%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT119^1 : 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 : n018.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 07:48:54 AM UTC 2026
% Result : Theorem 2.21s 0.58s
% Output : Refutation 2.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT119^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:00:41 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 2.21/0.58 % (432341)Will run a generic schedule for satisfiability detection.
% 2.21/0.58 % (432366)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3487121079_2999 on theBenchmark for (2999ds/0Mi)
% 2.21/0.58 % (432367)% WARNING: option uhcvi not known.
% 2.21/0.58 % (432369)dis+10_1_sil=32000:sp=arity:random_seed=2102544454:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.21/0.58 % (432367)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3222988378:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.21/0.58 % (432368)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2650666930:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.21/0.58 % (432372)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=94251174:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.21/0.58 % (432370)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3239204891:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.21/0.58 % (432371)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=723659076:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.21/0.58 % Exception at run slice level
% 2.21/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.21/0.58 % (432367)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.21/0.58 % (432370)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.21/0.58 % (432390)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2656617770:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.21/0.58 % (432367)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.21/0.58 % Exception at run slice level
% 2.21/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.21/0.58 % (432398)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=390570266:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.21/0.58 % (432369)Instruction limit reached!
% 2.21/0.58 % (432369)------------------------------
% 2.21/0.58 % (432369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.58 % (432369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.58 % (432369)CaDiCaL version: 2.1.3
% 2.21/0.58 % (432369)Termination reason: Instruction limit
% 2.21/0.58 % (432369)Termination phase: Saturation
% 2.21/0.58 % (432369)Time elapsed: 0.049 s
% 2.21/0.58 % (432369)Peak memory usage: 12 MB
% 2.21/0.58 % (432369)Instructions burned: 104 (million)
% 2.21/0.58 % (432370)Instruction limit reached!
% 2.21/0.58 % (432370)------------------------------
% 2.21/0.58 % (432370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.58 % (432370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.58 % (432370)CaDiCaL version: 2.1.3
% 2.21/0.58 % (432370)Termination reason: Instruction limit
% 2.21/0.58 % (432370)Termination phase: Saturation
% 2.21/0.58 % (432370)Time elapsed: 0.055 s
% 2.21/0.58 % (432370)Peak memory usage: 13 MB
% 2.21/0.58 % (432370)Instructions burned: 117 (million)
% 2.21/0.58 % (432371)Instruction limit reached!
% 2.21/0.58 % (432371)------------------------------
% 2.21/0.58 % (432371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.58 % (432371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.58 % (432371)CaDiCaL version: 2.1.3
% 2.21/0.58 % (432371)Termination reason: Instruction limit
% 2.21/0.58 % (432371)Termination phase: Saturation
% 2.21/0.58 % (432371)Time elapsed: 0.062 s
% 2.21/0.58 % (432371)Peak memory usage: 13 MB
% 2.21/0.58 % (432371)Instructions burned: 131 (million)
% 2.21/0.58 % (432406)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=922733125:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.21/0.58 % (432410)ott-21_1_sil=16000:fs=off:random_seed=1203151480:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.21/0.58 % (432372)Instruction limit reached!
% 2.21/0.58 % (432372)------------------------------
% 2.21/0.58 % (432372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.58 % (432372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.58 % (432372)CaDiCaL version: 2.1.3
% 2.21/0.58 % (432372)Termination reason: Instruction limit
% 2.21/0.58 % (432372)Termination phase: Saturation
% 2.21/0.58 % (432372)Time elapsed: 0.081 s
% 2.21/0.58 % (432372)Peak memory usage: 14 MB
% 2.21/0.58 % (432372)Instructions burned: 159 (million)
% 2.21/0.58 % (432414)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=219226577:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.21/0.58 % (432398)Instruction limit reached!
