%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP075^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP075^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n007.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 19:45:41 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.34 % (3832293)Will run a generic schedule for satisfiability detection.
% 0.20/0.34 % (3832313)dis+10_1_sil=32000:sp=arity:random_seed=1288147126:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.34 % (3832311)% WARNING: option uhcvi not known.
% 0.20/0.34 % (3832310)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2135841658_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.34 % (3832311)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1071394987:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.34 % (3832312)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3399599683:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.34 % (3832316)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1633714761:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.34 % (3832314)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=131799994:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.34 % (3832315)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1951730962:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (3832311)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % (3832314)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.34 % (3832313)Instruction limit reached!
% 0.20/0.34 % (3832313)------------------------------
% 0.20/0.34 % (3832313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3832313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3832313)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3832313)Termination reason: Instruction limit
% 0.20/0.34 % (3832313)Termination phase: Saturation
% 0.20/0.34 % (3832313)Time elapsed: 0.024 s
% 0.20/0.34 % (3832313)Peak memory usage: 12 MB
% 0.20/0.34 % (3832313)Instructions burned: 104 (million)
% 0.20/0.34 % (3832347)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1672946122:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (3832311)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.34 % Exception at run slice level
% 0.20/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.34 % (3832358)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2707238711:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.34 % (3832314)Instruction limit reached!
% 0.20/0.34 % (3832314)------------------------------
% 0.20/0.34 % (3832314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3832314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3832314)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3832314)Termination reason: Instruction limit
% 0.20/0.34 % (3832314)Termination phase: Saturation
% 0.20/0.34 % (3832314)Time elapsed: 0.051 s
% 0.20/0.34 % (3832314)Peak memory usage: 13 MB
% 0.20/0.34 % (3832314)Instructions burned: 117 (million)
% 0.20/0.34 % (3832311) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3832293-3832311"...
% 0.20/0.34 % (3832311)...printing done.
% 0.20/0.34 % (3832315)Instruction limit reached!
% 0.20/0.34 % (3832315)------------------------------
% 0.20/0.34 % (3832315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3832315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3832315)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3832315)Termination reason: Instruction limit
% 0.20/0.34 % (3832315)Termination phase: Saturation
% 0.20/0.34 % (3832315)Time elapsed: 0.058 s
% 0.20/0.34 % (3832315)Peak memory usage: 13 MB
% 0.20/0.34 % (3832311)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% 0.20/0.34 thf(type_def_5, type, hF_Mirabelle_hf: $tType).
% 0.20/0.34 thf(type_def_6, type, set: $tType > $tType).
% 0.20/0.34 thf(type_def_7, type, nat: $tType).
% 0.20/0.34 thf(type_def_8, type, int: $tType).
% 0.20/0.34 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.34 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_3, type, minus: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_4, type, bot: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_5, type, group_add: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_6, type, lattice: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_7, type, semiring_1: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_8, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_9, type, order_bot: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_10, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_11, type, semilattice_inf: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_12, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_13, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_14, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_16, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_17, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.20/0.34 thf(func_def_18, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_19, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_20, type, hF_Mirabelle_HBall: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > $o)).
% 0.20/0.34 thf(func_def_21, type, hF_Mirabelle_HBex: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > $o)).
% 0.20/0.34 thf(func_def_22, type, hF_Mir1687042746ollect: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_23, type, hF_Mirabelle_HF: (set @ hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_24, type, hF_Mirabelle_HInter: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_25, type, hF_Mirabelle_HUnion: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_26, type, hF_Mir569462966eplace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_27, type, hF_Mirabelle_RepFun: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_28, type, hF_Mirabelle_Replace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_29, type, hF_Mirabelle_hcard: (hF_Mirabelle_hf > nat)).
% 0.20/0.34 thf(func_def_30, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_31, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set @ hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_32, type, hF_Mirabelle_hfst: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_33, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_34, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.20/0.34 thf(func_def_35, type, hF_Mirabelle_hpair: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_36, type, hF_Mirabelle_hsnd: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_37, type, hF_Mirabelle_hsplit: !>[X0: $tType]:(((hF_Mirabelle_hf > hF_Mirabelle_hf > X0) > hF_Mirabelle_hf > X0))).
% 0.20/0.34 thf(func_def_38, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_39, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_40, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.20/0.34 thf(func_def_41, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.20/0.34 thf(func_def_42, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_43, type, least: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_44, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.34 thf(func_def_45, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.20/0.34 thf(func_def_46, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.20/0.34 thf(func_def_47, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.20/0.34 thf(func_def_48, type, a: hF_Mirabelle_hf).
