%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT179^1 : 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 : n001.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 1.97s 0.90s
% Output : Refutation 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT179^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n001.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 18:12:21 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 1.97/0.90 % (1621170)Will run a generic schedule for satisfiability detection.
% 1.97/0.90 % (1621178)dis+10_1_sil=32000:sp=arity:random_seed=3294092573:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.97/0.90 % (1621176)% WARNING: option uhcvi not known.
% 1.97/0.90 % (1621175)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1803479614_2999 on theBenchmark for (2999ds/0Mi)
% 1.97/0.90 % (1621177)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2377172438:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.97/0.90 % (1621176)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3116837098:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.97/0.90 % (1621179)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2119247187:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.97/0.90 % (1621180)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2964907437:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.97/0.90 % (1621181)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3721466466:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.97/0.90 % (1621176)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.97/0.90 % (1621179)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.97/0.90 % (1621178)Instruction limit reached!
% 1.97/0.90 % (1621178)------------------------------
% 1.97/0.90 % (1621178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621178)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621178)Termination reason: Instruction limit
% 1.97/0.90 % (1621178)Termination phase: Saturation
% 1.97/0.90 % (1621178)Time elapsed: 0.027 s
% 1.97/0.90 % (1621178)Peak memory usage: 13 MB
% 1.97/0.90 % (1621178)Instructions burned: 106 (million)
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621176)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.97/0.90 % (1621189)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4048398169:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621179)Instruction limit reached!
% 1.97/0.90 % (1621179)------------------------------
% 1.97/0.90 % (1621179)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621179)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621179)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621179)Termination reason: Instruction limit
% 1.97/0.90 % (1621179)Termination phase: Saturation
% 1.97/0.90 % (1621179)Time elapsed: 0.054 s
% 1.97/0.90 % (1621179)Peak memory usage: 13 MB
% 1.97/0.90 % (1621179)Instructions burned: 116 (million)
% 1.97/0.90 % (1621192)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=1188696225:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.97/0.90 % (1621180)Instruction limit reached!
% 1.97/0.90 % (1621180)------------------------------
% 1.97/0.90 % (1621180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621180)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621180)Termination reason: Instruction limit
% 1.97/0.90 % (1621180)Termination phase: Saturation
% 1.97/0.90 % (1621180)Time elapsed: 0.063 s
% 1.97/0.90 % (1621180)Peak memory usage: 13 MB
% 1.97/0.90 % (1621180)Instructions burned: 132 (million)
% 1.97/0.90 % (1621192)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.97/0.90 % (1621190)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1971004825:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.97/0.90 % (1621193)ott-21_1_sil=16000:fs=off:random_seed=1886519029:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.97/0.90 % (1621192)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.97/0.90 % (1621181)Instruction limit reached!
% 1.97/0.90 % (1621181)------------------------------
% 1.97/0.90 % (1621181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621181)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621181)Termination reason: Instruction limit
% 1.97/0.90 % (1621181)Termination phase: Saturation
% 1.97/0.90 % (1621181)Time elapsed: 0.079 s
% 1.97/0.90 % (1621181)Peak memory usage: 14 MB
% 1.97/0.90 % (1621181)Instructions burned: 160 (million)
% 1.97/0.90 % (1621195)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=511864708:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.97/0.90 % (1621198)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=250455977:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621201)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3167147947:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.97/0.90 % (1621193)Instruction limit reached!
% 1.97/0.90 % (1621193)------------------------------
% 1.97/0.90 % (1621193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621193)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621193)Termination reason: Instruction limit
% 1.97/0.90 % (1621193)Termination phase: Saturation
% 1.97/0.90 % (1621193)Time elapsed: 0.083 s
% 1.97/0.90 % (1621193)Peak memory usage: 13 MB
% 1.97/0.90 % (1621193)Instructions burned: 180 (million)
% 1.97/0.90 % (1621203)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4267104601:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.97/0.90 % (1621190)Instruction limit reached!