% 2.21/0.58 % (432398)------------------------------
% 2.21/0.58 % (432398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.58 % (432398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.58 % (432398)CaDiCaL version: 2.1.3
% 2.21/0.58 % (432398)Termination reason: Instruction limit
% 2.21/0.58 % (432398)Termination phase: Saturation
% 2.21/0.58 % (432398)Time elapsed: 0.035 s
% 2.21/0.58 % (432398)Peak memory usage: 13 MB
% 2.21/0.58 % (432398)Instructions burned: 132 (million)
% 2.21/0.58 % (432406)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.21/0.58 % (432422)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=248939064:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.21/0.58 % (432420)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=692939186:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.21/0.58 % (432406)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.21/0.58 % Exception at run slice level
% 2.21/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.21/0.58 % (432441)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2507957021:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.21/0.58 % (432410)Instruction limit reached!
% 2.21/0.58 % (432410)------------------------------
% 2.21/0.58 % (432410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.58 % (432410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.58 % (432410)CaDiCaL version: 2.1.3
% 2.21/0.58 % (432410)Termination reason: Instruction limit
% 2.21/0.58 % (432410)Termination phase: Saturation
% 2.21/0.58 % (432410)Time elapsed: 0.081 s
% 2.21/0.58 % (432410)Peak memory usage: 13 MB
% 2.21/0.58 % (432410)Instructions burned: 181 (million)
% 2.21/0.58 % (432451)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3681500629:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.21/0.58 % Exception at run slice level
% 2.21/0.58 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.21/0.58 % (432451)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.21/0.58 % (432471)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2190237816:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.21/0.58 % (432471)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.21/0.58 % (432367) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-432341-432367"...
% 2.21/0.58 % (432367)...printing done.
% 2.21/0.58 % (432367)Refutation found. Thanks to Tanya!
% 2.21/0.58 % SZS status Theorem for theBenchmark
% 2.21/0.58 % SZS output start Proof for theBenchmark
% 2.21/0.58 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 2.21/0.58 thf(type_def_6, type, extended_enat: $tType).
% 2.21/0.58 thf(type_def_7, type, set: $tType > $tType).
% 2.21/0.58 thf(type_def_8, type, nat: $tType).
% 2.21/0.58 thf(type_def_9, type, itself: $tType > $tType).
% 2.21/0.58 thf(type_def_10, type, a: $tType).
% 2.21/0.58 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 2.21/0.58 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_3, type, mult_zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_4, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_5, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_6, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_7, type, ordered_ring: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_8, type, semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_9, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_10, type, linordered_ring: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_11, type, ordered_semiring: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_12, type, comm_monoid_diff: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_13, type, ab_semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_14, type, ordered_semiring_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_16, type, linord581940658strict: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_17, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_18, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_19, type, semiri1193490041visors: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_20, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_21, type, semiri1923998003cancel: !>[X0: $tType]:((itself @ X0 > $o))).
% 2.21/0.58 thf(func_def_22, type, coindu1928975208n_lset: !>[X0: $tType]:((set @ X0 > coindu1593790203_llist @ X0 > set @ X0))).
% 2.21/0.58 thf(func_def_23, type, coindu1529956631erates: !>[X0: $tType]:(((X0 > X0) > X0 > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_24, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_25, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 2.21/0.58 thf(func_def_26, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 2.21/0.58 thf(func_def_27, type, coindu300403952lexord: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 2.21/0.58 thf(func_def_28, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_29, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 2.21/0.58 thf(func_def_30, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0))).
% 2.21/0.58 thf(func_def_31, type, coindu1244876290_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coindu1593790203_llist @ X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 2.21/0.58 thf(func_def_32, type, coindu44415597_llist: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > $o))).
% 2.21/0.58 thf(func_def_33, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 2.21/0.58 thf(func_def_34, type, coindu1055736764_lsetp: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o))).
% 2.21/0.58 thf(func_def_35, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 2.21/0.58 thf(func_def_36, type, coinductive_enat_set: set @ extended_enat).
