%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP072^2 : 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 08:10:35 AM UTC 2026
% Result : Theorem 0.73s 0.36s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP072^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n007.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:45:11 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.73/0.36 % (3830614)Will run a generic schedule for satisfiability detection.
% 0.73/0.36 % (3830637)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=454943129_2999 on theBenchmark for (2999ds/0Mi)
% 0.73/0.36 % (3830638)% WARNING: option uhcvi not known.
% 0.73/0.36 % (3830639)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3811770689:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.73/0.36 % (3830638)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=34628071:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.73/0.36 % (3830643)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2991786386:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.73/0.36 % (3830640)dis+10_1_sil=32000:sp=arity:random_seed=1811401348:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.73/0.36 % (3830641)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=526081566:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.73/0.36 % (3830644)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=619921746:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.73/0.36 % Exception at run slice level
% 0.73/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.73/0.36 % (3830638)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.73/0.36 % (3830641)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.73/0.36 % (3830670)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=267726848:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.73/0.36 % (3830638)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.73/0.36 % Exception at run slice level
% 0.73/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.73/0.36 % (3830640)Instruction limit reached!
% 0.73/0.36 % (3830640)------------------------------
% 0.73/0.36 % (3830640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.36 % (3830640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.36 % (3830640)CaDiCaL version: 2.1.3
% 0.73/0.36 % (3830640)Termination reason: Instruction limit
% 0.73/0.36 % (3830640)Termination phase: Saturation
% 0.73/0.36 % (3830640)Time elapsed: 0.046 s
% 0.73/0.36 % (3830640)Peak memory usage: 12 MB
% 0.73/0.36 % (3830640)Instructions burned: 105 (million)
% 0.73/0.36 % (3830641)Instruction limit reached!
% 0.73/0.36 % (3830641)------------------------------
% 0.73/0.36 % (3830641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.36 % (3830641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.36 % (3830641)CaDiCaL version: 2.1.3
% 0.73/0.36 % (3830641)Termination reason: Instruction limit
% 0.73/0.36 % (3830641)Termination phase: Saturation
% 0.73/0.36 % (3830641)Time elapsed: 0.052 s
% 0.73/0.36 % (3830641)Peak memory usage: 13 MB
% 0.73/0.36 % (3830641)Instructions burned: 116 (million)
% 0.73/0.36 % (3830677)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=231363162:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.73/0.36 % (3830643)Instruction limit reached!
% 0.73/0.36 % (3830643)------------------------------
% 0.73/0.36 % (3830643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.36 % (3830643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.36 % (3830643)CaDiCaL version: 2.1.3
% 0.73/0.36 % (3830643)Termination reason: Instruction limit
% 0.73/0.36 % (3830643)Termination phase: Saturation
% 0.73/0.36 % (3830643)Time elapsed: 0.060 s
% 0.73/0.36 % (3830643)Peak memory usage: 13 MB
% 0.73/0.36 % (3830643)Instructions burned: 133 (million)
% 0.73/0.36 % (3830678)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3431052902:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.73/0.36 % (3830680)ott-21_1_sil=16000:fs=off:random_seed=1448775356:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.73/0.36 % (3830644)Instruction limit reached!
% 0.73/0.36 % (3830644)------------------------------
% 0.73/0.36 % (3830644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.36 % (3830644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.36 % (3830644)CaDiCaL version: 2.1.3
% 0.73/0.36 % (3830644)Termination reason: Instruction limit
% 0.73/0.36 % (3830644)Termination phase: Saturation
% 0.73/0.36 % (3830644)Time elapsed: 0.076 s
% 0.73/0.36 % (3830644)Peak memory usage: 14 MB
% 0.73/0.36 % (3830644)Instructions burned: 161 (million)
% 0.73/0.36 % (3830681)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1150961335:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.73/0.36 % (3830678)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.73/0.36 % (3830638) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3830614-3830638"...
% 0.73/0.36 % (3830677)Instruction limit reached!
% 0.73/0.36 % (3830677)------------------------------
% 0.73/0.36 % (3830677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.36 % (3830677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.36 % (3830677)CaDiCaL version: 2.1.3
% 0.73/0.36 % (3830677)Termination reason: Instruction limit
% 0.73/0.36 % (3830677)Termination phase: Saturation
% 0.73/0.36 % (3830677)Time elapsed: 0.032 s
% 0.73/0.36 % (3830677)Peak memory usage: 13 MB
% 0.73/0.36 % (3830677)Instructions burned: 133 (million)
% 0.73/0.36 % (3830638)...printing done.
