%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT162^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:59 AM UTC 2026
% Result : Theorem 0.90s 0.40s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT162^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n016.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 18:08:20 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.90/0.40 % (706997)Will run a generic schedule for satisfiability detection.
% 0.90/0.40 % (707011)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1210217469_2999 on theBenchmark for (2999ds/0Mi)
% 0.90/0.40 % (707014)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=123526041:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.90/0.40 % (707016)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3020995940:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.90/0.40 % (707015)dis+10_1_sil=32000:sp=arity:random_seed=1925463210:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.90/0.40 % (707013)% WARNING: option uhcvi not known.
% 0.90/0.40 % Exception at run slice level
% 0.90/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.90/0.40 % (707013)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=383463140:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.90/0.40 % (707016)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.90/0.40 % (707024)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2498485827:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.90/0.40 % (707017)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1251828585:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.90/0.40 % (707018)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1626863631:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.90/0.40 % Exception at run slice level
% 0.90/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.90/0.40 % (707013)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.90/0.40 % (707030)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2938303224:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.90/0.40 % (707015)Instruction limit reached!
% 0.90/0.40 % (707015)------------------------------
% 0.90/0.40 % (707015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.40 % (707015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.40 % (707015)CaDiCaL version: 2.1.3
% 0.90/0.40 % (707015)Termination reason: Instruction limit
% 0.90/0.40 % (707015)Termination phase: Saturation
% 0.90/0.40 % (707015)Time elapsed: 0.050 s
% 0.90/0.40 % (707015)Peak memory usage: 12 MB
% 0.90/0.40 % (707015)Instructions burned: 104 (million)
% 0.90/0.40 % (707016)Instruction limit reached!
% 0.90/0.40 % (707016)------------------------------
% 0.90/0.40 % (707016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.40 % (707016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.40 % (707016)CaDiCaL version: 2.1.3
% 0.90/0.40 % (707016)Termination reason: Instruction limit
% 0.90/0.40 % (707016)Termination phase: Saturation
% 0.90/0.40 % (707016)Time elapsed: 0.057 s
% 0.90/0.40 % (707016)Peak memory usage: 12 MB
% 0.90/0.40 % (707016)Instructions burned: 117 (million)
% 0.90/0.40 % (707013)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.90/0.40 % (707033)ott-21_1_sil=16000:fs=off:random_seed=2568387660:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.90/0.40 % (707030)Instruction limit reached!
% 0.90/0.40 % (707030)------------------------------
% 0.90/0.40 % (707030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.40 % (707030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.40 % (707030)CaDiCaL version: 2.1.3
% 0.90/0.40 % (707030)Termination reason: Instruction limit
% 0.90/0.40 % (707030)Termination phase: Saturation
% 0.90/0.40 % (707030)Time elapsed: 0.031 s
% 0.90/0.40 % (707030)Peak memory usage: 13 MB
% 0.90/0.40 % (707030)Instructions burned: 132 (million)
% 0.90/0.40 % (707032)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=916904675:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.90/0.40 % (707017)Instruction limit reached!
% 0.90/0.40 % (707017)------------------------------
% 0.90/0.40 % (707017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.40 % (707017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.40 % (707017)CaDiCaL version: 2.1.3
% 0.90/0.40 % (707017)Termination reason: Instruction limit
% 0.90/0.40 % (707017)Termination phase: Saturation
% 0.90/0.40 % (707017)Time elapsed: 0.060 s
% 0.90/0.40 % (707017)Peak memory usage: 13 MB
% 0.90/0.40 % (707017)Instructions burned: 131 (million)
% 0.90/0.40 % (707035)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2378703981:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.90/0.40 % (707032)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.90/0.40 % (707037)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2363136410:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.90/0.40 % (707032)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.90/0.40 % (707018)Instruction limit reached!
% 0.90/0.40 % (707018)------------------------------
% 0.90/0.40 % (707018)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.40 % (707018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.40 % (707018)CaDiCaL version: 2.1.3
% 0.90/0.40 % (707018)Termination reason: Instruction limit
% 0.90/0.40 % (707018)Termination phase: Saturation
% 0.90/0.40 % (707018)Time elapsed: 0.107 s
% 0.90/0.40 % (707018)Peak memory usage: 13 MB
% 0.90/0.40 % (707018)Instructions burned: 159 (million)
% 0.90/0.40 % Exception at run slice level
% 0.90/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.90/0.40 % (707032) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-706997-707032"...
