%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT178^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:00 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT178^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 18:06:17 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.30 % (455756)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (455767)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2886474185:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (455762)% WARNING: option uhcvi not known.
% 0.20/0.30 % (455761)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3226807563_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (455762)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=523183614:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (455764)dis+10_1_sil=32000:sp=arity:random_seed=322571202:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (455763)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3770043925:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (455765)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2600500708:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (455766)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3081653119:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (455762)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (455765)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (455767) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-455756-455767"...
% 0.20/0.30 % (455767)...printing done.
% 0.20/0.30 % (455767)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.20/0.30 thf(type_def_6, type, set: $tType > $tType).
% 0.20/0.30 thf(type_def_7, type, itself: $tType > $tType).
% 0.20/0.30 thf(type_def_8, type, a: $tType).
% 0.20/0.30 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_2, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_3, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_4, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_5, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_6, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.20/0.30 thf(func_def_7, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_8, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.20/0.30 thf(func_def_9, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_10, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_11, type, coinductive_lfilter: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_12, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_13, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_14, type, coinductive_llexord: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_15, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_16, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.20/0.30 thf(func_def_17, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_18, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.20/0.30 thf(func_def_19, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_20, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_21, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.30 thf(func_def_22, type, undefined: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_23, type, lList2435255213lllsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_24, type, lList21511617539llstsp: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_25, type, lList2236698231inlsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_26, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0))).
% 0.20/0.30 thf(func_def_27, type, lList2860480441nlstsp: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > $o))).
% 0.20/0.30 thf(func_def_28, type, lList22096119349pslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_29, type, lList21612149805nflsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_30, type, lList2370560421utlast: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_31, type, lList2170638824_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_32, type, lList2281150353e_lrev: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_33, type, lList21148268032oslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_34, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.30 thf(func_def_35, type, top_top: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_36, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.20/0.30 thf(func_def_37, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.20/0.30 thf(func_def_38, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.20/0.30 thf(func_def_39, type, a2: set @ a).
% 0.20/0.30 thf(func_def_40, type, p: (coinductive_llist @ a > $o)).
% 0.20/0.30 thf(func_def_41, type, l: coinductive_llist @ a).
% 0.20/0.30 thf(func_def_42, type, la: coinductive_llist @ a).
% 0.20/0.30 thf(func_def_43, type, xs: coinductive_llist @ a).
% 0.20/0.30 thf(func_def_47, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.30 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_50, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_53, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_56, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_59, type, sK0: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_60, type, sK1: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_61, type, sK2: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_62, type, sK3: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_63, type, sK4: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.20/0.30 thf(func_def_64, type, sK5: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_65, type, sK6: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_66, type, sK7: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_67, type, sK8: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.20/0.30 thf(func_def_68, type, sK9: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_69, type, sK10: !>[X0: $tType]:((set @ X0 > X0))).
% 0.20/0.30 thf(func_def_70, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_71, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.30 thf(func_def_72, type, sK13: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_73, type, sK14: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_74, type, sK15: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_75, type, sK16: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_76, type, sK17: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_77, type, sK18: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_78, type, sK19: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_79, type, sK20: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_80, type, sK21: !>[X0: $tType]:(((X0 > $o) > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_81, type, sK22: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_82, type, sK23: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_83, type, sK24: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_84, type, sK25: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_85, type, sK26: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_86, type, sK27: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_87, type, sK28: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_88, type, sK29: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_89, type, sK30: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_90, type, sK31: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_91, type, sK32: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_92, type, sK33: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_93, type, sK34: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_94, type, sK35: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_95, type, sK36: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_96, type, sK37: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_97, type, sK38: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_98, type, sK39: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_99, type, sK40: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_100, type, sK41: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.20/0.30 thf(func_def_101, type, sK42: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_102, type, sK43: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_103, type, sK44: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.20/0.30 thf(func_def_104, type, sK45: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_105, type, sK46: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_106, type, sK47: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.20/0.30 thf(func_def_107, type, sK48: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_108, type, sK49: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_109, type, sK50: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.20/0.30 thf(func_def_110, type, sK51: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_111, type, sK52: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_112, type, sK53: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_113, type, sK54: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_114, type, sK55: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_115, type, sK56: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_116, type, sK57: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_117, type, sK58: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_118, type, sK59: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_119, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_120, type, sK61: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_121, type, sK62: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_122, type, sK63: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_123, type, sK64: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_124, type, sK65: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_125, type, sK66: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_126, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_127, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_128, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_129, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_130, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_131, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_132, type, sK73: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_133, type, sK74: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_134, type, sK75: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_135, type, sK76: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 0.20/0.30 thf(func_def_136, type, sK77: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_137, type, sK78: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_138, type, sK79: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_139, type, sK80: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_140, type, sK81: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_141, type, sK82: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_142, type, sK83: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_143, type, sK84: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.20/0.30 thf(func_def_144, type, sK85: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.20/0.30 thf(func_def_145, type, sK86: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_146, type, sK87: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.20/0.30 thf(func_def_147, type, sK88: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.20/0.30 thf(func_def_148, type, sK89: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_149, type, sK90: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_150, type, sK91: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(func_def_151, type, sK92: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.20/0.30 thf(func_def_152, type, sK93: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.20/0.30 thf(func_def_153, type, sK94: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.20/0.30 thf(f1,axiom,(
% 0.20/0.30 (p @ coinductive_LNil @ a)),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_init)).