% 0.73/0.36 % (3830638)Refutation found. Thanks to Tanya!
% 0.73/0.36 % SZS status Theorem for theBenchmark
% 0.73/0.36 % SZS output start Proof for theBenchmark
% 0.73/0.36 thf(type_def_5, type, hF_Mirabelle_hf: $tType).
% 0.73/0.36 thf(type_def_6, type, set: $tType > $tType).
% 0.73/0.36 thf(type_def_7, type, nat: $tType).
% 0.73/0.36 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.73/0.36 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_4, type, neg_numeral: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_7, type, semiring_1: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_8, type, finite_finite: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_11, type, order_bot: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_12, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_13, type, semiring_bit_shifts: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_15, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_16, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_19, type, unique788075200shifts: !>[X0: $tType]:($o)).
% 0.73/0.36 thf(func_def_20, type, finite_card: !>[X0: $tType]:((set @ X0 > nat))).
% 0.73/0.36 thf(func_def_21, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.73/0.36 thf(func_def_22, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.73/0.36 thf(func_def_23, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.73/0.36 thf(func_def_24, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.73/0.36 thf(func_def_25, type, hF_Mirabelle_HF: (set @ hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.73/0.36 thf(func_def_26, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)).
% 0.73/0.36 thf(func_def_27, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set @ hF_Mirabelle_hf)).
% 0.73/0.36 thf(func_def_28, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.73/0.36 thf(func_def_29, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.73/0.36 thf(func_def_30, type, lattic1704895705min_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_31, type, semiring_1_Nats: !>[X0: $tType]:(set @ X0)).
% 0.73/0.36 thf(func_def_32, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 0.73/0.36 thf(func_def_33, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 0.73/0.36 thf(func_def_34, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.73/0.36 thf(func_def_35, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.73/0.36 thf(func_def_36, type, semiri2097166173op_bit: !>[X0: $tType]:((nat > X0 > X0))).
% 0.73/0.36 thf(func_def_37, type, semiri1924326578sh_bit: !>[X0: $tType]:((nat > X0 > X0))).
% 0.73/0.36 thf(func_def_38, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.73/0.36 thf(func_def_39, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.73/0.36 thf(func_def_40, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.73/0.36 thf(func_def_41, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_42, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.73/0.36 thf(func_def_43, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.73/0.36 thf(func_def_44, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.73/0.36 thf(func_def_46, type, z: hF_Mirabelle_hf).
% 0.73/0.36 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.73/0.36 thf(func_def_49, type, db0: !>[X0: $tType]:(X0)).
% 0.73/0.36 thf(func_def_50, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.73/0.36 thf(func_def_51, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.73/0.36 thf(func_def_52, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.73/0.36 thf(func_def_53, type, db2: !>[X0: $tType]:(X0)).
% 0.73/0.36 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.73/0.36 thf(func_def_57, type, vNOT: ($o > $o)).
% 0.73/0.36 thf(func_def_58, type, vAND: ($o > $o > $o)).
% 0.73/0.36 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.73/0.36 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.73/0.36 thf(func_def_61, type, db3: !>[X0: $tType]:(X0)).
% 0.73/0.36 thf(func_def_62, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.73/0.36 thf(func_def_63, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.73/0.36 thf(func_def_64, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.73/0.36 thf(func_def_65, type, sP3: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > $o))).