% 0.20/0.34 thf(func_def_49, type, p: $o).
% 0.20/0.34 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_55, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.34 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.34 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.34 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_59, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.34 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 0.20/0.34 thf(func_def_61, type, vOR: ($o > $o > $o)).
% 0.20/0.34 thf(func_def_62, type, vNOT: ($o > $o)).
% 0.20/0.34 thf(func_def_63, type, vIMP: ($o > $o > $o)).
% 0.20/0.34 thf(func_def_64, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_65, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.34 thf(func_def_66, type, sK0: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_67, type, sK1: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_68, type, sK2: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_69, type, sK3: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_70, type, sK4: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_71, type, sK5: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_72, type, sK6: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_73, type, sK7: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_74, type, sK8: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_75, type, sK9: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_76, type, sK10: ((hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_77, type, sK11: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_78, type, sK12: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_79, type, sK13: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_80, type, sK14: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_81, type, sK15: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_82, type, sK16: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_83, type, sK17: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_84, type, sK18: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_85, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.20/0.34 thf(func_def_86, type, sK20: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_87, type, sK21: ((hF_Mirabelle_hf > hF_Mirabelle_hf) > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_88, type, sK22: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_89, type, sK23: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_90, type, sK24: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_91, type, sK25: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_92, type, sK26: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_93, type, sK27: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_94, type, sK28: !>[X0: $tType]:((set @ X0 > X0))).
% 0.20/0.34 thf(func_def_95, type, sK29: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.20/0.34 thf(func_def_96, type, sK30: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_97, type, sK31: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_98, type, sK32: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_99, type, sK33: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_100, type, sK34: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_101, type, sK35: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_102, type, sK36: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_103, type, sK37: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_104, type, sK38: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.20/0.34 thf(func_def_105, type, sK39: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.20/0.34 thf(func_def_106, type, sK40: ((nat > $o) > nat)).
% 0.20/0.34 thf(func_def_107, type, sK41: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.20/0.34 thf(func_def_108, type, sK42: (int > nat)).
% 0.20/0.34 thf(func_def_109, type, sK43: (int > nat)).
% 0.20/0.34 thf(func_def_110, type, sK44: (int > nat)).
% 0.20/0.34 thf(func_def_111, type, sK45: (int > nat)).
% 0.20/0.34 thf(func_def_112, type, sK46: hF_Mirabelle_hf).
% 0.20/0.34 thf(func_def_113, type, sK47: hF_Mirabelle_hf).
% 0.20/0.34 thf(func_def_114, type, sK48: hF_Mirabelle_hf).
% 0.20/0.34 thf(func_def_115, type, sK49: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.20/0.34 thf(func_def_116, type, sK50: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.20/0.34 thf(func_def_117, type, sK51: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.20/0.34 thf(func_def_118, type, sK52: !>[X0: $tType]:((set @ X0 > X0))).
% 0.20/0.34 thf(func_def_119, type, sK53: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_120, type, sK54: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.20/0.34 thf(func_def_121, type, sK55: !>[X0: $tType]:((set @ X0 > X0))).
% 0.20/0.34 thf(func_def_122, type, sK56: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_123, type, sK57: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_124, type, sK58: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_125, type, sK59: (hF_Mirabelle_hf > hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_126, type, sK60: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_127, type, sK61: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_128, type, sK62: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_129, type, sK63: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_130, type, sK64: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_131, type, sK65: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_132, type, sK66: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_133, type, sK67: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_134, type, sK68: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_135, type, sK69: (hF_Mirabelle_hf > hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_136, type, sK70: (hF_Mirabelle_hf > hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_137, type, sK71: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_138, type, sK72: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_139, type, sK73: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_140, type, sK74: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_141, type, sK75: ($o > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_142, type, sK76: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_143, type, sK77: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_144, type, sK78: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_145, type, sK79: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_146, type, sK80: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_147, type, sK81: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_148, type, sK82: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_149, type, sK83: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_150, type, sK84: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_151, type, sK85: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_152, type, sK86: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_153, type, sK87: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_154, type, sK88: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_155, type, sK89: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_156, type, sK90: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_157, type, sK91: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(func_def_158, type, sK92: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.20/0.34 thf(f6,axiom,(
% 0.20/0.34 (hF_Mirabelle_HBex = (^[X0 : hF_Mirabelle_hf, X1 : (hF_Mirabelle_hf > $o)] : (? [X2 : hF_Mirabelle_hf] : ((X1 @ X2) & (hF_Mirabelle_hmem @ X2 @ X0)))))),
% 0.20/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_HBex__def)).
