%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT187^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:00 AM UTC 2026
% Result : Theorem 0.97s 0.37s
% Output : Refutation 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT187^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.16 % Computer : n006.cluster.edu
% 0.06/0.16 % Model : x86_64 x86_64
% 0.06/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.16 % Memory : 8046.5625MB
% 0.06/0.16 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 18:06:25 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 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
% 0.97/0.36 % (1114991)Will run a generic schedule for satisfiability detection.
% 0.97/0.36 % (1115000)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2997231890:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.97/0.36 % (1114997)% WARNING: option uhcvi not known.
% 0.97/0.36 % (1114997)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2367372667:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.97/0.36 % (1114996)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3772158364_2999 on theBenchmark for (2999ds/0Mi)
% 0.97/0.36 % (1114998)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2959494672:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.97/0.36 % (1114999)dis+10_1_sil=32000:sp=arity:random_seed=982268799:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.97/0.36 % (1115002)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2270851669:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.97/0.36 % (1115001)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=145882003:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.97/0.36 % (1115000)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.97/0.36 % (1114997)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.97/0.36 % (1115000)Instruction limit reached!
% 0.97/0.36 % (1115000)------------------------------
% 0.97/0.36 % (1115000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1115000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1115000)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1115000)Termination reason: Instruction limit
% 0.97/0.36 % (1115000)Termination phase: Saturation
% 0.97/0.36 % (1115000)Time elapsed: 0.027 s
% 0.97/0.36 % (1115000)Peak memory usage: 12 MB
% 0.97/0.36 % (1115000)Instructions burned: 118 (million)
% 0.97/0.36 % (1115010)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2043192626:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.97/0.36 % Exception at run slice level
% 0.97/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.97/0.36 % (1114997)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.97/0.36 % (1114999)Instruction limit reached!
% 0.97/0.36 % (1114999)------------------------------
% 0.97/0.36 % (1114999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1114999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.36 % (1114999)CaDiCaL version: 2.1.3
% 0.97/0.36 % (1114999)Termination reason: Instruction limit
% 0.97/0.36 % (1114999)Termination phase: Saturation
% 0.97/0.36 % (1114999)Time elapsed: 0.044 s
% 0.97/0.36 % (1114999)Peak memory usage: 12 MB
% 0.97/0.36 % (1114999)Instructions burned: 103 (million)
% 0.97/0.36 % Exception at run slice level
% 0.97/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.97/0.36 % (1115001)Instruction limit reached!
% 0.97/0.36 % (1115001)------------------------------
% 0.97/0.36 % (1115001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.36 % (1115001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.37 % (1115001)CaDiCaL version: 2.1.3
% 0.97/0.37 % (1115001)Termination reason: Instruction limit
% 0.97/0.37 % (1115001)Termination phase: Saturation
% 0.97/0.37 % (1115001)Time elapsed: 0.056 s
% 0.97/0.37 % (1115001)Peak memory usage: 13 MB
% 0.97/0.37 % (1115001)Instructions burned: 131 (million)
% 0.97/0.37 % (1115012)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2192867358:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.97/0.37 % (1115014)ott-21_1_sil=16000:fs=off:random_seed=2021568578:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.97/0.37 % (1115013)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=2352520341:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.97/0.37 % (1115002)Instruction limit reached!
% 0.97/0.37 % (1115002)------------------------------
% 0.97/0.37 % (1115002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.37 % (1115002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.37 % (1115002)CaDiCaL version: 2.1.3
% 0.97/0.37 % (1115002)Termination reason: Instruction limit
% 0.97/0.37 % (1115002)Termination phase: Saturation
% 0.97/0.37 % (1115002)Time elapsed: 0.071 s
% 0.97/0.37 % (1115002)Peak memory usage: 13 MB
% 0.97/0.37 % (1115002)Instructions burned: 159 (million)
% 0.97/0.37 % (1115015)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3734036797:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.97/0.37 % (1115013)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.97/0.37 % (1115019)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4068544881:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.97/0.37 % (1115014)Instruction limit reached!