% 1.97/0.90 % (1621190)------------------------------
% 1.97/0.90 % (1621190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621190)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621190)Termination reason: Instruction limit
% 1.97/0.90 % (1621190)Termination phase: Saturation
% 1.97/0.90 % (1621190)Time elapsed: 0.117 s
% 1.97/0.90 % (1621190)Peak memory usage: 13 MB
% 1.97/0.90 % (1621190)Instructions burned: 131 (million)
% 1.97/0.90 % (1621205)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=1731708074: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)
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621192)Instruction limit reached!
% 1.97/0.90 % (1621192)------------------------------
% 1.97/0.90 % (1621192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621192)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621192)Termination reason: Instruction limit
% 1.97/0.90 % (1621192)Termination phase: Saturation
% 1.97/0.90 % (1621192)Time elapsed: 0.159 s
% 1.97/0.90 % (1621192)Peak memory usage: 15 MB
% 1.97/0.90 % (1621192)Instructions burned: 686 (million)
% 1.97/0.90 % (1621205)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.97/0.90 % (1621208)fmb+10_1_sil=64000:random_seed=227907865:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 1.97/0.90 % (1621207)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2307487164:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.97/0.90 % (1621208)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.97/0.90 % (1621207)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621211)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1784778651:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621213)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2248070546:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 1.97/0.90 % (1621195)Instruction limit reached!
% 1.97/0.90 % (1621195)------------------------------
% 1.97/0.90 % (1621195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621195)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621195)Termination reason: Instruction limit
% 1.97/0.90 % (1621195)Termination phase: Saturation
% 1.97/0.90 % (1621195)Time elapsed: 0.240 s
% 1.97/0.90 % (1621195)Peak memory usage: 14 MB
% 1.97/0.90 % (1621195)Instructions burned: 478 (million)
% 1.97/0.90 % (1621215)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3175229155:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 1.97/0.90 % (1621215)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.97/0.90 % Exception at run slice level
% 1.97/0.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.97/0.90 % (1621217)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2934418280:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 1.97/0.90 % (1621217)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.97/0.90 % (1621217)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.97/0.90 % (1621201) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1621170-1621201"...
% 1.97/0.90 % (1621201)...printing done.
% 1.97/0.90 % (1621201)Refutation found. Thanks to Tanya!
% 1.97/0.90 % SZS status Theorem for theBenchmark
% 1.97/0.90 % SZS output start Proof for theBenchmark
% 1.97/0.90 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 1.97/0.90 thf(type_def_6, type, option: $tType > $tType).
% 1.97/0.90 thf(type_def_7, type, set: $tType > $tType).
% 1.97/0.90 thf(type_def_8, type, num: $tType).
% 1.97/0.90 thf(type_def_9, type, nat: $tType).
% 1.97/0.90 thf(type_def_10, type, int: $tType).
% 1.97/0.90 thf(type_def_11, type, itself: $tType > $tType).
% 1.97/0.90 thf(type_def_12, type, a: $tType).
% 1.97/0.90 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 1.97/0.90 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_3, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_4, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_5, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_6, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_7, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_8, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_9, type, archim1727834104eiling: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_10, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_11, type, archim1804426504_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_12, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_13, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_14, type, ordere516151231imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.97/0.90 thf(func_def_15, type, archimedean_round: !>[X0: $tType]:((X0 > int))).
% 1.97/0.90 thf(func_def_16, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 1.97/0.90 thf(func_def_17, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.97/0.90 thf(func_def_18, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.97/0.90 thf(func_def_19, type, hilbert_GreatestM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_20, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_21, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.97/0.90 thf(func_def_22, type, nat2: (int > nat)).
% 1.97/0.90 thf(func_def_23, type, lList2435255213lllsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.97/0.90 thf(func_def_24, type, lList22096119349pslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.97/0.90 thf(func_def_25, type, lList21612149805nflsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.97/0.90 thf(func_def_26, type, lList2370560421utlast: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.97/0.90 thf(func_def_27, type, lList2228235758e_ll2f: !>[X0: $tType]:((coinductive_llist @ X0 > nat > option @ X0))).
% 1.97/0.90 thf(func_def_28, type, lList21232602520length: !>[X0: $tType]:((coinductive_llist @ X0 > nat))).
