%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT129^1 : 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 : n008.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 07:48:55 AM UTC 2026
% Result : Theorem 3.84s 1.04s
% Output : Refutation 3.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT129^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 % Computer : n008.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 17:59:25 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.27/0.28 Running first-order model finding
% 0.27/0.28 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
% 3.84/1.04 % (3513327)Will run a generic schedule for satisfiability detection.
% 3.84/1.04 % (3513337)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=595707626:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.84/1.04 % (3513338)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3601597641:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.84/1.04 % (3513334)% WARNING: option uhcvi not known.
% 3.84/1.04 % (3513337)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.84/1.04 % (3513333)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3265350119_2999 on theBenchmark for (2999ds/0Mi)
% 3.84/1.04 % (3513335)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=25298598:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.84/1.04 % (3513334)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=706923851:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.84/1.04 % (3513336)dis+10_1_sil=32000:sp=arity:random_seed=2706116448:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.84/1.04 % (3513339)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1195314816:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.84/1.04 % (3513334)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.84/1.04 % (3513337)Instruction limit reached!
% 3.84/1.04 % (3513337)------------------------------
% 3.84/1.04 % (3513337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513337)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513337)Termination reason: Instruction limit
% 3.84/1.04 % (3513337)Termination phase: Saturation
% 3.84/1.04 % (3513337)Time elapsed: 0.053 s
% 3.84/1.04 % (3513337)Peak memory usage: 13 MB
% 3.84/1.04 % (3513337)Instructions burned: 117 (million)
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513334)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.84/1.04 % (3513347)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3863862200:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.84/1.04 % (3513349)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1149033774:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513336)Instruction limit reached!
% 3.84/1.04 % (3513336)------------------------------
% 3.84/1.04 % (3513336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513336)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513336)Termination reason: Instruction limit
% 3.84/1.04 % (3513336)Termination phase: Saturation
% 3.84/1.04 % (3513336)Time elapsed: 0.089 s
% 3.84/1.04 % (3513336)Peak memory usage: 13 MB
% 3.84/1.04 % (3513336)Instructions burned: 104 (million)
% 3.84/1.04 % (3513353)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=3809556026:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.84/1.04 % (3513354)ott-21_1_sil=16000:fs=off:random_seed=3525530284:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.84/1.04 % (3513338)Instruction limit reached!
% 3.84/1.04 % (3513338)------------------------------
% 3.84/1.04 % (3513338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513338)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513338)Termination reason: Instruction limit
% 3.84/1.04 % (3513338)Termination phase: Saturation
% 3.84/1.04 % (3513338)Time elapsed: 0.119 s
% 3.84/1.04 % (3513338)Peak memory usage: 13 MB
% 3.84/1.04 % (3513338)Instructions burned: 131 (million)
% 3.84/1.04 % (3513353)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.84/1.04 % (3513339)Instruction limit reached!
% 3.84/1.04 % (3513339)------------------------------
% 3.84/1.04 % (3513339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513339)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513339)Termination reason: Instruction limit
% 3.84/1.04 % (3513339)Termination phase: Saturation
% 3.84/1.04 % (3513339)Time elapsed: 0.124 s
% 3.84/1.04 % (3513339)Peak memory usage: 13 MB
% 3.84/1.04 % (3513339)Instructions burned: 159 (million)
% 3.84/1.04 % (3513353)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.84/1.04 % (3513357)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1072867360:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.84/1.04 % (3513358)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=685108357:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.84/1.04 % (3513349)Instruction limit reached!
% 3.84/1.04 % (3513349)------------------------------
% 3.84/1.04 % (3513349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513349)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513349)Termination reason: Instruction limit
% 3.84/1.04 % (3513349)Termination phase: Saturation
% 3.84/1.04 % (3513349)Time elapsed: 0.112 s
% 3.84/1.04 % (3513349)Peak memory usage: 13 MB
% 3.84/1.04 % (3513349)Instructions burned: 131 (million)
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513363)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1152590091:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 3.84/1.04 % (3513364)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3489649143:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.84/1.04 % (3513354)Instruction limit reached!
% 3.84/1.04 % (3513354)------------------------------
% 3.84/1.04 % (3513354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513354)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513354)Termination reason: Instruction limit
% 3.84/1.04 % (3513354)Termination phase: Saturation
% 3.84/1.04 % (3513354)Time elapsed: 0.146 s
% 3.84/1.04 % (3513354)Peak memory usage: 13 MB
% 3.84/1.04 % (3513354)Instructions burned: 180 (million)
% 3.84/1.04 % (3513367)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=4288203202:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 3.84/1.04 % (3513367)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513369)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2014401547:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 3.84/1.04 % (3513369)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.84/1.04 % (3513353)Instruction limit reached!