% 0.20/0.34 thf(f39,axiom,(
% 0.20/0.34 (hF_Mirabelle_hmem = (^[X0 : hF_Mirabelle_hf, X1 : hF_Mirabelle_hf] : ((member @ hF_Mirabelle_hf @ X0 @ (hF_Mirabelle_hfset @ X1)))))),
% 0.20/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_hmem__def)).
% 0.20/0.34 thf(f310,conjecture,(
% 0.20/0.34 (((hF_Mirabelle_HBex @ a @ (^[X0 : hF_Mirabelle_hf] : (p)))) = p & ? [X0 : hF_Mirabelle_hf] : (hF_Mirabelle_hmem @ X0 @ a))),
% 0.20/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.20/0.34 thf(f311,negated_conjecture,(
% 0.20/0.34 ~ (((hF_Mirabelle_HBex @ a @ (^[X0 : hF_Mirabelle_hf] : (p)))) = p & ? [X0 : hF_Mirabelle_hf] : (hF_Mirabelle_hmem @ X0 @ a))),
% 0.20/0.34 inference(negated_conjecture,[status(cth)],[f310])).
% 0.20/0.34 thf(f319,plain,(
% 0.20/0.34 (hF_Mirabelle_HBex = (^[X0 : hF_Mirabelle_hf, X1 : (hF_Mirabelle_hf > $o)] : (? [X2 : hF_Mirabelle_hf] : ((X1 @ X2) & (hF_Mirabelle_hmem @ X2 @ X0)))))),
% 0.20/0.34 inference(rectify,[],[f6])).
% 0.20/0.34 thf(f320,plain,(
% 0.20/0.34 (hF_Mirabelle_HBex = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ Y2 @ Y0) & (Y1 @ Y2))))))))),
% 0.20/0.34 inference(fool_elimination,[],[f319])).
% 0.20/0.34 thf(f381,plain,(
% 0.20/0.34 (hF_Mirabelle_hmem = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))))),
% 0.20/0.34 inference(fool_elimination,[],[f39])).
% 0.20/0.34 thf(f798,plain,(
% 0.20/0.34 ~ (((hF_Mirabelle_HBex @ a @ (^[X0 : hF_Mirabelle_hf] : (p)))) = p & ? [X1 : hF_Mirabelle_hf] : (hF_Mirabelle_hmem @ X1 @ a))),
% 0.20/0.34 inference(rectify,[],[f311])).
% 0.20/0.34 thf(f799,plain,(
% 0.20/0.34 ~ (((hF_Mirabelle_HBex @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)))),
% 0.20/0.34 inference(fool_elimination,[],[f798])).
% 0.20/0.34 thf(f834,plain,(
% 0.20/0.34 (((hF_Mirabelle_HBex @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) != (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)))),
% 0.20/0.34 inference(flattening,[],[f799])).
% 0.20/0.34 thf(f1044,plain,(
% 0.20/0.34 (hF_Mirabelle_HBex = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((hF_Mirabelle_hmem @ Y2 @ Y0) & (Y1 @ Y2))))))))),
% 0.20/0.34 inference(cnf_transformation,[],[f320])).
% 0.20/0.34 thf(f1089,plain,(
% 0.20/0.34 (hF_Mirabelle_hmem = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))))),
% 0.20/0.34 inference(cnf_transformation,[],[f381])).
% 0.20/0.34 thf(f1396,plain,(
% 0.20/0.34 (((hF_Mirabelle_HBex @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) != (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)))),
% 0.20/0.34 inference(cnf_transformation,[],[f834])).
% 0.20/0.34 thf(f1402,plain,(
% 0.20/0.34 (hF_Mirabelle_HBex = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))))),
% 0.20/0.34 inference(definition_unfolding,[],[f1044,f1089])).
% 0.20/0.34 thf(f1494,plain,(
% 0.20/0.34 ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) != (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a))) & p)))),
% 0.20/0.34 inference(definition_unfolding,[],[f1396,f1402,f1089])).