% 1.97/0.90 thf(func_def_29, type, lList22119844313_ltake: !>[X0: $tType]:((coinductive_llist @ X0 > nat > coinductive_llist @ X0))).
% 1.97/0.90 thf(func_def_30, type, lList21148268032oslsts: !>[X0: $tType]:((set @ X0 > set @ coinductive_llist @ X0))).
% 1.97/0.90 thf(func_def_31, type, suc: (nat > nat)).
% 1.97/0.90 thf(func_def_32, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 1.97/0.90 thf(func_def_33, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 1.97/0.90 thf(func_def_34, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 1.97/0.90 thf(func_def_35, type, nat_tr1645093318rphism: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > $o))).
% 1.97/0.90 thf(func_def_36, type, nat_tsub: (int > int > int)).
% 1.97/0.90 thf(func_def_37, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 1.97/0.90 thf(func_def_38, type, bind: !>[X0: $tType, X1: $tType]:((option @ X0 > (X0 > option @ X1) > option @ X1))).
% 1.97/0.90 thf(func_def_39, type, combine_options: !>[X0: $tType]:(((X0 > X0 > X0) > option @ X0 > option @ X0 > option @ X0))).
% 1.97/0.90 thf(func_def_40, type, is_none: !>[X0: $tType]:((option @ X0 > $o))).
% 1.97/0.90 thf(func_def_41, type, none: !>[X0: $tType]:(option @ X0)).
% 1.97/0.90 thf(func_def_42, type, some: !>[X0: $tType]:((X0 > option @ X0))).
% 1.97/0.90 thf(func_def_43, type, case_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 1.97/0.90 thf(func_def_44, type, pred_option: !>[X0: $tType]:(((X0 > $o) > option @ X0 > $o))).
% 1.97/0.90 thf(func_def_45, type, rec_option: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > option @ X1 > X0))).
% 1.97/0.90 thf(func_def_46, type, set_option: !>[X0: $tType]:((option @ X0 > set @ X0))).
% 1.97/0.90 thf(func_def_47, type, size_option: !>[X0: $tType]:(((X0 > nat) > option @ X0 > nat))).
% 1.97/0.90 thf(func_def_48, type, the: !>[X0: $tType]:((option @ X0 > X0))).
% 1.97/0.90 thf(func_def_49, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.97/0.90 thf(func_def_50, type, type2: !>[X0: $tType]:(itself @ X0)).
% 1.97/0.90 thf(func_def_51, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.97/0.90 thf(func_def_52, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.97/0.90 thf(func_def_53, type, q: $o).
% 1.97/0.90 thf(func_def_54, type, i: nat).
% 1.97/0.90 thf(func_def_55, type, j: nat).
% 1.97/0.90 thf(func_def_56, type, t: coinductive_llist @ a).
% 1.97/0.90 thf(func_def_57, type, x: a).
% 1.97/0.90 thf(func_def_61, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.97/0.90 thf(func_def_62, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.97/0.90 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 1.97/0.90 thf(func_def_64, type, db0: !>[X0: $tType]:(X0)).
% 1.97/0.90 thf(func_def_65, type, db1: !>[X0: $tType]:(X0)).
% 1.97/0.90 thf(func_def_66, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.97/0.90 thf(func_def_67, type, vAND: ($o > $o > $o)).
% 1.97/0.90 thf(func_def_68, type, vNOT: ($o > $o)).
% 1.97/0.90 thf(func_def_69, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.97/0.90 thf(func_def_70, type, vOR: ($o > $o > $o)).
% 1.97/0.90 thf(func_def_71, type, vIMP: ($o > $o > $o)).
% 1.97/0.90 thf(func_def_72, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 1.97/0.90 thf(func_def_73, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 1.97/0.90 thf(func_def_74, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 1.97/0.90 thf(func_def_75, type, sP3: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > $o))).