% 0.73/0.36 thf(func_def_66, type, sK4: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.73/0.36 thf(func_def_67, type, sK5: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.73/0.36 thf(func_def_68, type, sK6: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.73/0.36 thf(func_def_69, type, sK7: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.73/0.36 thf(func_def_70, type, sK8: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_71, type, sK9: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_72, type, sK10: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_73, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_74, type, sK12: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_75, type, sK13: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_76, type, sK14: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_77, type, sK15: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_78, type, sK16: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.73/0.36 thf(func_def_79, type, sK17: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.73/0.36 thf(func_def_80, type, sK18: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_81, type, sK19: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_82, type, sK20: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.73/0.36 thf(func_def_83, type, sK21: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_84, type, sK22: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_85, type, sK23: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.73/0.36 thf(func_def_86, type, sK24: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.73/0.36 thf(func_def_87, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 0.73/0.36 thf(func_def_88, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_89, type, sK27: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_90, type, sK28: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_91, type, sK29: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_92, type, sK30: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_93, type, sK31: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_94, type, sK32: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_95, type, sK33: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_96, type, sK34: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_97, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_98, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_99, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_100, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_101, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.73/0.36 thf(func_def_102, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.73/0.36 thf(func_def_103, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_104, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_105, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.73/0.36 thf(func_def_106, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.73/0.36 thf(func_def_107, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_108, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_109, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_110, type, sK48: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_111, type, sK49: !>[X0: $tType]:((nat > set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_112, type, sK50: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_113, type, sK51: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_114, type, sK52: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_115, type, sK53: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_116, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (set @ X1 > $o) > X1))).
% 0.73/0.36 thf(func_def_117, type, sK55: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (set @ X1 > $o) > set @ X1))).
% 0.73/0.36 thf(func_def_118, type, sK56: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_119, type, sK57: !>[X0: $tType]:((nat > set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_120, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_121, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_122, type, sK60: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_123, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_124, type, sK62: !>[X0: $tType]:((set @ X0 > nat > set @ X0))).
% 0.73/0.36 thf(func_def_125, type, sK63: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > X0))).
% 0.73/0.36 thf(func_def_126, type, sK64: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > X0))).
% 0.73/0.36 thf(func_def_127, type, sK65: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1 > $o) > X1))).
% 0.73/0.36 thf(func_def_128, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ X0 > set @ X1 > X0))).
% 0.73/0.36 thf(func_def_129, type, sK67: ((nat > $o) > nat)).
% 0.73/0.36 thf(func_def_130, type, sK68: (nat > (nat > $o) > nat)).
% 0.73/0.36 thf(func_def_131, type, sK69: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_132, type, sK70: ((nat > $o) > nat)).
% 0.73/0.36 thf(func_def_133, type, sK71: (nat > (nat > $o) > nat)).
% 0.73/0.36 thf(func_def_134, type, sK72: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > X1 > X0))).
% 0.73/0.36 thf(func_def_135, type, sK73: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 0.73/0.36 thf(func_def_136, type, sK74: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 0.73/0.36 thf(func_def_137, type, sK75: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 0.73/0.36 thf(func_def_138, type, sK76: !>[X0: $tType, X1: $tType]:((set @ X0 > X0 > set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_139, type, sK77: !>[X0: $tType, X1: $tType]:((set @ X0 > X0 > set @ X1 > (X1 > X0) > set @ X1))).
% 0.73/0.36 thf(func_def_140, type, sK78: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_141, type, sK79: hF_Mirabelle_hf).
% 0.73/0.36 thf(func_def_142, type, sK80: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_143, type, sK81: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_144, type, sK82: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_145, type, sK83: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_146, type, sK84: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_147, type, sK85: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_148, type, sK86: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_149, type, sK87: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_150, type, sK88: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_151, type, sK89: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_152, type, sK90: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_153, type, sK91: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_154, type, sK92: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_155, type, sK93: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_156, type, sK94: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_157, type, sK95: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_158, type, sK96: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_159, type, sK97: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_160, type, sK98: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_161, type, sK99: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_162, type, sK100: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_163, type, sK101: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_164, type, sK102: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_165, type, sK103: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_166, type, sK104: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0))).
% 0.73/0.36 thf(func_def_167, type, sK105: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 0.73/0.36 thf(func_def_168, type, sK106: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 0.73/0.36 thf(func_def_169, type, sK107: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0))).
% 0.73/0.36 thf(func_def_170, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 0.73/0.36 thf(func_def_171, type, sK109: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_172, type, sK110: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0))).