% 3.84/1.04 % (3513353)------------------------------
% 3.84/1.04 % (3513353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513353)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513353)Termination reason: Instruction limit
% 3.84/1.04 % (3513353)Termination phase: Saturation
% 3.84/1.04 % (3513353)Time elapsed: 0.290 s
% 3.84/1.04 % (3513353)Peak memory usage: 15 MB
% 3.84/1.04 % (3513353)Instructions burned: 687 (million)
% 3.84/1.04 % (3513371)fmb+10_1_sil=64000:random_seed=1844277946:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.84/1.04 % (3513371)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513373)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4150611165:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513375)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=682903192:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 3.84/1.04 % Exception at run slice level
% 3.84/1.04 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.84/1.04 % (3513357)Instruction limit reached!
% 3.84/1.04 % (3513357)------------------------------
% 3.84/1.04 % (3513357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513357)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513357)Termination reason: Instruction limit
% 3.84/1.04 % (3513357)Termination phase: Saturation
% 3.84/1.04 % (3513357)Time elapsed: 0.421 s
% 3.84/1.04 % (3513357)Peak memory usage: 14 MB
% 3.84/1.04 % (3513357)Instructions burned: 478 (million)
% 3.84/1.04 % (3513379)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2082642426:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 3.84/1.04 % (3513380)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3036604722:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 3.84/1.04 % (3513379)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.84/1.04 % (3513380)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.84/1.04 % (3513380)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.84/1.04 % (3513334) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3513327-3513334"...
% 3.84/1.04 % (3513334)...printing done.
% 3.84/1.04 % (3513334)Refutation found. Thanks to Tanya!
% 3.84/1.04 % SZS status Theorem for theBenchmark
% 3.84/1.04 % SZS output start Proof for theBenchmark
% 3.84/1.04 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 3.84/1.04 thf(type_def_6, type, extended_enat: $tType).
% 3.84/1.04 thf(type_def_7, type, nat: $tType).
% 3.84/1.04 thf(type_def_8, type, itself: $tType > $tType).
% 3.84/1.04 thf(type_def_9, type, a: $tType).
% 3.84/1.04 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 3.84/1.04 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_2, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_3, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_5, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_6, type, monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_7, type, ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_8, type, comm_monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_9, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_10, type, comm_monoid_diff: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_11, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_12, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_13, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_14, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_17, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_19, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_20, type, ordere223160158up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_21, type, strict2144017051up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_22, type, ordere516151231imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.84/1.04 thf(func_def_23, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 3.84/1.04 thf(func_def_24, type, coindu191418589_ldrop: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 3.84/1.04 thf(func_def_25, type, coindu531130065ldropn: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 3.84/1.04 thf(func_def_26, type, coindu2000965700_llast: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 3.84/1.04 thf(func_def_27, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 3.84/1.04 thf(func_def_28, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 3.84/1.04 thf(func_def_29, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 3.84/1.04 thf(func_def_30, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 3.84/1.04 thf(func_def_31, type, extended_enat2: (nat > extended_enat)).
% 3.84/1.04 thf(func_def_32, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 3.84/1.04 thf(func_def_33, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 3.84/1.04 thf(func_def_34, type, extended_size_enat: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_35, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 3.84/1.04 thf(func_def_36, type, extended_the_enat: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_37, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.84/1.04 thf(func_def_38, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.84/1.04 thf(func_def_39, type, zero_zero: !>[X0: $tType]:(X0)).
% 3.84/1.04 thf(func_def_40, type, suc: (nat > nat)).
% 3.84/1.04 thf(func_def_41, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 3.84/1.04 thf(func_def_42, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.84/1.04 thf(func_def_43, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.84/1.04 thf(func_def_44, type, n: extended_enat).
% 3.84/1.04 thf(func_def_45, type, n2: nat).
% 3.84/1.04 thf(func_def_46, type, n_a: nat).
% 3.84/1.04 thf(func_def_47, type, xs: coindu1593790203_llist @ a).
% 3.84/1.04 thf(func_def_48, type, xsa: coindu1593790203_llist @ a).
% 3.84/1.04 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.84/1.04 thf(func_def_53, type, vNOT: ($o > $o)).