% 0.20/0.34 thf(f1511,plain,(
% 0.20/0.34 ($true = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | ($true = (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a))) & p)))),
% 0.20/0.34 inference(xor_proxy_clausification,[],[f1494])).
% 0.20/0.34 thf(f1512,plain,(
% 0.20/0.34 ($false = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | ($false = (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a))) & p)))),
% 0.20/0.34 inference(xor_proxy_clausification,[],[f1494])).
% 0.20/0.34 thf(f1513,plain,(
% 0.20/0.34 ($false = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | (p = $false) | ($false = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a)))))),
% 0.20/0.34 inference(and_proxy_clausification,[],[f1512])).
% 0.20/0.34 thf(f1514,plain,(
% 0.20/0.34 ( ! [X1 : hF_Mirabelle_hf] : (($false = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | (p = $false) | ($false = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a)) @ X1)))) )),
% 0.20/0.34 inference(pi_proxy_clausification,[],[f1513])).
% 0.20/0.34 thf(f1515,plain,(
% 0.20/0.34 ( ! [X1 : hF_Mirabelle_hf] : (($false = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) & p))))) | (p = $false) | ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ a))))) )),
% 0.20/0.34 inference(beta-eta_normalization,[],[f1514])).
% 0.20/0.34 thf(f1516,plain,(
% 0.20/0.34 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = (((^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) & p)) @ X2))) | (p = $false) | ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ a))))) )),
% 0.20/0.34 inference(pi_proxy_clausification,[],[f1515])).
% 0.20/0.34 thf(f1517,plain,(
% 0.20/0.34 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($false = (((member @ hF_Mirabelle_hf @ X2 @ (hF_Mirabelle_hfset @ a)) & p))) | (p = $false) | ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ a))))) )),
% 0.20/0.34 inference(beta-eta_normalization,[],[f1516])).
% 0.20/0.34 thf(f1518,plain,(
% 0.20/0.34 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((p = $false) | (p = $false) | ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ a)))) | ($false = ((member @ hF_Mirabelle_hf @ X2 @ (hF_Mirabelle_hfset @ a))))) )),
% 0.20/0.34 inference(and_proxy_clausification,[],[f1517])).
% 0.20/0.34 thf(f1519,plain,(
% 0.20/0.34 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((p = $false) | ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ a)))) | ($false = ((member @ hF_Mirabelle_hf @ X2 @ (hF_Mirabelle_hfset @ a))))) )),
% 0.20/0.34 inference(duplicate_literal_removal,[],[f1518])).
% 0.20/0.34 thf(f1520,plain,(
% 0.20/0.34 ($true = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | (p = $true)),
% 0.20/0.34 inference(and_proxy_clausification,[],[f1511])).
% 0.20/0.34 thf(f1521,plain,(
% 0.20/0.34 ($true = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | ($true = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a)))))),
% 0.20/0.34 inference(and_proxy_clausification,[],[f1511])).
% 0.20/0.34 thf(f1522,plain,(
% 0.20/0.34 ($true = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: (((^[Y3 : hF_Mirabelle_hf]: ((^[Y4 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y3 @ (hF_Mirabelle_hfset @ Y4))))) @ Y2 @ Y0) & (Y1 @ Y2))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p))))) | ($true = (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ a)) @ sK46)))),
% 0.20/0.34 inference(sigma_proxy_clausification,[],[f1521])).
% 0.20/0.34 thf(f1523,plain,(
% 0.20/0.34 ($true = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) & p))))) | ($true = ((member @ hF_Mirabelle_hf @ sK46 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 inference(beta-eta_normalization,[],[f1522])).
% 0.20/0.34 thf(f1524,plain,(
% 0.20/0.34 ($true = (((^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) & p)) @ sK47))) | ($true = ((member @ hF_Mirabelle_hf @ sK46 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 inference(sigma_proxy_clausification,[],[f1523])).
% 0.20/0.34 thf(f1525,plain,(
% 0.20/0.34 ($true = (((member @ hF_Mirabelle_hf @ sK47 @ (hF_Mirabelle_hfset @ a)) & p))) | ($true = ((member @ hF_Mirabelle_hf @ sK46 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 inference(beta-eta_normalization,[],[f1524])).
% 0.20/0.34 thf(f1527,plain,(
% 0.20/0.34 ($true = ((member @ hF_Mirabelle_hf @ sK47 @ (hF_Mirabelle_hfset @ a)))) | ($true = ((member @ hF_Mirabelle_hf @ sK46 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 inference(and_proxy_clausification,[],[f1525])).