% 0.73/0.36 thf(func_def_173, type, sK111: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 0.73/0.36 thf(func_def_174, type, sK112: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_175, type, sK113: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_176, type, sK114: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_177, type, sK115: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_178, type, sK116: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_179, type, sK117: !>[X0: $tType, X1: $tType]:((X1 > set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_180, type, sK118: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_181, type, sK119: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_182, type, sK120: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 0.73/0.36 thf(func_def_183, type, sK121: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 0.73/0.36 thf(func_def_184, type, sK122: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_185, type, sK123: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_186, type, sK124: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_187, type, sK125: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_188, type, sK126: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_189, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_190, type, sK128: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_191, type, sK129: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_192, type, sK130: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_193, type, sK131: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.73/0.36 thf(func_def_194, type, sK132: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_195, type, sK133: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_196, type, sK134: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_197, type, sK135: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_198, type, sK136: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_199, type, sK137: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_200, type, sK138: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_201, type, sK139: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_202, type, sK140: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_203, type, sK141: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.73/0.36 thf(func_def_204, type, sK142: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_205, type, sK143: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(func_def_206, type, sK144: !>[X0: $tType]:((X0 > set @ X0 > X0 > set @ X0 > set @ X0))).
% 0.73/0.36 thf(func_def_207, type, sK145: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_208, type, sK146: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.73/0.36 thf(func_def_209, type, sK147: !>[X0: $tType]:((set @ X0 > X0))).
% 0.73/0.36 thf(f3,axiom,(
% 0.73/0.36 ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)),
% 0.73/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hmem__hempty)).
% 0.73/0.36 thf(f6,axiom,(
% 0.73/0.36 (hF_Mirabelle_hmem = (^[X0 : hF_Mirabelle_hf, X1 : hF_Mirabelle_hf] : ((member @ hF_Mirabelle_hf @ X0 @ (hF_Mirabelle_hfset @ X1)))))),
% 0.73/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hmem__def)).
% 0.73/0.36 thf(f10,axiom,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf = ((hF_Mirabelle_HF @ bot_bot @ set @ hF_Mirabelle_hf)))),
% 0.73/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_Zero__hf__def)).
% 0.73/0.36 thf(f15,axiom,(
% 0.73/0.36 ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ X0))) = X0)),
% 0.73/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_HF__hfset)).
% 0.73/0.36 thf(f54,axiom,(
% 0.73/0.36 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : ~(member @ X0 @ X2 @ X1) => (X1 = bot_bot @ set @ X0))),
% 0.73/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_equals0I)).
% 0.73/0.36 thf(f290,conjecture,(
% 0.73/0.36 ((z = zero_zero @ hF_Mirabelle_hf) = ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ z))),
% 0.73/0.36 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.73/0.36 thf(f291,negated_conjecture,(
% 0.73/0.36 ~ ((z = zero_zero @ hF_Mirabelle_hf) = ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ z))),
% 0.73/0.36 inference(negated_conjecture,[status(cth)],[f290])).
% 0.73/0.36 thf(f296,plain,(
% 0.73/0.36 ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)),
% 0.73/0.36 inference(rectify,[],[f3])).
% 0.73/0.36 thf(f297,plain,(
% 0.73/0.36 ! [X0 : hF_Mirabelle_hf] : ~ (((hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)) = $true)),
% 0.73/0.36 inference(fool_elimination,[],[f296])).
% 0.73/0.36 thf(f302,plain,(
% 0.73/0.36 (hF_Mirabelle_hmem = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))))),
% 0.73/0.36 inference(fool_elimination,[],[f6])).
% 0.73/0.36 thf(f368,plain,(
% 0.73/0.36 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : ~(member @ X0 @ X2 @ X1) => (X1 = bot_bot @ set @ X0))),
% 0.73/0.36 inference(rectify,[],[f54])).
% 0.73/0.36 thf(f369,plain,(
% 0.73/0.36 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : ~ (((member @ X0 @ X2 @ X1)) = $true) => (bot_bot @ set @ X0 = X1))),
% 0.73/0.36 inference(fool_elimination,[],[f368])).
% 0.73/0.36 thf(f801,plain,(
% 0.73/0.36 ~ ((z = zero_zero @ hF_Mirabelle_hf) = ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ z))),
% 0.73/0.36 inference(rectify,[],[f291])).
% 0.73/0.36 thf(f802,plain,(
% 0.73/0.36 ~ (((zero_zero @ hF_Mirabelle_hf = z)) = ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (~ (hF_Mirabelle_hmem @ Y0 @ z))))))),
% 0.73/0.36 inference(fool_elimination,[],[f801])).
% 0.73/0.36 thf(f804,plain,(
% 0.73/0.36 ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)) != $true)),
% 0.73/0.36 inference(flattening,[],[f297])).