% 3.84/1.04 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 3.84/1.04 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 3.84/1.04 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.84/1.04 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 3.84/1.04 thf(func_def_58, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.84/1.04 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 3.84/1.04 thf(func_def_60, type, db2: !>[X0: $tType]:(X0)).
% 3.84/1.04 thf(func_def_61, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.84/1.04 thf(func_def_62, type, sP0: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_63, type, sP1: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_64, type, sP2: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_65, type, sP3: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_66, type, sP4: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_67, type, sP5: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_68, type, sP6: (extended_enat > extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_69, type, sP7: (extended_enat > extended_enat > $o)).
% 3.84/1.04 thf(func_def_70, type, sK8: nat).
% 3.84/1.04 thf(func_def_71, type, sK9: !>[X0: $tType]:((nat > (X0 > extended_enat) > X0))).
% 3.84/1.04 thf(func_def_72, type, sK10: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 3.84/1.04 thf(func_def_73, type, sK11: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_74, type, sK12: ((extended_enat > $o) > extended_enat)).
% 3.84/1.04 thf(func_def_75, type, sK13: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.84/1.04 thf(func_def_76, type, sK14: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.84/1.04 thf(func_def_77, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.84/1.04 thf(func_def_78, type, sK16: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 3.84/1.04 thf(func_def_79, type, sK17: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_80, type, sK18: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_81, type, sK19: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_82, type, sK20: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 3.84/1.04 thf(func_def_83, type, sK21: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 3.84/1.04 thf(func_def_84, type, sK22: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 3.84/1.04 thf(func_def_85, type, sK23: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 3.84/1.04 thf(func_def_86, type, sK24: (nat > nat)).
% 3.84/1.04 thf(func_def_87, type, sK25: (nat > nat > nat)).
% 3.84/1.04 thf(func_def_88, type, sK26: (nat > nat > nat)).
% 3.84/1.04 thf(func_def_89, type, sK27: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_90, type, sK28: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_91, type, sK29: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_92, type, sK30: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_93, type, sK31: ((nat > $o) > nat > nat)).
% 3.84/1.04 thf(func_def_94, type, sK32: ((nat > $o) > nat > nat)).
% 3.84/1.04 thf(func_def_95, type, sK33: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_96, type, sK34: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_97, type, sK35: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_98, type, sK36: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_99, type, sK37: ((nat > nat > $o) > nat)).
% 3.84/1.04 thf(func_def_100, type, sK38: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_101, type, sK39: (nat > nat)).
% 3.84/1.04 thf(func_def_102, type, sK40: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_103, type, sK41: (nat > nat)).
% 3.84/1.04 thf(func_def_104, type, sK42: (nat > extended_enat > nat)).
% 3.84/1.04 thf(func_def_105, type, sK43: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 3.84/1.04 thf(func_def_106, type, sK44: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_107, type, sK45: ((extended_enat > $o) > nat)).
% 3.84/1.04 thf(func_def_108, type, sK46: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_109, type, sK47: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_110, type, sK48: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_111, type, sK49: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_112, type, sK50: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_113, type, sK51: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_114, type, sK52: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_115, type, sK53: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_116, type, sK54: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_117, type, sK55: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_118, type, sK56: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_119, type, sK57: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_120, type, sK58: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_121, type, sK59: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_122, type, sK60: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_123, type, sK61: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_124, type, sK62: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_125, type, sK63: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_126, type, sK64: ((nat > $o) > nat)).
% 3.84/1.04 thf(func_def_127, type, sK65: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_128, type, sK66: (extended_enat > nat)).
% 3.84/1.04 thf(func_def_129, type, sK67: (nat > nat > nat)).
% 3.84/1.04 thf(func_def_130, type, sK68: (nat > nat)).
% 3.84/1.04 thf(func_def_131, type, sK69: (nat > nat > nat)).
% 3.84/1.04 thf(func_def_133, type, sK71: ((extended_enat > $o) > nat)).
% 3.84/1.04 thf(func_def_134, type, sK72: ((extended_enat > $o) > extended_enat)).
% 3.84/1.04 thf(f3,axiom,(
% 3.84/1.04 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))),
% 3.84/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Suc_Oprems)).
% 3.84/1.04 thf(f11,axiom,(
% 3.84/1.04 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : (((coindu191418589_ldrop @ X0 @ (extended_enat2 @ X1) @ X2)) = ((coindu531130065ldropn @ X0 @ X1 @ X2)))),
% 3.84/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ldrop__enat)).
% 3.84/1.04 thf(f21,axiom,(
% 3.84/1.04 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2)) => (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))))),
% 3.84/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_llast__ldropn)).