% 0.20/0.30 thf(f2,axiom,(
% 0.20/0.30 (la = coinductive_LNil @ a)),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_LNil__fin_Ohyps)).
% 0.20/0.30 thf(f4,axiom,(
% 0.20/0.30 ! [X0 : $tType] : (((lList2281150353e_lrev @ X0 @ coinductive_LNil @ X0)) = coinductive_LNil @ X0)),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lrev__LNil)).
% 0.20/0.30 thf(f273,conjecture,(
% 0.20/0.30 (p @ (lList2281150353e_lrev @ a @ la))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.20/0.30 thf(f274,negated_conjecture,(
% 0.20/0.30 ~(p @ (lList2281150353e_lrev @ a @ la))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f273])).
% 0.20/0.30 thf(f275,plain,(
% 0.20/0.30 (p @ coinductive_LNil @ a)),
% 0.20/0.30 inference(rectify,[],[f1])).
% 0.20/0.30 thf(f276,plain,(
% 0.20/0.30 (((p @ coinductive_LNil @ a)) = $true)),
% 0.20/0.30 inference(fool_elimination,[],[f275])).
% 0.20/0.30 thf(f728,plain,(
% 0.20/0.30 ~(p @ (lList2281150353e_lrev @ a @ la))),
% 0.20/0.30 inference(rectify,[],[f274])).
% 0.20/0.30 thf(f729,plain,(
% 0.20/0.30 ~ (((p @ (lList2281150353e_lrev @ a @ la))) = $true)),
% 0.20/0.30 inference(fool_elimination,[],[f728])).
% 0.20/0.30 thf(f770,plain,(
% 0.20/0.30 (((p @ (lList2281150353e_lrev @ a @ la))) != $true)),
% 0.20/0.30 inference(flattening,[],[f729])).
% 0.20/0.30 thf(f1015,plain,(
% 0.20/0.30 (((p @ coinductive_LNil @ a)) = $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f276])).
% 0.20/0.30 thf(f1016,plain,(
% 0.20/0.30 (coinductive_LNil @ a = la)),
% 0.20/0.30 inference(cnf_transformation,[],[f2])).
% 0.20/0.30 thf(f1018,plain,(
% 0.20/0.30 ( ! [X0 : $tType] : ((coinductive_LNil @ X0 = ((lList2281150353e_lrev @ X0 @ coinductive_LNil @ X0)))) )),
% 0.20/0.30 inference(cnf_transformation,[],[f4])).
% 0.20/0.30 thf(f1376,plain,(
% 0.20/0.30 (((p @ (lList2281150353e_lrev @ a @ la))) != $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f770])).
% 0.20/0.30 thf(f2041,plain,(
% 0.20/0.30 ($true = ((p @ la)))),
% 0.20/0.30 inference(constrained_superposition,[],[f1015,f1016])).
% 0.20/0.30 thf(f2044,plain,(
% 0.20/0.30 (la = ((lList2281150353e_lrev @ a @ la)))),
% 0.20/0.30 inference(constrained_superposition,[],[f1018,f1016])).
% 0.20/0.30 thf(f2046,plain,(
% 0.20/0.30 ($true != ((p @ la)))),
% 0.20/0.30 inference(constrained_superposition,[],[f1376,f2044])).
% 0.20/0.30 thf(f2048,plain,(
% 0.20/0.30 ($true != $true)),
% 0.20/0.30 inference(constrained_superposition,[],[f2046,f2041])).
% 0.20/0.30 thf(f2049,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f2048])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (455767)------------------------------
% 0.20/0.30 % (455767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (455767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (455767)CaDiCaL version: 2.1.3
% 0.20/0.30 % (455767)Termination reason: Refutation
% 0.20/0.30 % (455767)Time elapsed: 0.036 s
% 0.20/0.30 % (455767)Peak memory usage: 14 MB
% 0.20/0.30 % (455767)Instructions burned: 143 (million)
% 0.20/0.30 % (455756)Success in time 0.078 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------