%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP074^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:10:36 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP074^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n014.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:47:30 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 0.20/0.28 % (3124819)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (3124826)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4259913141:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (3124825)% WARNING: option uhcvi not known.
% 0.20/0.28 % (3124824)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2213440652_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (3124825)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2307154719:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (3124827)dis+10_1_sil=32000:sp=arity:random_seed=40641787:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (3124828)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=246866746:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (3124825)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3124828)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (3124826) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3124819-3124826"...
% 0.20/0.28 % (3124826)...printing done.
% 0.20/0.28 % (3124826)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, hF_Mirabelle_hf: $tType).
% 0.20/0.28 thf(type_def_6, type, set: $tType > $tType).
% 0.20/0.28 thf(type_def_7, type, nat: $tType).
% 0.20/0.28 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_2, type, minus: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_4, type, group_add: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_5, type, lattice: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_6, type, semiring_1: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_8, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_9, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_10, type, semiring_1_cancel: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_11, type, distrib_lattice: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_12, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_13, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_15, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_16, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.20/0.28 thf(func_def_19, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.28 thf(func_def_20, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_21, type, hF_Mir1687042746ollect: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.28 thf(func_def_22, type, hF_Mirabelle_HF: (set @ hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.28 thf(func_def_23, type, hF_Mirabelle_HInter: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.28 thf(func_def_24, type, hF_Mirabelle_HUnion: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.28 thf(func_def_25, type, hF_Mir569462966eplace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_26, type, hF_Mirabelle_RepFun: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_27, type, hF_Mirabelle_Replace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_28, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_29, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set @ hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_30, type, hF_Mirabelle_hfst: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_31, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_32, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.20/0.29 thf(func_def_33, type, hF_Mirabelle_hpair: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_34, type, hF_Mirabelle_hsnd: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_35, type, hF_Mirabelle_hsplit: !>[X0: $tType]:(((hF_Mirabelle_hf > hF_Mirabelle_hf > X0) > hF_Mirabelle_hf > X0))).
% 0.20/0.29 thf(func_def_36, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.29 thf(func_def_37, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.29 thf(func_def_38, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.20/0.29 thf(func_def_39, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 0.20/0.29 thf(func_def_40, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_41, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.20/0.29 thf(func_def_42, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.20/0.29 thf(func_def_43, type, x: hF_Mirabelle_hf).
% 0.20/0.29 thf(func_def_44, type, y: hF_Mirabelle_hf).
% 0.20/0.29 thf(func_def_46, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.29 thf(func_def_47, type, vAND: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_53, type, vOR: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_55, type, vIMP: ($o > $o > $o)).
% 0.20/0.29 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.29 thf(func_def_57, type, vNOT: ($o > $o)).
% 0.20/0.29 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_59, type, sK0: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_60, type, sK1: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_61, type, sK2: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_62, type, sK3: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_63, type, sK4: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_64, type, sK5: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_65, type, sK6: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_66, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.29 thf(func_def_67, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.29 thf(func_def_68, type, sK9: ((hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_69, type, sK10: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_70, type, sK11: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_71, type, sK12: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_72, type, sK13: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_73, type, sK14: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_74, type, sK15: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_75, type, sK16: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_76, type, sK17: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_77, type, sK18: ((hF_Mirabelle_hf > hF_Mirabelle_hf) > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_78, type, sK19: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_79, type, sK20: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_80, type, sK21: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_81, type, sK22: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_82, type, sK23: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_83, type, sK24: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_84, type, sK25: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_85, type, sK26: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_86, type, sK27: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_87, type, sK28: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_88, type, sK29: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_89, type, sK30: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_90, type, sK31: ((nat > $o) > nat)).
% 0.20/0.29 thf(func_def_91, type, sK32: (nat > (nat > $o) > nat)).
% 0.20/0.29 thf(func_def_92, type, sK33: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_93, type, sK34: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_94, type, sK35: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_95, type, sK36: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_96, type, sK37: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_97, type, sK38: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_98, type, sK39: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_99, type, sK40: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_100, type, sK41: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_101, type, sK42: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_102, type, sK43: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_103, type, sK44: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_104, type, sK45: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_105, type, sK46: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.20/0.29 thf(func_def_106, type, sK47: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_107, type, sK48: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_108, type, sK49: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_109, type, sK50: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_110, type, sK51: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_111, type, sK52: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_112, type, sK53: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_113, type, sK54: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_114, type, sK55: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_115, type, sK56: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_116, type, sK57: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_117, type, sK58: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_118, type, sK59: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_119, type, sK60: (hF_Mirabelle_hf > hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_120, type, sK61: (hF_Mirabelle_hf > hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_121, type, sK62: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_122, type, sK63: (hF_Mirabelle_hf > hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.20/0.29 thf(func_def_123, type, sK64: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.29 thf(f14,axiom,(
% 0.20/0.29 (hF_Mirabelle_hpair = (^[X0 : hF_Mirabelle_hf, X1 : hF_Mirabelle_hf] : ((hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ X0 @ zero_zero @ hF_Mirabelle_hf) @ (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ X0 @ (hF_Mirabelle_hinsert @ X1 @ zero_zero @ hF_Mirabelle_hf)) @ zero_zero @ hF_Mirabelle_hf)))))),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_hpair__def)).