% 0.73/0.36 thf(f813,plain,(
% 0.73/0.36 ! [X0 : $tType,X1 : set @ X0] : (! [X2 : X0] : (((member @ X0 @ X2 @ X1)) != $true) => (bot_bot @ set @ X0 = X1))),
% 0.73/0.36 inference(flattening,[],[f369])).
% 0.73/0.36 thf(f835,plain,(
% 0.73/0.36 (((zero_zero @ hF_Mirabelle_hf = z)) != ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (~ (hF_Mirabelle_hmem @ Y0 @ z))))))),
% 0.73/0.36 inference(flattening,[],[f802])).
% 0.73/0.36 thf(f864,plain,(
% 0.73/0.36 ! [X0 : $tType,X1 : set @ X0] : ((bot_bot @ set @ X0 = X1) | ? [X2 : X0] : (((member @ X0 @ X2 @ X1)) = $true))),
% 0.73/0.36 inference(ennf_transformation,[],[f813])).
% 0.73/0.36 thf(f1095,plain,(
% 0.73/0.36 ! [X0 : $tType,X1 : set @ X0] : ((bot_bot @ set @ X0 = X1) | ($true = ((member @ X0 @ (sK12 @ X0 @ X1) @ X1))))),
% 0.73/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK5 @ X0)],[f864])).
% 0.73/0.36 thf(f1153,plain,(
% 0.73/0.36 ( ! [X0 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)) != $true)) )),
% 0.73/0.36 inference(cnf_transformation,[],[f804])).
% 0.73/0.36 thf(f1157,plain,(
% 0.73/0.36 (hF_Mirabelle_hmem = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))))),
% 0.73/0.36 inference(cnf_transformation,[],[f302])).
% 0.73/0.36 thf(f1161,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf = ((hF_Mirabelle_HF @ bot_bot @ set @ hF_Mirabelle_hf)))),
% 0.73/0.36 inference(cnf_transformation,[],[f10])).
% 0.73/0.36 thf(f1166,plain,(
% 0.73/0.36 ( ! [X0 : hF_Mirabelle_hf] : ((((hF_Mirabelle_HF @ (hF_Mirabelle_hfset @ X0))) = X0)) )),
% 0.73/0.36 inference(cnf_transformation,[],[f15])).
% 0.73/0.36 thf(f1210,plain,(
% 0.73/0.36 ( ! [X0 : $tType,X1 : set @ X0] : (($true = ((member @ X0 @ (sK12 @ X0 @ X1) @ X1))) | (bot_bot @ set @ X0 = X1)) )),
% 0.73/0.36 inference(cnf_transformation,[],[f1095])).
% 0.73/0.36 thf(f1545,plain,(
% 0.73/0.36 (((zero_zero @ hF_Mirabelle_hf = z)) != ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (~ (hF_Mirabelle_hmem @ Y0 @ z))))))),
% 0.73/0.36 inference(cnf_transformation,[],[f835])).
% 0.73/0.36 thf(f1550,plain,(
% 0.73/0.36 ( ! [X0 : hF_Mirabelle_hf] : (($true != (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y0 @ (hF_Mirabelle_hfset @ Y1))))) @ X0 @ zero_zero @ hF_Mirabelle_hf)))) )),
% 0.73/0.36 inference(definition_unfolding,[],[f1153,f1157])).
% 0.73/0.36 thf(f1588,plain,(
% 0.73/0.36 (((zero_zero @ hF_Mirabelle_hf = z)) != ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (~ ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ z))))))),
% 0.73/0.36 inference(definition_unfolding,[],[f1545,f1157])).
% 0.73/0.36 thf(f1605,plain,(
% 0.73/0.36 ($true = ((zero_zero @ hF_Mirabelle_hf = z))) | ($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 @ z))))))),
% 0.73/0.36 inference(xor_proxy_clausification,[],[f1588])).
% 0.73/0.36 thf(f1606,plain,(
% 0.73/0.36 (((zero_zero @ hF_Mirabelle_hf = z)) = $false) | ($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 @ z))))))),
% 0.73/0.36 inference(xor_proxy_clausification,[],[f1588])).
% 0.73/0.36 thf(f1607,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf != z) | ($false = ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (~ ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ z))))))),
% 0.73/0.36 inference(equality_proxy_clausification,[],[f1606])).