% 0.20/0.34 thf(f1528,plain,(
% 0.20/0.34 ($true = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) & p))))) | (p = $true)),
% 0.20/0.34 inference(beta-eta_normalization,[],[f1520])).
% 0.20/0.34 thf(f1529,plain,(
% 0.20/0.34 ($true = (((^[Y0 : hF_Mirabelle_hf]: ((member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ a)) & p)) @ sK48))) | (p = $true)),
% 0.20/0.34 inference(sigma_proxy_clausification,[],[f1528])).
% 0.20/0.34 thf(f1530,plain,(
% 0.20/0.34 ($true = (((member @ hF_Mirabelle_hf @ sK48 @ (hF_Mirabelle_hfset @ a)) & p))) | (p = $true)),
% 0.20/0.34 inference(beta-eta_normalization,[],[f1529])).
% 0.20/0.34 thf(f1531,plain,(
% 0.20/0.34 (p = $true) | (p = $true)),
% 0.20/0.34 inference(and_proxy_clausification,[],[f1530])).
% 0.20/0.34 thf(f1533,plain,(
% 0.20/0.34 (p = $true)),
% 0.20/0.34 inference(duplicate_literal_removal,[],[f1531])).
% 0.20/0.34 thf(f2222,definition,(
% 0.20/0.34 spl93_1 <=> ! [X2 : hF_Mirabelle_hf] : ($false = ((member @ hF_Mirabelle_hf @ X2 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 introduced(definition,[new_symbols(definition,[spl93_1])],[avatar_definition])).
% 0.20/0.34 thf(f2223,plain,(
% 0.20/0.34 ( ! [X2 : hF_Mirabelle_hf] : (($false = ((member @ hF_Mirabelle_hf @ X2 @ (hF_Mirabelle_hfset @ a))))) ) | ~spl93_1),
% 0.20/0.34 inference(avatar_component_clause,[],[f2222])).
% 0.20/0.34 thf(f2225,definition,(
% 0.20/0.34 spl93_2 <=> (p = $false)),
% 0.20/0.34 introduced(definition,[new_symbols(definition,[spl93_2])],[avatar_definition])).
% 0.20/0.34 thf(f2227,plain,(
% 0.20/0.34 (p = $false) | ~spl93_2),
% 0.20/0.34 inference(avatar_component_clause,[],[f2225])).
% 0.20/0.34 thf(f2228,plain,(
% 0.20/0.34 spl93_1 | spl93_1 | spl93_2),
% 0.20/0.34 inference(avatar_split_clause,[],[f1519,f2225,f2222,f2222])).
% 0.20/0.34 thf(f2230,definition,(
% 0.20/0.34 spl93_3 <=> ($true = ((member @ hF_Mirabelle_hf @ sK46 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 introduced(definition,[new_symbols(definition,[spl93_3])],[avatar_definition])).
% 0.20/0.34 thf(f2232,plain,(
% 0.20/0.34 ($true = ((member @ hF_Mirabelle_hf @ sK46 @ (hF_Mirabelle_hfset @ a)))) | ~spl93_3),
% 0.20/0.34 inference(avatar_component_clause,[],[f2230])).
% 0.20/0.34 thf(f2234,definition,(
% 0.20/0.34 spl93_4 <=> ($true = ((member @ hF_Mirabelle_hf @ sK47 @ (hF_Mirabelle_hfset @ a))))),
% 0.20/0.34 introduced(definition,[new_symbols(definition,[spl93_4])],[avatar_definition])).
% 0.20/0.34 thf(f2236,plain,(
% 0.20/0.34 ($true = ((member @ hF_Mirabelle_hf @ sK47 @ (hF_Mirabelle_hfset @ a)))) | ~spl93_4),
% 0.20/0.34 inference(avatar_component_clause,[],[f2234])).
% 0.20/0.34 thf(f2237,plain,(
% 0.20/0.34 spl93_3 | spl93_4),
% 0.20/0.34 inference(avatar_split_clause,[],[f1527,f2234,f2230])).
% 0.20/0.34 thf(f2239,definition,(
% 0.20/0.34 spl93_5 <=> (p = $true)),
% 0.20/0.34 introduced(definition,[new_symbols(definition,[spl93_5])],[avatar_definition])).
% 0.20/0.34 thf(f2241,plain,(
% 0.20/0.34 (p = $true) | ~spl93_5),
% 0.20/0.34 inference(avatar_component_clause,[],[f2239])).