% 0.90/0.40 % (707032)...printing done.
% 0.90/0.40 % (707032)Refutation found. Thanks to Tanya!
% 0.90/0.40 % SZS status Theorem for theBenchmark
% 0.90/0.40 % SZS output start Proof for theBenchmark
% 0.90/0.40 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.90/0.40 thf(type_def_6, type, set: $tType > $tType).
% 0.90/0.40 thf(type_def_7, type, nat: $tType).
% 0.90/0.40 thf(type_def_8, type, itself: $tType > $tType).
% 0.90/0.40 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.90/0.40 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_1, type, dvd: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_2, type, one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_3, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_5, type, semiring_gcd: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_6, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_7, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_8, type, monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_9, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_10, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_11, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_12, type, semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_13, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_14, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_15, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_16, type, comm_monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_17, type, algebraic_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_18, type, ab_semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_19, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_20, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.90/0.40 thf(func_def_21, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.90/0.40 thf(func_def_22, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.90/0.40 thf(func_def_23, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.90/0.40 thf(func_def_24, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.90/0.40 thf(func_def_25, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.90/0.40 thf(func_def_26, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.90/0.40 thf(func_def_27, type, coinductive_lsetp: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_28, type, coindu63249387sorted: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.90/0.40 thf(func_def_29, type, one_one: !>[X0: $tType]:(X0)).
% 0.90/0.40 thf(func_def_30, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.90/0.40 thf(func_def_31, type, hammin2015774020amming: coinductive_llist @ nat).
% 0.90/0.40 thf(func_def_32, type, hammin1328233080lmerge: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.90/0.40 thf(func_def_33, type, hammin1138290136lmerge: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.90/0.40 thf(func_def_34, type, hammin1195055315smooth: (nat > $o)).
% 0.90/0.40 thf(func_def_35, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_37, type, prime: (nat > $o)).
% 0.90/0.40 thf(func_def_38, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.90/0.40 thf(func_def_39, type, dvd_dvd: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_40, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.90/0.40 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.90/0.40 thf(func_def_42, type, n: nat).
% 0.90/0.40 thf(func_def_43, type, n2: nat).
% 0.90/0.40 thf(func_def_44, type, na: nat).
% 0.90/0.40 thf(func_def_45, type, p: nat).
% 0.90/0.40 thf(func_def_49, type, vNOT: ($o > $o)).
% 0.90/0.40 thf(func_def_50, type, vAND: ($o > $o > $o)).
% 0.90/0.40 thf(func_def_51, type, vOR: ($o > $o > $o)).
% 0.90/0.40 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.90/0.40 thf(func_def_53, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_54, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.90/0.40 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.90/0.40 thf(func_def_56, type, db2: !>[X0: $tType]:(X0)).
% 0.90/0.40 thf(func_def_57, type, db1: !>[X0: $tType]:(X0)).
% 0.90/0.40 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.90/0.40 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.90/0.40 thf(func_def_60, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_61, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_62, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.90/0.40 thf(func_def_63, type, sK3: nat).
% 0.90/0.40 thf(func_def_64, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_65, type, sK5: nat).
% 0.90/0.40 thf(func_def_66, type, sK6: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.90/0.40 thf(func_def_67, type, sK7: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_68, type, sK8: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.90/0.40 thf(func_def_69, type, sK9: ((nat > $o) > nat)).
% 0.90/0.40 thf(func_def_70, type, sK10: ((nat > $o) > nat)).
% 0.90/0.40 thf(func_def_71, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.90/0.40 thf(func_def_72, type, sK12: (nat > nat)).
% 0.90/0.40 thf(func_def_73, type, sK13: (nat > nat)).
% 0.90/0.40 thf(func_def_74, type, sK14: (nat > nat)).
% 0.90/0.40 thf(func_def_75, type, sK15: (nat > nat)).
% 0.90/0.40 thf(func_def_76, type, sK16: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.90/0.40 thf(func_def_77, type, sK17: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.90/0.40 thf(func_def_78, type, sK18: ((nat > nat) > nat)).
% 0.90/0.40 thf(func_def_79, type, sK19: ((nat > nat) > nat)).