% 2.21/0.58 thf(func_def_37, type, coindu530039314t_setp: (extended_enat > $o)).
% 2.21/0.58 thf(func_def_38, type, coindu1491768222unfold: !>[X0: $tType]:(((X0 > $o) > (X0 > X0) > X0 > extended_enat))).
% 2.21/0.58 thf(func_def_39, type, extended_eSuc: (extended_enat > extended_enat)).
% 2.21/0.58 thf(func_def_40, type, extended_enat2: (nat > extended_enat)).
% 2.21/0.58 thf(func_def_41, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 2.21/0.58 thf(func_def_42, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 2.21/0.58 thf(func_def_43, type, extended_size_enat: (extended_enat > nat)).
% 2.21/0.58 thf(func_def_44, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_45, type, extended_the_enat: (extended_enat > nat)).
% 2.21/0.58 thf(func_def_46, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.21/0.58 thf(func_def_47, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.21/0.58 thf(func_def_48, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_49, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.21/0.58 thf(func_def_50, type, suc: (nat > nat)).
% 2.21/0.58 thf(func_def_51, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 2.21/0.58 thf(func_def_52, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 2.21/0.58 thf(func_def_53, type, nat_triangle: (nat > nat)).
% 2.21/0.58 thf(func_def_54, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.21/0.58 thf(func_def_55, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.21/0.58 thf(func_def_56, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.21/0.58 thf(func_def_57, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.21/0.58 thf(func_def_58, type, na: nat).
% 2.21/0.58 thf(func_def_59, type, thesis: $o).
% 2.21/0.58 thf(func_def_60, type, xsa: coindu1593790203_llist @ a).
% 2.21/0.58 thf(func_def_62, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.21/0.58 thf(func_def_63, type, vAND: ($o > $o > $o)).
% 2.21/0.58 thf(func_def_64, type, vOR: ($o > $o > $o)).
% 2.21/0.58 thf(func_def_65, type, db0: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_66, type, db1: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_67, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.21/0.58 thf(func_def_70, type, vNOT: ($o > $o)).
% 2.21/0.58 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.21/0.58 thf(func_def_72, type, db3: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_73, type, db2: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_74, type, db4: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_75, type, db5: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_76, type, db6: !>[X0: $tType]:(X0)).
% 2.21/0.58 thf(func_def_77, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.21/0.58 thf(func_def_78, type, sP0: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > $o))).
% 2.21/0.58 thf(func_def_79, type, sP1: (extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_80, type, sP2: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_81, type, sP3: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_82, type, sP4: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_83, type, sP5: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_84, type, sP6: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_85, type, sP7: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_86, type, sP8: (extended_enat > extended_enat > extended_enat > $o)).
% 2.21/0.58 thf(func_def_87, type, sK9: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_88, type, sK10: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > X0))).
% 2.21/0.58 thf(func_def_89, type, sK11: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > X0))).
% 2.21/0.58 thf(func_def_90, type, sK12: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_91, type, sK13: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_92, type, sK14: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > X0))).
% 2.21/0.58 thf(func_def_93, type, sK15: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > X0))).
% 2.21/0.58 thf(func_def_94, type, sK16: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > X0))).
% 2.21/0.58 thf(func_def_95, type, sK17: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_96, type, sK18: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_97, type, sK19: !>[X0: $tType]:(((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_98, type, sK20: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_99, type, sK21: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_100, type, sK22: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 2.21/0.58 thf(func_def_101, type, sK23: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.58 thf(func_def_102, type, sK24: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 2.21/0.58 thf(func_def_103, type, sK25: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0))).
% 2.21/0.58 thf(func_def_104, type, sK26: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_105, type, sK27: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_106, type, sK28: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_107, type, sK29: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.21/0.59 thf(func_def_108, type, sK30: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_109, type, sK31: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_110, type, sK32: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.21/0.59 thf(func_def_111, type, sK33: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_112, type, sK34: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_113, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.21/0.59 thf(func_def_114, type, sK36: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_115, type, sK37: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_116, type, sK38: (extended_enat > extended_enat)).