% 0.20/0.34 thf(f2248,plain,(
% 0.20/0.34 spl93_5),
% 0.20/0.34 inference(avatar_split_clause,[],[f1533,f2239])).
% 0.20/0.34 thf(f2265,plain,(
% 0.20/0.34 ($true = $false) | (~spl93_2 | ~spl93_5)),
% 0.20/0.34 inference(forward_demodulation,[],[f2241,f2227])).
% 0.20/0.34 thf(f2266,plain,(
% 0.20/0.34 $false | (~spl93_2 | ~spl93_5)),
% 0.20/0.34 inference(trivial_inequality_removal,[],[f2265])).
% 0.20/0.34 thf(f2267,plain,(
% 0.20/0.34 ~spl93_2 | ~spl93_5),
% 0.20/0.34 inference(avatar_contradiction_clause,[],[f2266])).
% 0.20/0.34 thf(f2269,plain,(
% 0.20/0.34 ($true = $false) | (~spl93_1 | ~spl93_3)),
% 0.20/0.34 inference(forward_demodulation,[],[f2232,f2223])).
% 0.20/0.34 thf(f2270,plain,(
% 0.20/0.34 $false | (~spl93_1 | ~spl93_3)),
% 0.20/0.34 inference(trivial_inequality_removal,[],[f2269])).
% 0.20/0.34 thf(f2271,plain,(
% 0.20/0.34 ~spl93_1 | ~spl93_3),
% 0.20/0.34 inference(avatar_contradiction_clause,[],[f2270])).
% 0.20/0.34 thf(f2273,plain,(
% 0.20/0.34 ($true = $false) | (~spl93_1 | ~spl93_4)),
% 0.20/0.34 inference(forward_demodulation,[],[f2236,f2223])).
% 0.20/0.34 thf(f2274,plain,(
% 0.20/0.34 $false | (~spl93_1 | ~spl93_4)),
% 0.20/0.34 inference(trivial_inequality_removal,[],[f2273])).
% 0.20/0.34 thf(f2275,plain,(
% 0.20/0.34 ~spl93_1 | ~spl93_4),
% 0.20/0.34 inference(avatar_contradiction_clause,[],[f2274])).
% 0.20/0.34 cnf(s1, plain, spl93_1 | spl93_1 | spl93_2, inference(sat_conversion,[],[f2228])).
% 0.20/0.34 cnf(s2, plain, spl93_1 | spl93_2, inference(rat,[],[s1])).
% 0.20/0.34 cnf(s3, plain, spl93_3 | spl93_4, inference(sat_conversion,[],[f2237])).
% 0.20/0.34 cnf(s6, plain, spl93_5, inference(sat_conversion,[],[f2248])).
% 0.20/0.34 cnf(s11, plain, ~spl93_2 | ~spl93_5, inference(sat_conversion,[],[f2267])).
% 0.20/0.34 cnf(s12, plain, ~spl93_1 | ~spl93_3, inference(sat_conversion,[],[f2271])).
% 0.20/0.34 cnf(s13, plain, ~spl93_1 | ~spl93_4, inference(sat_conversion,[],[f2275])).
% 0.20/0.34 cnf(s14, plain, ~spl93_2, inference(rat,[],[s11,s6])).
% 0.20/0.34 cnf(s15, plain, spl93_1, inference(rat,[],[s2,s14])).
% 0.20/0.34 cnf(s16, plain, ~spl93_4, inference(rat,[],[s13,s15])).
% 0.20/0.34 cnf(s17, plain, ~spl93_3, inference(rat,[],[s12,s15])).
% 0.20/0.34 cnf(s18, plain, $false, inference(rat,[],[s3,s16,s17])).
% 0.20/0.34 thf(f2276,plain,(
% 0.20/0.34 $false),
% 0.20/0.34 inference(avatar_sat_refutation,[],[s18])).
% 0.20/0.34 % SZS output end Proof for theBenchmark
% 0.20/0.34 % (3832311)------------------------------
% 0.20/0.34 % (3832311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3832311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3832311)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3832311)Termination reason: Refutation
% 0.20/0.34 % (3832311)Time elapsed: 0.054 s
% 0.20/0.34 % (3832311)Peak memory usage: 14 MB
% 0.20/0.34 % (3832311)Instructions burned: 121 (million)
% 0.20/0.34 % (3832293)Success in time 0.115 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------