% 1.97/0.90 thf(func_def_76, type, sK4: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_77, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.97/0.90 thf(func_def_78, type, sK6: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_79, type, sK7: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_80, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_81, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_82, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.97/0.90 thf(func_def_83, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.97/0.90 thf(func_def_84, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.97/0.90 thf(func_def_85, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.97/0.90 thf(func_def_86, type, sK14: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.97/0.90 thf(func_def_87, type, sK15: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.97/0.90 thf(func_def_88, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.97/0.90 thf(func_def_89, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.97/0.90 thf(func_def_90, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 1.97/0.90 thf(func_def_91, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 1.97/0.90 thf(func_def_92, type, sK20: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_93, type, sK21: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_94, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X1 > $o) > X1))).
% 1.97/0.90 thf(func_def_95, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1 > (X1 > $o) > X1))).
% 1.97/0.90 thf(func_def_96, type, sK24: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.97/0.90 thf(func_def_97, type, sK25: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.97/0.90 thf(func_def_98, type, sK26: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_99, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.97/0.90 thf(func_def_100, type, sK28: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.97/0.90 thf(func_def_101, type, sK29: !>[X0: $tType]:((nat > coinductive_llist @ X0 > X0))).
% 1.97/0.90 thf(func_def_102, type, sK30: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_103, type, sK31: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_104, type, sK32: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_105, type, sK33: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_106, type, sK34: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_107, type, sK35: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_108, type, sK36: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_109, type, sK37: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_110, type, sK38: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_111, type, sK39: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.97/0.90 thf(func_def_112, type, sK40: ((nat > $o) > nat)).
% 1.97/0.90 thf(func_def_113, type, sK41: (nat > nat)).
% 1.97/0.90 thf(func_def_114, type, sK42: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X1))).
% 1.97/0.90 thf(func_def_115, type, sK43: !>[X0: $tType, X1: $tType]:(((option @ X1 > option @ X0 > $o) > option @ X1 > option @ X0 > X0))).
% 1.97/0.90 thf(func_def_116, type, sK44: !>[X0: $tType]:(((option @ X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_117, type, sK45: !>[X0: $tType]:((option @ X0 > X0))).
% 1.97/0.90 thf(func_def_118, type, sK46: !>[X0: $tType]:(((nat > X0) > nat))).
% 1.97/0.90 thf(func_def_119, type, sK47: !>[X0: $tType]:(((nat > X0) > nat))).
% 1.97/0.90 thf(func_def_120, type, sK48: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.97/0.90 thf(func_def_121, type, sK49: !>[X0: $tType]:((X0 > nat))).
% 1.97/0.90 thf(func_def_122, type, sK50: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_123, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > option @ X0) > (X1 > option @ X0) > option @ X1 > X1))).
% 1.97/0.90 thf(func_def_124, type, sK52: !>[X0: $tType]:(((X0 > $o) > option @ X0 > X0))).
% 1.97/0.90 thf(func_def_125, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > option @ X0) > (X1 > option @ X0) > option @ X1 > X1))).
% 1.97/0.90 thf(func_def_126, type, sK54: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > option @ X0 > X0))).
% 1.97/0.90 thf(func_def_127, type, sK55: !>[X0: $tType]:(((X0 > $o) > option @ X0 > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_128, type, sK56: (int > nat)).
% 1.97/0.90 thf(func_def_129, type, sK57: (int > nat)).
% 1.97/0.90 thf(func_def_130, type, sK58: (int > nat)).
% 1.97/0.90 thf(func_def_131, type, sK59: ((nat > $o) > nat)).
% 1.97/0.90 thf(func_def_132, type, sK60: ((nat > nat > $o) > nat)).
% 1.97/0.90 thf(func_def_133, type, sK61: ((nat > nat > $o) > nat)).
% 1.97/0.90 thf(func_def_134, type, sK62: ((nat > nat > $o) > nat)).
% 1.97/0.90 thf(func_def_135, type, sK63: ((nat > nat > $o) > nat)).
% 1.97/0.90 thf(func_def_136, type, sK64: ((nat > $o) > nat)).
% 1.97/0.90 thf(func_def_137, type, sK65: (nat > nat)).
% 1.97/0.90 thf(func_def_138, type, sK66: ((nat > $o) > nat)).