% 3.84/1.04 thf(f283,conjecture,(
% 3.84/1.04 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) = ((coindu2000965700_llast @ a @ xsa)))),
% 3.84/1.04 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 3.84/1.04 thf(f284,negated_conjecture,(
% 3.84/1.04 ~ (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) = ((coindu2000965700_llast @ a @ xsa)))),
% 3.84/1.04 inference(negated_conjecture,[status(cth)],[f283])).
% 3.84/1.04 thf(f287,plain,(
% 3.84/1.04 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))),
% 3.84/1.04 inference(rectify,[],[f3])).
% 3.84/1.04 thf(f288,plain,(
% 3.84/1.04 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) = $true)),
% 3.84/1.04 inference(fool_elimination,[],[f287])).
% 3.84/1.04 thf(f307,plain,(
% 3.84/1.04 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2)) => (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))))),
% 3.84/1.04 inference(rectify,[],[f21])).
% 3.84/1.04 thf(f308,plain,(
% 3.84/1.04 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2))) = $true) => (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))))),
% 3.84/1.04 inference(fool_elimination,[],[f307])).
% 3.84/1.04 thf(f711,plain,(
% 3.84/1.04 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) != ((coindu2000965700_llast @ a @ xsa)))),
% 3.84/1.04 inference(flattening,[],[f284])).
% 3.84/1.04 thf(f721,plain,(
% 3.84/1.04 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))) | (((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2))) != $true))),
% 3.84/1.04 inference(ennf_transformation,[],[f308])).
% 3.84/1.04 thf(f970,plain,(
% 3.84/1.04 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) = $true)),
% 3.84/1.04 inference(cnf_transformation,[],[f288])).
% 3.84/1.04 thf(f978,plain,(
% 3.84/1.04 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : nat] : ((((coindu191418589_ldrop @ X0 @ (extended_enat2 @ X1) @ X2)) = ((coindu531130065ldropn @ X0 @ X1 @ X2)))) )),
% 3.84/1.04 inference(cnf_transformation,[],[f11])).
% 3.84/1.04 thf(f989,plain,(
% 3.84/1.04 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : nat] : ((((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2))) != $true) | (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2)))) )),
% 3.84/1.04 inference(cnf_transformation,[],[f721])).
% 3.84/1.04 thf(f1318,plain,(
% 3.84/1.04 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) != ((coindu2000965700_llast @ a @ xsa)))),
% 3.84/1.04 inference(cnf_transformation,[],[f711])).
% 3.84/1.04 thf(f8551,plain,(
% 3.84/1.04 (((coindu2000965700_llast @ a @ xsa)) != ((coindu2000965700_llast @ a @ (coindu531130065ldropn @ a @ (suc @ n_a) @ xsa))))),
% 3.84/1.04 inference(constrained_superposition,[],[f1318,f978])).
% 3.84/1.04 thf(f10148,plain,(
% 3.84/1.04 ($true != $true) | (((coindu2000965700_llast @ a @ xsa)) = ((coindu2000965700_llast @ a @ (coindu531130065ldropn @ a @ (suc @ n_a) @ xsa))))),
% 3.84/1.04 inference(constrained_superposition,[],[f989,f970])).
% 3.84/1.04 thf(f10149,plain,(
% 3.84/1.04 (((coindu2000965700_llast @ a @ xsa)) = ((coindu2000965700_llast @ a @ (coindu531130065ldropn @ a @ (suc @ n_a) @ xsa))))),
% 3.84/1.04 inference(trivial_inequality_removal,[],[f10148])).
% 3.84/1.04 thf(f10151,plain,(
% 3.84/1.04 $false),
% 3.84/1.04 inference(forward_subsumption_resolution,[],[f10149,f8551])).
% 3.84/1.04 % SZS output end Proof for theBenchmark
% 3.84/1.04 % (3513334)------------------------------
% 3.84/1.04 % (3513334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.84/1.04 % (3513334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.84/1.04 % (3513334)CaDiCaL version: 2.1.3
% 3.84/1.04 % (3513334)Termination reason: Refutation
% 3.84/1.04 % (3513334)Time elapsed: 0.692 s
% 3.84/1.04 % (3513334)Peak memory usage: 17 MB
% 3.84/1.04 % (3513334)Instructions burned: 926 (million)
% 3.84/1.04 % (3513327)Success in time 0.748 s
% 3.84/1.04 % Vampire exiting
%------------------------------------------------------------------------------