% 0.90/0.40 thf(func_def_80, type, sK20: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_81, type, sK21: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_82, type, sK22: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_83, type, sK23: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_84, type, sK24: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_85, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_86, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_87, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_88, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.40 thf(func_def_89, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.40 thf(func_def_90, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_91, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_92, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.40 thf(func_def_93, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.40 thf(func_def_94, type, sK34: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_95, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_96, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_97, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_98, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.90/0.40 thf(func_def_99, type, sK39: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_100, type, sK40: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_101, type, sK41: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_102, type, sK42: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_103, type, sK43: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_104, type, sK44: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_105, type, sK45: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_106, type, sK46: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_107, type, sK47: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_108, type, sK48: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_109, type, sK49: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.90/0.40 thf(func_def_110, type, sK50: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_111, type, sK51: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_112, type, sK52: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_113, type, sK53: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.40 thf(func_def_114, type, sK54: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_115, type, sK55: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_116, type, sK56: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_117, type, sK57: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_118, type, sK58: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_119, type, sK59: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.40 thf(func_def_120, type, sK60: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_121, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.40 thf(func_def_122, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.41 thf(func_def_123, type, sK63: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.41 thf(func_def_124, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.41 thf(func_def_125, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.90/0.41 thf(func_def_126, type, sK66: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.41 thf(func_def_127, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.90/0.41 thf(func_def_128, type, sK68: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.41 thf(func_def_129, type, sK69: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.41 thf(func_def_130, type, sK70: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.90/0.41 thf(func_def_131, type, sK71: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.90/0.41 thf(func_def_132, type, sK72: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.90/0.41 thf(func_def_133, type, sK73: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.90/0.41 thf(func_def_134, type, sK74: (nat > nat)).
% 0.90/0.41 thf(func_def_135, type, sK75: (nat > nat)).
% 0.90/0.41 thf(func_def_136, type, sK76: nat).
% 0.90/0.41 thf(func_def_137, type, sK77: (nat > nat > nat)).
% 0.90/0.41 thf(func_def_138, type, sK78: (nat > nat)).
% 0.90/0.41 thf(func_def_139, type, sK79: (nat > nat)).
% 0.90/0.41 thf(func_def_140, type, sK80: (nat > nat)).
% 0.90/0.41 thf(func_def_141, type, sK81: (nat > nat)).
% 0.90/0.41 thf(func_def_142, type, sK82: (nat > nat)).
% 0.90/0.41 thf(f1,axiom,(
% 0.90/0.41 (hammin1195055315smooth @ n2)),
% 0.90/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062smooth_An_H_092_060close_062)).
% 0.90/0.41 thf(f2,axiom,(
% 0.90/0.41 (ord_less @ nat @ n2 @ na)),
% 0.90/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062n_H_A_060_An_092_060close_062)).
% 0.90/0.41 thf(f3,axiom,(
% 0.90/0.41 ! [X0 : nat] : ((ord_less @ nat @ X0 @ na) => ((hammin1195055315smooth @ X0) => (member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))))),
% 0.90/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_less_OIH)).
% 0.90/0.41 thf(f280,conjecture,(
% 0.90/0.41 (member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))),
% 0.90/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.90/0.41 thf(f281,negated_conjecture,(
% 0.90/0.41 ~(member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))),
% 0.90/0.41 inference(negated_conjecture,[status(cth)],[f280])).
% 0.90/0.41 thf(f282,plain,(
% 0.90/0.41 (hammin1195055315smooth @ n2)),
% 0.90/0.41 inference(rectify,[],[f1])).
% 0.90/0.41 thf(f283,plain,(
% 0.90/0.41 (((hammin1195055315smooth @ n2)) = $true)),
% 0.90/0.41 inference(fool_elimination,[],[f282])).
% 0.90/0.41 thf(f284,plain,(
% 0.90/0.41 (ord_less @ nat @ n2 @ na)),
% 0.90/0.41 inference(rectify,[],[f2])).
% 0.90/0.41 thf(f285,plain,(
% 0.90/0.41 (((ord_less @ nat @ n2 @ na)) = $true)),
% 0.90/0.41 inference(fool_elimination,[],[f284])).