% 1.97/0.90 thf(func_def_139, type, sK67: (nat > nat)).
% 1.97/0.90 thf(func_def_140, type, sK68: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0))).
% 1.97/0.90 thf(func_def_141, type, sK69: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_142, type, sK70: !>[X0: $tType]:(((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat))).
% 1.97/0.90 thf(func_def_143, type, sK71: ((nat > $o) > nat)).
% 1.97/0.90 thf(func_def_144, type, sK72: (nat > nat)).
% 1.97/0.90 thf(func_def_145, type, sK73: ((int > $o) > nat)).
% 1.97/0.90 thf(func_def_146, type, sK74: ((int > $o) > int)).
% 1.97/0.90 thf(func_def_147, type, sK75: ((int > $o) > int)).
% 1.97/0.90 thf(func_def_148, type, sK76: ((int > $o) > nat)).
% 1.97/0.90 thf(func_def_149, type, sK77: !>[X0: $tType, X1: $tType]:(((option @ X0 > $o) > option @ X1 > (X1 > option @ X0) > X1))).
% 1.97/0.90 thf(func_def_150, type, sK78: !>[X0: $tType, X1: $tType]:((option @ X1 > (X1 > option @ X0) > (option @ X0 > $o) > X1))).
% 1.97/0.90 thf(func_def_151, type, sK79: !>[X0: $tType, X1: $tType]:(((X1 > option @ X0) > X0 > option @ X1 > X1))).
% 1.97/0.90 thf(func_def_152, type, sK80: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.97/0.90 thf(func_def_153, type, sK81: !>[X0: $tType]:((option @ X0 > X0))).
% 1.97/0.90 thf(func_def_154, type, sK82: !>[X0: $tType]:((option @ X0 > X0))).
% 1.97/0.90 thf(f1,axiom,(
% 1.97/0.90 ! [X3 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) = ((some @ a @ X3))) => q)),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_H)).
% 1.97/0.90 thf(f2,axiom,(
% 1.97/0.90 (ord_less_eq @ nat @ j @ i)),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_jlei)).
% 1.97/0.90 thf(f3,axiom,(
% 1.97/0.90 (((lList2228235758e_ll2f @ a @ t @ i)) = ((some @ a @ x)))),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_tisome)).
% 1.97/0.90 thf(f57,axiom,(
% 1.97/0.90 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat,X3 : nat] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X2)) = none @ X0) => ((ord_less_eq @ nat @ X2 @ X3) => (((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0)))),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_ll2f__None__le)).
% 1.97/0.90 thf(f77,axiom,(
% 1.97/0.90 ! [X0 : $tType] : (is_none @ X0 = (^[X1 : option @ X0] : ((X1 = none @ X0))))),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Option_Ois__none__def)).
% 1.97/0.90 thf(f93,axiom,(
% 1.97/0.90 ! [X0 : $tType,X1 : option @ X0] : ((X1 != none @ X0) => ~ ! [X2 : X0] : (X1 != ((some @ X0 @ X2))))),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_option_Oexhaust)).
% 1.97/0.90 thf(f96,axiom,(
% 1.97/0.90 ! [X0 : $tType,X1 : X0] : ~(is_none @ X0 @ (some @ X0 @ X1))),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_is__none__simps_I2_J)).
% 1.97/0.90 thf(f294,conjecture,(
% 1.97/0.90 q),
% 1.97/0.90 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.97/0.90 thf(f295,negated_conjecture,(
% 1.97/0.90 ~q),
% 1.97/0.90 inference(negated_conjecture,[status(cth)],[f294])).
% 1.97/0.90 thf(f296,plain,(
% 1.97/0.90 ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) = ((some @ a @ X0))) => q)),
% 1.97/0.90 inference(rectify,[],[f1])).
% 1.97/0.90 thf(f297,plain,(
% 1.97/0.90 ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) = ((some @ a @ X0))) => (q = $true))),
% 1.97/0.90 inference(fool_elimination,[],[f296])).
% 1.97/0.90 thf(f298,plain,(
% 1.97/0.90 (ord_less_eq @ nat @ j @ i)),
% 1.97/0.90 inference(rectify,[],[f2])).