% 0.97/0.37 % (1115014)------------------------------
% 0.97/0.37 % (1115014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.37 % (1115014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.37 % (1115014)CaDiCaL version: 2.1.3
% 0.97/0.37 % (1115014)Termination reason: Instruction limit
% 0.97/0.37 % (1115014)Termination phase: Saturation
% 0.97/0.37 % (1115014)Time elapsed: 0.043 s
% 0.97/0.37 % (1115014)Peak memory usage: 13 MB
% 0.97/0.37 % (1115014)Instructions burned: 183 (million)
% 0.97/0.37 % (1114997) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1114991-1114997"...
% 0.97/0.37 % (1115013)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.97/0.37 % (1114997)...printing done.
% 0.97/0.37 % (1114997)Refutation found. Thanks to Tanya!
% 0.97/0.37 % SZS status Theorem for theBenchmark
% 0.97/0.37 % SZS output start Proof for theBenchmark
% 0.97/0.37 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.97/0.37 thf(type_def_6, type, set: $tType > $tType).
% 0.97/0.37 thf(type_def_7, type, nat: $tType).
% 0.97/0.37 thf(type_def_8, type, itself: $tType > $tType).
% 0.97/0.37 thf(type_def_9, type, a: $tType).
% 0.97/0.37 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.97/0.37 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_2, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_3, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_4, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_5, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_6, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_7, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.97/0.37 thf(func_def_8, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_9, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_10, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_11, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_12, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.97/0.37 thf(func_def_13, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_14, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.97/0.37 thf(func_def_15, type, lList2435255213lllsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_16, type, lList2236698231inlsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_17, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0))).
% 0.97/0.37 thf(func_def_18, type, lList21202317876inpref: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_19, type, lList22096119349pslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_20, type, lList21015763786veness: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_21, type, lList21612149805nflsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_22, type, lList21015939545safety: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_23, type, lList2649413865nfsuff: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_24, type, lList2370560421utlast: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_25, type, lList2508575361_ldrop: !>[X0: $tType]:((coinductive_llist @ X0 > nat > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_26, type, lList21805353693veness: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_27, type, lList2170638824_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_28, type, lList21232602520length: !>[X0: $tType]:((coinductive_llist @ X0 > nat))).
% 0.97/0.37 thf(func_def_29, type, lList2281150353e_lrev: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_30, type, lList22119844313_ltake: !>[X0: $tType]:((coinductive_llist @ X0 > nat > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_31, type, lList2467029176inpref: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_32, type, lList21952340509veness: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_33, type, lList21148268032oslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_34, type, lList292406316safety: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_35, type, lList21974196564closed: !>[X0: $tType]:((set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_36, type, lList21638733016closed: !>[X0: $tType]:((set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_37, type, lList21350011628safety: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_38, type, lList21475143548e_suff: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_39, type, lList2736192599closed: !>[X0: $tType]:((set @ coinductive_llist @ X0 > $o))).
% 0.97/0.37 thf(func_def_40, type, suc: (nat > nat)).
% 0.97/0.37 thf(func_def_41, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.97/0.37 thf(func_def_42, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.97/0.37 thf(func_def_43, type, top_top: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_44, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.97/0.37 thf(func_def_45, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.97/0.37 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.97/0.37 thf(func_def_47, type, p: set @ coinductive_llist @ a).
% 0.97/0.37 thf(func_def_48, type, r: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_49, type, s: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_50, type, t: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_51, type, u: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_52, type, v: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.97/0.37 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.97/0.37 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.97/0.37 thf(func_def_59, type, db0: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_60, type, db2: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.97/0.37 thf(func_def_62, type, vAND: ($o > $o > $o)).
% 0.97/0.37 thf(func_def_63, type, db3: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_64, type, db1: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_65, type, db4: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_66, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.97/0.37 thf(func_def_67, type, vNOT: ($o > $o)).
% 0.97/0.37 thf(func_def_68, type, vOR: ($o > $o > $o)).
% 0.97/0.37 thf(func_def_69, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.97/0.37 thf(func_def_70, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.97/0.37 thf(func_def_71, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.97/0.37 thf(func_def_72, type, sK3: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_73, type, sK4: coinductive_llist @ a).