% 0.73/0.36 thf(f1608,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf != z) | ($false = (((^[Y0 : hF_Mirabelle_hf]: (~ ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ z))) @ sK79)))),
% 0.73/0.36 inference(sigma_proxy_clausification,[],[f1607])).
% 0.73/0.36 thf(f1609,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf != z) | ($false = ((~ (member @ hF_Mirabelle_hf @ sK79 @ (hF_Mirabelle_hfset @ z)))))),
% 0.73/0.36 inference(beta-eta_normalization,[],[f1608])).
% 0.73/0.36 thf(f1610,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf != z) | ($true = ((member @ hF_Mirabelle_hf @ sK79 @ (hF_Mirabelle_hfset @ z))))),
% 0.73/0.36 inference(not_proxy_clausification,[],[f1609])).
% 0.73/0.36 thf(f1611,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf = z) | ($true = ((!! @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (~ ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ z))))))),
% 0.73/0.36 inference(equality_proxy_clausification,[],[f1605])).
% 0.73/0.36 thf(f1612,plain,(
% 0.73/0.36 ( ! [X1 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf = z) | ($true = (((^[Y0 : hF_Mirabelle_hf]: (~ ((^[Y1 : hF_Mirabelle_hf]: ((^[Y2 : hF_Mirabelle_hf]: (member @ hF_Mirabelle_hf @ Y1 @ (hF_Mirabelle_hfset @ Y2))))) @ Y0 @ z))) @ X1)))) )),
% 0.73/0.36 inference(pi_proxy_clausification,[],[f1611])).
% 0.73/0.36 thf(f1613,plain,(
% 0.73/0.36 ( ! [X1 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf = z) | ($true = ((~ (member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ z)))))) )),
% 0.73/0.36 inference(beta-eta_normalization,[],[f1612])).
% 0.73/0.36 thf(f1614,plain,(
% 0.73/0.36 ( ! [X1 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf = z) | ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ z))))) )),
% 0.73/0.36 inference(not_proxy_clausification,[],[f1613])).
% 0.73/0.36 thf(f2665,plain,(
% 0.73/0.36 ( ! [X0 : hF_Mirabelle_hf] : (($true != ((member @ hF_Mirabelle_hf @ X0 @ (hF_Mirabelle_hfset @ zero_zero @ hF_Mirabelle_hf))))) )),
% 0.73/0.36 inference(beta-eta_normalization,[],[f1550])).
% 0.73/0.36 thf(f2669,definition,(
% 0.73/0.36 spl148_1 <=> ($true = ((member @ hF_Mirabelle_hf @ sK79 @ (hF_Mirabelle_hfset @ z))))),
% 0.73/0.36 introduced(definition,[new_symbols(definition,[spl148_1])],[avatar_definition])).
% 0.73/0.36 thf(f2671,plain,(
% 0.73/0.36 ($true = ((member @ hF_Mirabelle_hf @ sK79 @ (hF_Mirabelle_hfset @ z)))) | ~spl148_1),
% 0.73/0.36 inference(avatar_component_clause,[],[f2669])).
% 0.73/0.36 thf(f2673,definition,(
% 0.73/0.36 spl148_2 <=> (zero_zero @ hF_Mirabelle_hf = z)),
% 0.73/0.36 introduced(definition,[new_symbols(definition,[spl148_2])],[avatar_definition])).
% 0.73/0.36 thf(f2674,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf = z) | ~spl148_2),
% 0.73/0.36 inference(avatar_component_clause,[],[f2673])).
% 0.73/0.36 thf(f2676,plain,(
% 0.73/0.36 spl148_1 | ~spl148_2),
% 0.73/0.36 inference(avatar_split_clause,[],[f1610,f2673,f2669])).
% 0.73/0.36 thf(f2678,definition,(
% 0.73/0.36 spl148_3 <=> ! [X1 : hF_Mirabelle_hf] : ($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ z))))),
% 0.73/0.36 introduced(definition,[new_symbols(definition,[spl148_3])],[avatar_definition])).
% 0.73/0.36 thf(f2679,plain,(
% 0.73/0.36 ( ! [X1 : hF_Mirabelle_hf] : (($false = ((member @ hF_Mirabelle_hf @ X1 @ (hF_Mirabelle_hfset @ z))))) ) | ~spl148_3),
% 0.73/0.36 inference(avatar_component_clause,[],[f2678])).
