plain, ~spl4_1 | ~spl4_4, inference(sat_conversion,[],[f75])).
0.19/0.46	cnf(s11, plain, ~spl4_2 | ~spl4_4, inference(sat_conversion,[],[f102])).
0.19/0.46	cnf(s12, plain, ~spl4_1 | ~spl4_3, inference(sat_conversion,[],[f107])).
0.19/0.46	cnf(s13, plain, ~spl4_1 | ~spl4_5, inference(sat_conversion,[],[f111])).
0.19/0.46	cnf(s14, plain, spl4_1, inference(rat,[],[s11,s2,s3])).
0.19/0.46	cnf(s15, plain, ~spl4_5, inference(rat,[],[s13,s14])).
0.19/0.46	cnf(s16, plain, ~spl4_3, inference(rat,[],[s12,s14])).
0.19/0.46	cnf(s17, plain, ~spl4_4, inference(rat,[],[s10,s14])).
0.19/0.46	cnf(s19, plain, $false, inference(rat,[],[s6,s15,s17,s16])).
0.19/0.46	thf(f112,plain,(
0.19/0.46	  $false),
0.19/0.46	  inference(avatar_sat_refutation,[],[s19])).
0.19/0.46	% SZS output end Proof for theBenchmark
0.19/0.46	% (1099135)------------------------------
0.19/0.46	% (1099135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.19/0.46	% (1099135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.19/0.46	% (1099135)CaDiCaL version: 2.1.3
0.19/0.46	% (1099135)Termination reason: Refutation
0.19/0.46	% (1099135)Time elapsed: 0.003 s
0.19/0.46	% (1099135)Peak memory usage: 13 MB
0.19/0.46	% (1099135)Instructions burned: 7 (million)
0.19/0.46	% (1099130)Success in time 0.032 s
0.19/0.46	% Vampire exiting
0.19/0.46	EOF