% 0.97/0.37 thf(func_def_74, type, sK5: !>[X0: $tType]:((set @ X0 > X0))).
% 0.97/0.37 thf(func_def_75, type, sK6: !>[X0: $tType]:(X0)).
% 0.97/0.37 thf(func_def_76, type, sK7: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_77, type, sK8: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_78, type, sK9: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_79, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_80, type, sK11: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_81, type, sK12: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_82, type, sK13: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_83, type, sK14: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_84, type, sK15: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_85, type, sK16: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_86, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.97/0.37 thf(func_def_87, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.97/0.37 thf(func_def_88, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.37 thf(func_def_89, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.37 thf(func_def_90, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.37 thf(func_def_91, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.37 thf(func_def_92, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.37 thf(func_def_93, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.97/0.37 thf(func_def_94, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.37 thf(func_def_95, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.97/0.37 thf(func_def_96, type, sK27: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_97, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_98, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_99, type, sK30: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_100, type, sK31: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_101, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_102, type, sK33: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_103, type, sK34: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_104, type, sK35: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_105, type, sK36: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_106, type, sK37: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_107, type, sK38: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_108, type, sK39: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_109, type, sK40: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_110, type, sK41: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_111, type, sK42: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_112, type, sK43: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_113, type, sK44: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_114, type, sK45: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_115, type, sK46: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_116, type, sK47: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_117, type, sK48: !>[X0: $tType]:((set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_118, type, sK49: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_119, type, sK50: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_120, type, sK51: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_121, type, sK52: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_122, type, sK53: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_123, type, sK54: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_124, type, sK55: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_125, type, sK56: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_126, type, sK57: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_127, type, sK58: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_128, type, sK59: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_129, type, sK60: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_130, type, sK61: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_131, type, sK62: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_132, type, sK63: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_133, type, sK64: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.97/0.37 thf(func_def_134, type, sK65: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.97/0.37 thf(func_def_135, type, sK66: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_136, type, sK67: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_137, type, sK68: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_138, type, sK69: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > X0))).
% 0.97/0.37 thf(func_def_139, type, sK70: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_140, type, sK71: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_141, type, sK72: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.97/0.37 thf(func_def_142, type, sK73: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.97/0.37 thf(func_def_143, type, sK74: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_144, type, sK75: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_145, type, sK76: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_146, type, sK77: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_147, type, sK78: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_148, type, sK79: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_149, type, sK80: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_150, type, sK81: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_151, type, sK82: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_152, type, sK83: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_153, type, sK84: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_154, type, sK85: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_155, type, sK86: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_156, type, sK87: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_157, type, sK88: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_158, type, sK89: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_159, type, sK90: !>[X0: $tType]:((set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_160, type, sK91: !>[X0: $tType]:((coinductive_llist @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_161, type, sK92: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_162, type, sK93: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_163, type, sK94: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_164, type, sK95: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_165, type, sK96: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_166, type, sK97: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_167, type, sK98: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_168, type, sK99: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_169, type, sK100: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_170, type, sK101: !>[X0: $tType]:((set @ coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_171, type, sK102: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_172, type, sK103: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.97/0.37 thf(func_def_173, type, sK104: (coinductive_llist @ a > coinductive_llist @ a)).
% 0.97/0.37 thf(f1,axiom,(
% 0.97/0.37 (member @ coinductive_llist @ a @ t @ p)),
% 0.97/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_tP)).
% 0.97/0.37 thf(f2,axiom,(
% 0.97/0.37 (t = ((coinductive_lappend @ a @ r @ (coinductive_lappend @ a @ u @ v))))),
% 0.97/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062t_A_061_Ar_A_064_064_Au_A_064_064_Av_092_060close_062)).
% 0.97/0.37 thf(f6,axiom,(
% 0.97/0.37 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))),
% 0.97/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_alllsts__UNIV)).
% 0.97/0.37 thf(f280,conjecture,(
% 0.97/0.37 ? [X0 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p) & (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a)))),
% 0.97/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.97/0.37 thf(f281,negated_conjecture,(
% 0.97/0.37 ~ ? [X0 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p) & (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a)))),
% 0.97/0.37 inference(negated_conjecture,[status(cth)],[f280])).