% 0.20/0.29 thf(f19,axiom,(
% 0.20/0.29 ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (((hF_Mirabelle_hinsert @ X0 @ X1)) != zero_zero @ hF_Mirabelle_hf)),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_hinsert__nonempty)).
% 0.20/0.29 thf(f300,conjecture,(
% 0.20/0.29 (((hF_Mirabelle_hpair @ x @ y)) != zero_zero @ hF_Mirabelle_hf)),
% 0.20/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.20/0.29 thf(f301,negated_conjecture,(
% 0.20/0.29 ~ (((hF_Mirabelle_hpair @ x @ y)) != zero_zero @ hF_Mirabelle_hf)),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f300])).
% 0.20/0.29 thf(f306,plain,(
% 0.20/0.29 (hF_Mirabelle_hpair = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ Y0 @ zero_zero @ hF_Mirabelle_hf) @ (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ Y0 @ (hF_Mirabelle_hinsert @ Y1 @ zero_zero @ hF_Mirabelle_hf)) @ zero_zero @ hF_Mirabelle_hf))))))),
% 0.20/0.29 inference(fool_elimination,[],[f14])).
% 0.20/0.29 thf(f821,plain,(
% 0.20/0.29 (zero_zero @ hF_Mirabelle_hf = ((hF_Mirabelle_hpair @ x @ y)))),
% 0.20/0.29 inference(flattening,[],[f301])).
% 0.20/0.29 thf(f1078,plain,(
% 0.20/0.29 (hF_Mirabelle_hpair = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ Y0 @ zero_zero @ hF_Mirabelle_hf) @ (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ Y0 @ (hF_Mirabelle_hinsert @ Y1 @ zero_zero @ hF_Mirabelle_hf)) @ zero_zero @ hF_Mirabelle_hf))))))),
% 0.20/0.29 inference(cnf_transformation,[],[f306])).
% 0.20/0.29 thf(f1083,plain,(
% 0.20/0.29 ( ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf != ((hF_Mirabelle_hinsert @ X0 @ X1)))) )),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f1395,plain,(
% 0.20/0.29 (zero_zero @ hF_Mirabelle_hf = ((hF_Mirabelle_hpair @ x @ y)))),
% 0.20/0.29 inference(cnf_transformation,[],[f821])).
% 0.20/0.29 thf(f1457,plain,(
% 0.20/0.29 (zero_zero @ hF_Mirabelle_hf = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ Y0 @ zero_zero @ hF_Mirabelle_hf) @ (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ Y0 @ (hF_Mirabelle_hinsert @ Y1 @ zero_zero @ hF_Mirabelle_hf)) @ zero_zero @ hF_Mirabelle_hf))))) @ x @ y)))),
% 0.20/0.29 inference(definition_unfolding,[],[f1395,f1078])).
% 0.20/0.29 thf(f1471,plain,(
% 0.20/0.29 (zero_zero @ hF_Mirabelle_hf = ((hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ x @ zero_zero @ hF_Mirabelle_hf) @ (hF_Mirabelle_hinsert @ (hF_Mirabelle_hinsert @ x @ (hF_Mirabelle_hinsert @ y @ zero_zero @ hF_Mirabelle_hf)) @ zero_zero @ hF_Mirabelle_hf))))),
% 0.20/0.29 inference(beta-eta_normalization,[],[f1457])).
% 0.20/0.29 thf(f1917,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f1471,f1083])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (3124826)------------------------------
% 0.20/0.29 % (3124826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3124826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3124826)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3124826)Termination reason: Refutation
% 0.20/0.29 % (3124826)Time elapsed: 0.022 s
% 0.20/0.29 % (3124826)Peak memory usage: 13 MB
% 0.20/0.29 % (3124826)Instructions burned: 92 (million)
% 0.20/0.29 % (3124819)Success in time 0.061 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------