% 2.21/0.59 thf(func_def_117, type, sK39: (extended_enat > extended_enat)).
% 2.21/0.59 thf(func_def_118, type, sK40: ((extended_enat > $o) > extended_enat)).
% 2.21/0.59 thf(func_def_119, type, sK41: (extended_enat > extended_enat)).
% 2.21/0.59 thf(func_def_120, type, sK42: ((extended_enat > $o) > extended_enat)).
% 2.21/0.59 thf(func_def_121, type, sK43: (extended_enat > extended_enat)).
% 2.21/0.59 thf(func_def_122, type, sK44: (nat > nat)).
% 2.21/0.59 thf(func_def_123, type, sK45: ((nat > $o) > nat)).
% 2.21/0.59 thf(func_def_124, type, sK46: (nat > nat)).
% 2.21/0.59 thf(func_def_125, type, sK47: ((nat > $o) > nat)).
% 2.21/0.59 thf(func_def_126, type, sK48: ((nat > nat > $o) > nat)).
% 2.21/0.59 thf(func_def_127, type, sK49: ((nat > nat > $o) > nat)).
% 2.21/0.59 thf(func_def_128, type, sK50: ((nat > nat > $o) > nat)).
% 2.21/0.59 thf(func_def_129, type, sK51: ((nat > nat > $o) > nat)).
% 2.21/0.59 thf(func_def_130, type, sK52: ((nat > $o) > nat)).
% 2.21/0.59 thf(func_def_131, type, sK53: !>[X0: $tType]:(((X0 > X0) > (X0 > extended_enat) > (X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_132, type, sK54: (nat > nat)).
% 2.21/0.59 thf(func_def_133, type, sK55: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_134, type, sK56: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_135, type, sK57: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_136, type, sK58: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_137, type, sK59: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_138, type, sK60: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_139, type, sK61: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_140, type, sK62: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_141, type, sK63: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_142, type, sK64: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_143, type, sK65: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_144, type, sK66: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_145, type, sK67: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_146, type, sK68: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_147, type, sK69: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_148, type, sK70: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_149, type, sK71: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_150, type, sK72: ((extended_enat > $o) > nat)).
% 2.21/0.59 thf(func_def_151, type, sK73: ((nat > $o) > nat)).
% 2.21/0.59 thf(func_def_152, type, sK74: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0))).
% 2.21/0.59 thf(func_def_153, type, sK75: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_154, type, sK76: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat))).
% 2.21/0.59 thf(func_def_155, type, sK77: ((nat > nat > $o) > nat)).
% 2.21/0.59 thf(func_def_156, type, sK78: ((nat > nat > $o) > nat)).
% 2.21/0.59 thf(func_def_157, type, sK79: ((nat > $o) > nat)).
% 2.21/0.59 thf(func_def_158, type, sK80: !>[X0: $tType]:(((nat > X0) > nat))).
% 2.21/0.59 thf(func_def_159, type, sK81: !>[X0: $tType]:(((nat > X0) > nat))).
% 2.21/0.59 thf(func_def_160, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_161, type, sK83: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.21/0.59 thf(func_def_162, type, sK84: ((nat > $o) > nat)).
% 2.21/0.59 thf(func_def_163, type, sK85: (nat > nat)).
% 2.21/0.59 thf(func_def_164, type, sK86: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_165, type, sK87: (extended_enat > nat)).
% 2.21/0.59 thf(func_def_166, type, sK88: (extended_enat > extended_enat)).
% 2.21/0.59 thf(func_def_167, type, sK89: (extended_enat > extended_enat)).
% 2.21/0.59 thf(func_def_168, type, sK90: (nat > extended_enat > nat)).
% 2.21/0.59 thf(func_def_169, type, sK91: (extended_enat > nat > nat)).