% 0.97/0.37 thf(f282,plain,(
% 0.97/0.37 (member @ coinductive_llist @ a @ t @ p)),
% 0.97/0.37 inference(rectify,[],[f1])).
% 0.97/0.37 thf(f283,plain,(
% 0.97/0.37 (((member @ coinductive_llist @ a @ t @ p)) = $true)),
% 0.97/0.37 inference(fool_elimination,[],[f282])).
% 0.97/0.37 thf(f286,plain,(
% 0.97/0.37 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))),
% 0.97/0.37 inference(rectify,[],[f6])).
% 0.97/0.37 thf(f287,plain,(
% 0.97/0.37 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))) = $true)),
% 0.97/0.37 inference(fool_elimination,[],[f286])).
% 0.97/0.37 thf(f759,plain,(
% 0.97/0.37 ~ ? [X0 : coinductive_llist @ a] : ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p) & (member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a)))),
% 0.97/0.37 inference(rectify,[],[f281])).
% 0.97/0.37 thf(f760,plain,(
% 0.97/0.37 ~ ? [X0 : coinductive_llist @ a] : ((((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p)) = $true) & (((member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a))) = $true))),
% 0.97/0.37 inference(fool_elimination,[],[f759])).
% 0.97/0.37 thf(f1019,plain,(
% 0.97/0.37 ! [X0 : coinductive_llist @ a] : ((((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p)) != $true) | (((member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a))) != $true))),
% 0.97/0.37 inference(ennf_transformation,[],[f760])).
% 0.97/0.37 thf(f1074,plain,(
% 0.97/0.37 (((member @ coinductive_llist @ a @ t @ p)) = $true)),
% 0.97/0.37 inference(cnf_transformation,[],[f283])).
% 0.97/0.37 thf(f1075,plain,(
% 0.97/0.37 (t = ((coinductive_lappend @ a @ r @ (coinductive_lappend @ a @ u @ v))))),
% 0.97/0.37 inference(cnf_transformation,[],[f2])).
% 0.97/0.37 thf(f1079,plain,(
% 0.97/0.37 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((member @ coinductive_llist @ X0 @ X1 @ (lList2435255213lllsts @ X0 @ top_top @ set @ X0))) = $true)) )),
% 0.97/0.37 inference(cnf_transformation,[],[f287])).
% 0.97/0.37 thf(f1436,plain,(
% 0.97/0.37 ( ! [X0 : coinductive_llist @ a] : ((((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p)) != $true) | (((member @ coinductive_llist @ a @ X0 @ (lList2435255213lllsts @ a @ top_top @ set @ a))) != $true)) )),
% 0.97/0.37 inference(cnf_transformation,[],[f1019])).
% 0.97/0.37 thf(f3009,plain,(
% 0.97/0.37 ( ! [X0 : coinductive_llist @ a] : ((((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ r @ X0) @ p)) != $true)) )),
% 0.97/0.37 inference(backward_subsumption_resolution,[],[f1436,f1079])).
% 0.97/0.37 thf(f3056,plain,(
% 0.97/0.37 (((member @ coinductive_llist @ a @ t @ p)) != $true)),
% 0.97/0.37 inference(constrained_superposition,[],[f3009,f1075])).
% 0.97/0.37 thf(f3061,plain,(
% 0.97/0.37 $false),
% 0.97/0.37 inference(forward_subsumption_resolution,[],[f3056,f1074])).
% 0.97/0.37 % SZS output end Proof for theBenchmark
% 0.97/0.37 % (1114997)------------------------------
% 0.97/0.37 % (1114997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.97/0.37 % (1114997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.97/0.37 % (1114997)CaDiCaL version: 2.1.3
% 0.97/0.37 % (1114997)Termination reason: Refutation
% 0.97/0.37 % (1114997)Time elapsed: 0.109 s
% 0.97/0.37 % (1114997)Peak memory usage: 14 MB
% 0.97/0.37 % (1114997)Instructions burned: 221 (million)
% 0.97/0.37 % (1114991)Success in time 0.157 s
% 0.97/0.37 % Vampire exiting
%------------------------------------------------------------------------------