% 0.90/0.41 thf(f286,plain,(
% 0.90/0.41 ! [X0 : nat] : ((ord_less @ nat @ X0 @ na) => ((hammin1195055315smooth @ X0) => (member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))))),
% 0.90/0.41 inference(rectify,[],[f3])).
% 0.90/0.41 thf(f287,plain,(
% 0.90/0.41 ! [X0 : nat] : ((((ord_less @ nat @ X0 @ na)) = $true) => ((((hammin1195055315smooth @ X0)) = $true) => (((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)))),
% 0.90/0.41 inference(fool_elimination,[],[f286])).
% 0.90/0.41 thf(f815,plain,(
% 0.90/0.41 ~(member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))),
% 0.90/0.41 inference(rectify,[],[f281])).
% 0.90/0.41 thf(f816,plain,(
% 0.90/0.41 ~ (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)),
% 0.90/0.41 inference(fool_elimination,[],[f815])).
% 0.90/0.41 thf(f855,plain,(
% 0.90/0.41 (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) != $true)),
% 0.90/0.41 inference(flattening,[],[f816])).
% 0.90/0.41 thf(f856,plain,(
% 0.90/0.41 ! [X0 : nat] : (((((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true) | (((hammin1195055315smooth @ X0)) != $true)) | (((ord_less @ nat @ X0 @ na)) != $true))),
% 0.90/0.41 inference(ennf_transformation,[],[f287])).
% 0.90/0.41 thf(f857,plain,(
% 0.90/0.41 ! [X0 : nat] : ((((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true) | (((hammin1195055315smooth @ X0)) != $true) | (((ord_less @ nat @ X0 @ na)) != $true))),
% 0.90/0.41 inference(flattening,[],[f856])).
% 0.90/0.41 thf(f1205,plain,(
% 0.90/0.41 (((hammin1195055315smooth @ n2)) = $true)),
% 0.90/0.41 inference(cnf_transformation,[],[f283])).
% 0.90/0.41 thf(f1206,plain,(
% 0.90/0.41 (((ord_less @ nat @ n2 @ na)) = $true)),
% 0.90/0.41 inference(cnf_transformation,[],[f285])).
% 0.90/0.41 thf(f1207,plain,(
% 0.90/0.41 ( ! [X0 : nat] : ((((ord_less @ nat @ X0 @ na)) != $true) | (((hammin1195055315smooth @ X0)) != $true) | (((member @ nat @ X0 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)) )),
% 0.90/0.41 inference(cnf_transformation,[],[f857])).
% 0.90/0.41 thf(f1557,plain,(
% 0.90/0.41 (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) != $true)),
% 0.90/0.41 inference(cnf_transformation,[],[f855])).
% 0.90/0.41 thf(f2460,plain,(
% 0.90/0.41 ($true != $true) | (((hammin1195055315smooth @ n2)) != $true) | (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)),
% 0.90/0.41 inference(constrained_superposition,[],[f1207,f1206])).
% 0.90/0.41 thf(f2461,plain,(
% 0.90/0.41 (((hammin1195055315smooth @ n2)) != $true) | (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)),
% 0.90/0.41 inference(trivial_inequality_removal,[],[f2460])).
% 0.90/0.41 thf(f2463,plain,(
% 0.90/0.41 (((member @ nat @ n2 @ (coinductive_lset @ nat @ hammin2015774020amming))) = $true)),
% 0.90/0.41 inference(forward_subsumption_resolution,[],[f2461,f1205])).
% 0.90/0.41 thf(f2464,plain,(
% 0.90/0.41 $false),
% 0.90/0.41 inference(forward_subsumption_resolution,[],[f2463,f1557])).
% 0.90/0.41 % SZS output end Proof for theBenchmark
% 0.90/0.41 % (707032)------------------------------
% 0.90/0.41 % (707032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.41 % (707032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.41 % (707032)CaDiCaL version: 2.1.3
% 0.90/0.41 % (707032)Termination reason: Refutation
% 0.90/0.41 % (707032)Time elapsed: 0.055 s
% 0.90/0.41 % (707032)Peak memory usage: 14 MB
% 0.90/0.41 % (707032)Instructions burned: 113 (million)
% 0.90/0.41 % (706997)Success in time 0.185 s
% 0.90/0.41 % Vampire exiting
%------------------------------------------------------------------------------