% 0.73/0.36 thf(f2680,plain,(
% 0.73/0.36 spl148_3 | spl148_2),
% 0.73/0.36 inference(avatar_split_clause,[],[f1614,f2673,f2678])).
% 0.73/0.36 thf(f2992,plain,(
% 0.73/0.36 ($true = $false) | (bot_bot @ set @ hF_Mirabelle_hf = ((hF_Mirabelle_hfset @ z))) | ~spl148_3),
% 0.73/0.36 inference(constrained_superposition,[],[f2679,f1210])).
% 0.73/0.36 thf(f2995,plain,(
% 0.73/0.36 (bot_bot @ set @ hF_Mirabelle_hf = ((hF_Mirabelle_hfset @ z))) | ~spl148_3),
% 0.73/0.36 inference(trivial_inequality_removal,[],[f2992])).
% 0.73/0.36 thf(f3018,plain,(
% 0.73/0.36 (((hF_Mirabelle_HF @ bot_bot @ set @ hF_Mirabelle_hf)) = z) | ~spl148_3),
% 0.73/0.36 inference(constrained_superposition,[],[f1166,f2995])).
% 0.73/0.36 thf(f3266,plain,(
% 0.73/0.36 (zero_zero @ hF_Mirabelle_hf = z) | ~spl148_3),
% 0.73/0.36 inference(constrained_superposition,[],[f1161,f3018])).
% 0.73/0.37 thf(f3274,plain,(
% 0.73/0.37 spl148_2 | ~spl148_3),
% 0.73/0.37 inference(avatar_split_clause,[],[f3266,f2678,f2673])).
% 0.73/0.37 thf(f3275,plain,(
% 0.73/0.37 ( ! [X0 : hF_Mirabelle_hf] : (($true != ((member @ hF_Mirabelle_hf @ X0 @ (hF_Mirabelle_hfset @ z))))) ) | ~spl148_2),
% 0.73/0.37 inference(constrained_superposition,[],[f2665,f2674])).
% 0.73/0.37 thf(f3285,plain,(
% 0.73/0.37 $false | (~spl148_1 | ~spl148_2)),
% 0.73/0.37 inference(backward_subsumption_resolution,[],[f2671,f3275])).
% 0.73/0.37 thf(f3290,plain,(
% 0.73/0.37 ~spl148_1 | ~spl148_2),
% 0.73/0.37 inference(avatar_contradiction_clause,[],[f3285])).
% 0.73/0.37 cnf(s1, plain, spl148_1 | ~spl148_2, inference(sat_conversion,[],[f2676])).
% 0.73/0.37 cnf(s2, plain, spl148_2 | spl148_3, inference(sat_conversion,[],[f2680])).
% 0.73/0.37 cnf(s8, plain, spl148_2 | ~spl148_3, inference(sat_conversion,[],[f3274])).
% 0.73/0.37 cnf(s10, plain, ~spl148_1 | ~spl148_2, inference(sat_conversion,[],[f3290])).
% 0.73/0.37 cnf(s12, plain, spl148_2, inference(rat,[],[s2,s8])).
% 0.73/0.37 cnf(s14, plain, ~spl148_1, inference(rat,[],[s10,s12])).
% 0.73/0.37 cnf(s15, plain, $false, inference(rat,[],[s1,s12,s14])).
% 0.73/0.37 thf(f3292,plain,(
% 0.73/0.37 $false),
% 0.73/0.37 inference(avatar_sat_refutation,[],[s15])).
% 0.73/0.37 % SZS output end Proof for theBenchmark
% 0.73/0.37 % (3830638)------------------------------
% 0.73/0.37 % (3830638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.37 % (3830638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.37 % (3830638)CaDiCaL version: 2.1.3
% 0.73/0.37 % (3830638)Termination reason: Refutation
% 0.73/0.37 % (3830638)Time elapsed: 0.086 s
% 0.73/0.37 % (3830638)Peak memory usage: 15 MB
% 0.73/0.37 % (3830638)Instructions burned: 174 (million)
% 0.73/0.37 % (3830614)Success in time 0.141 s
% 0.73/0.37 % Vampire exiting
%------------------------------------------------------------------------------