% 2.21/0.59 thf(func_def_170, type, sK92: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 2.21/0.59 thf(func_def_171, type, sK93: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 2.21/0.59 thf(f1,axiom,(
% 2.21/0.59 (((coindu1018505716length @ a @ xsa)) = ((extended_enat2 @ (suc @ na))))),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_len)).
% 2.21/0.59 thf(f35,axiom,(
% 2.21/0.59 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((X1 != coindu1598213697e_LNil @ X0) => ~ ! [X2 : X0,X3 : coindu1593790203_llist @ X0] : (X1 != ((coindu1121789889_LCons @ X0 @ X2 @ X3))))),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_llist_Oexhaust)).
% 2.21/0.59 thf(f55,axiom,(
% 2.21/0.59 ! [X0 : $tType] : (((coindu1018505716length @ X0 @ coindu1598213697e_LNil @ X0)) = zero_zero @ extended_enat)),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_llength__LNil)).
% 2.21/0.59 thf(f90,axiom,(
% 2.21/0.59 ! [X0 : nat] : (zero_zero @ nat != ((suc @ X0)))),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Zero__not__Suc)).
% 2.21/0.59 thf(f106,axiom,(
% 2.21/0.59 ! [X0 : nat] : ((((extended_enat2 @ X0)) = zero_zero @ extended_enat) = (X0 = zero_zero @ nat))),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_enat__0__iff_I1_J)).
% 2.21/0.59 thf(f287,axiom,(
% 2.21/0.59 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((xsa = ((coindu1121789889_LCons @ a @ X0 @ X1))) => thesis)),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 2.21/0.59 thf(f288,conjecture,(
% 2.21/0.59 thesis),
% 2.21/0.59 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 2.21/0.59 thf(f289,negated_conjecture,(
% 2.21/0.59 ~thesis),
% 2.21/0.59 inference(negated_conjecture,[status(cth)],[f288])).
% 2.21/0.59 thf(f401,plain,(
% 2.21/0.59 ! [X0 : nat] : ((((extended_enat2 @ X0) = zero_zero @ extended_enat)) = ((zero_zero @ nat = X0)))),
% 2.21/0.59 inference(fool_elimination,[],[f106])).
% 2.21/0.59 thf(f660,plain,(
% 2.21/0.59 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((xsa = ((coindu1121789889_LCons @ a @ X0 @ X1))) => thesis)),
% 2.21/0.59 inference(rectify,[],[f287])).
% 2.21/0.59 thf(f661,plain,(
% 2.21/0.59 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((xsa = ((coindu1121789889_LCons @ a @ X0 @ X1))) => (thesis = $true))),
% 2.21/0.59 inference(fool_elimination,[],[f660])).
% 2.21/0.59 thf(f662,plain,(
% 2.21/0.59 ~thesis),
% 2.21/0.59 inference(rectify,[],[f289])).
% 2.21/0.59 thf(f663,plain,(
% 2.21/0.59 ~ (thesis = $true)),
% 2.21/0.59 inference(fool_elimination,[],[f662])).
% 2.21/0.59 thf(f681,plain,(
% 2.21/0.59 (thesis != $true)),
% 2.21/0.59 inference(flattening,[],[f663])).
% 2.21/0.59 thf(f700,plain,(
% 2.21/0.59 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (? [X2 : X0,X3 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ X2 @ X3)) = X1) | (coindu1598213697e_LNil @ X0 = X1))),
% 2.21/0.59 inference(ennf_transformation,[],[f35])).
% 2.21/0.59 thf(f851,plain,(
% 2.21/0.59 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((thesis = $true) | (xsa != ((coindu1121789889_LCons @ a @ X0 @ X1))))),
% 2.21/0.59 inference(ennf_transformation,[],[f661])).
% 2.21/0.59 thf(f876,plain,(
% 2.21/0.59 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((((coindu1121789889_LCons @ X0 @ (sK32 @ X0 @ X1) @ (sK33 @ X0 @ X1))) = X1) | (coindu1598213697e_LNil @ X0 = X1))),
% 2.21/0.59 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X6,sK12 @ X0 @ X2 @ X1),skolemize(X6,sK12 @ X0 @ X2 @ X1)],[f700])).
% 2.21/0.59 thf(f934,plain,(
% 2.21/0.59 (((coindu1018505716length @ a @ xsa)) = ((extended_enat2 @ (suc @ na))))),
% 2.21/0.59 inference(cnf_transformation,[],[f1])).
% 2.21/0.59 thf(f988,plain,(
% 2.21/0.59 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((((coindu1121789889_LCons @ X0 @ (sK32 @ X0 @ X1) @ (sK33 @ X0 @ X1))) = X1) | (coindu1598213697e_LNil @ X0 = X1)) )),
% 2.21/0.59 inference(cnf_transformation,[],[f876])).
% 2.21/0.59 thf(f1010,plain,(
% 2.21/0.59 ( ! [X0 : $tType] : ((((coindu1018505716length @ X0 @ coindu1598213697e_LNil @ X0)) = zero_zero @ extended_enat)) )),
% 2.21/0.59 inference(cnf_transformation,[],[f55])).
% 2.21/0.59 thf(f1054,plain,(
% 2.21/0.59 ( ! [X0 : nat] : ((((suc @ X0)) != zero_zero @ nat)) )),
% 2.21/0.59 inference(cnf_transformation,[],[f90])).
% 2.21/0.59 thf(f1073,plain,(
% 2.21/0.59 ( ! [X0 : nat] : (((((extended_enat2 @ X0) = zero_zero @ extended_enat)) = ((zero_zero @ nat = X0)))) )),
% 2.21/0.59 inference(cnf_transformation,[],[f401])).
% 2.21/0.59 thf(f1304,plain,(
% 2.21/0.59 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((thesis = $true) | (xsa != ((coindu1121789889_LCons @ a @ X0 @ X1)))) )),
% 2.21/0.59 inference(cnf_transformation,[],[f851])).
% 2.21/0.59 thf(f1305,plain,(
% 2.21/0.59 (thesis != $true)),
% 2.21/0.59 inference(cnf_transformation,[],[f681])).
% 2.21/0.59 thf(f1599,plain,(
% 2.21/0.59 ( ! [X0 : nat] : (((((extended_enat2 @ X0) = zero_zero @ extended_enat)) = $false) | ($true = ((zero_zero @ nat = X0)))) )),
% 2.21/0.59 inference(iff_proxy_clausification,[],[f1073])).
% 2.21/0.59 thf(f1600,plain,(
% 2.21/0.59 ( ! [X0 : nat] : ((((extended_enat2 @ X0)) != zero_zero @ extended_enat) | ($true = ((zero_zero @ nat = X0)))) )),
% 2.21/0.59 inference(equality_proxy_clausification,[],[f1599])).
% 2.21/0.59 thf(f1601,plain,(
% 2.21/0.59 ( ! [X0 : nat] : ((((extended_enat2 @ X0)) != zero_zero @ extended_enat) | (zero_zero @ nat = X0)) )),
% 2.21/0.59 inference(equality_proxy_clausification,[],[f1600])).
% 2.21/0.59 thf(f1798,definition,(
% 2.21/0.59 spl94_1 <=> ! [X0 : a,X1 : coindu1593790203_llist @ a] : (xsa != ((coindu1121789889_LCons @ a @ X0 @ X1)))),
% 2.21/0.59 introduced(definition,[new_symbols(definition,[spl94_1])],[avatar_definition])).
% 2.21/0.59 thf(f1799,plain,(
% 2.21/0.59 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((xsa != ((coindu1121789889_LCons @ a @ X0 @ X1)))) ) | ~spl94_1),
% 2.21/0.59 inference(avatar_component_clause,[],[f1798])).
% 2.21/0.59 thf(f1801,definition,(
% 2.21/0.59 spl94_2 <=> (thesis = $true)),
% 2.21/0.59 introduced(definition,[new_symbols(definition,[spl94_2])],[avatar_definition])).
% 2.21/0.59 thf(f1804,plain,(
% 2.21/0.59 spl94_1 | spl94_2),
% 2.21/0.59 inference(avatar_split_clause,[],[f1304,f1801,f1798])).
% 2.21/0.59 thf(f1805,plain,(
% 2.21/0.59 ~spl94_2),
% 2.21/0.59 inference(avatar_split_clause,[],[f1305,f1801])).
% 2.21/0.59 thf(f1871,plain,(
% 2.21/0.59 (((coindu1018505716length @ a @ xsa)) != zero_zero @ extended_enat) | (((suc @ na)) = zero_zero @ nat)),
% 2.21/0.59 inference(constrained_superposition,[],[f1601,f934])).
% 2.21/0.59 thf(f1872,plain,(
% 2.21/0.59 (((coindu1018505716length @ a @ xsa)) != zero_zero @ extended_enat)),
% 2.21/0.59 inference(forward_subsumption_resolution,[],[f1871,f1054])).
% 2.21/0.59 thf(f6497,plain,(
% 2.21/0.59 ( ! [X0 : coindu1593790203_llist @ a] : ((xsa != X0) | (coindu1598213697e_LNil @ a = X0)) ) | ~spl94_1),
% 2.21/0.59 inference(constrained_superposition,[],[f1799,f988])).
% 2.21/0.59 thf(f6939,plain,(
% 2.21/0.59 (xsa = coindu1598213697e_LNil @ a) | ~spl94_1),
% 2.21/0.59 inference(equality_resolution,[],[f6497])).
% 2.21/0.59 thf(f6981,plain,(
% 2.21/0.59 (((coindu1018505716length @ a @ xsa)) = zero_zero @ extended_enat) | ~spl94_1),
% 2.21/0.59 inference(constrained_superposition,[],[f1010,f6939])).
% 2.21/0.59 thf(f6985,plain,(
% 2.21/0.59 $false | ~spl94_1),
% 2.21/0.59 inference(forward_subsumption_resolution,[],[f6981,f1872])).
% 2.21/0.59 thf(f6986,plain,(
% 2.21/0.59 ~spl94_1),
% 2.21/0.59 inference(avatar_contradiction_clause,[],[f6985])).
% 2.21/0.59 cnf(s1, plain, spl94_1 | spl94_2, inference(sat_conversion,[],[f1804])).
% 2.21/0.59 cnf(s2, plain, ~spl94_2, inference(sat_conversion,[],[f1805])).
% 2.21/0.59 cnf(s300, plain, ~spl94_1, inference(sat_conversion,[],[f6986])).
% 2.21/0.59 cnf(s508, plain, $false, inference(rat,[],[s1,s2,s300])).
% 2.21/0.59 thf(f6987,plain,(
% 2.21/0.59 $false),
% 2.21/0.59 inference(avatar_sat_refutation,[],[s508])).
% 2.21/0.59 % SZS output end Proof for theBenchmark
% 2.21/0.59 % (432367)------------------------------
% 2.21/0.59 % (432367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.59 % (432367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.59 % (432367)CaDiCaL version: 2.1.3
% 2.21/0.59 % (432367)Termination reason: Refutation
% 2.21/0.59 % (432367)Time elapsed: 0.288 s
% 2.21/0.59 % (432367)Peak memory usage: 17 MB
% 2.21/0.59 % (432367)Instructions burned: 590 (million)
% 2.21/0.59 % (432341)Success in time 0.347 s
% 2.21/0.59 % Vampire exiting
%------------------------------------------------------------------------------