% 1.97/0.90 thf(f299,plain,(
% 1.97/0.90 (((ord_less_eq @ nat @ j @ i)) = $true)),
% 1.97/0.90 inference(fool_elimination,[],[f298])).
% 1.97/0.90 thf(f391,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat,X3 : nat] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X2)) = none @ X0) => ((ord_less_eq @ nat @ X2 @ X3) => (((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0)))),
% 1.97/0.90 inference(rectify,[],[f57])).
% 1.97/0.90 thf(f392,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat,X3 : nat] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X2)) = none @ X0) => ((((ord_less_eq @ nat @ X2 @ X3)) = $true) => (((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0)))),
% 1.97/0.90 inference(fool_elimination,[],[f391])).
% 1.97/0.90 thf(f411,plain,(
% 1.97/0.90 ! [X0 : $tType] : (is_none @ X0 = (^[Y0 : option @ X0]: (none @ X0 = Y0)))),
% 1.97/0.90 inference(fool_elimination,[],[f77])).
% 1.97/0.90 thf(f436,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : X0] : ~(is_none @ X0 @ (some @ X0 @ X1))),
% 1.97/0.90 inference(rectify,[],[f96])).
% 1.97/0.90 thf(f437,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : X0] : ~ (((is_none @ X0 @ (some @ X0 @ X1))) = $true)),
% 1.97/0.90 inference(fool_elimination,[],[f436])).
% 1.97/0.90 thf(f741,plain,(
% 1.97/0.90 ~q),
% 1.97/0.90 inference(rectify,[],[f295])).
% 1.97/0.90 thf(f742,plain,(
% 1.97/0.90 ~ (q = $true)),
% 1.97/0.90 inference(fool_elimination,[],[f741])).
% 1.97/0.90 thf(f749,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : X0] : (((is_none @ X0 @ (some @ X0 @ X1))) != $true)),
% 1.97/0.90 inference(flattening,[],[f437])).
% 1.97/0.90 thf(f757,plain,(
% 1.97/0.90 (q != $true)),
% 1.97/0.90 inference(flattening,[],[f742])).
% 1.97/0.90 thf(f758,plain,(
% 1.97/0.90 ! [X0 : a] : ((q = $true) | (((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0))))),
% 1.97/0.90 inference(ennf_transformation,[],[f297])).
% 1.97/0.90 thf(f828,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat,X3 : nat] : (((((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0) | (((ord_less_eq @ nat @ X2 @ X3)) != $true)) | (((lList2228235758e_ll2f @ X0 @ X1 @ X2)) != none @ X0))),
% 1.97/0.90 inference(ennf_transformation,[],[f392])).
% 1.97/0.90 thf(f829,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat,X3 : nat] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0) | (((ord_less_eq @ nat @ X2 @ X3)) != $true) | (((lList2228235758e_ll2f @ X0 @ X1 @ X2)) != none @ X0))),
% 1.97/0.90 inference(flattening,[],[f828])).
% 1.97/0.90 thf(f849,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : option @ X0] : (? [X2 : X0] : (((some @ X0 @ X2)) = X1) | (none @ X0 = X1))),
% 1.97/0.90 inference(ennf_transformation,[],[f93])).
% 1.97/0.90 thf(f1011,plain,(
% 1.97/0.90 ! [X0 : $tType,X1 : option @ X0] : ((((some @ X0 @ (sK45 @ X0 @ X1))) = X1) | (none @ X0 = X1))),
% 1.97/0.90 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK4 @ X0 @ X3 @ X1)],[f849])).
% 1.97/0.90 thf(f1037,plain,(
% 1.97/0.90 ( ! [X0 : a] : ((q = $true) | (((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0)))) )),
% 1.97/0.90 inference(cnf_transformation,[],[f758])).
% 1.97/0.90 thf(f1038,plain,(
% 1.97/0.90 (((ord_less_eq @ nat @ j @ i)) = $true)),
% 1.97/0.90 inference(cnf_transformation,[],[f299])).
% 1.97/0.90 thf(f1039,plain,(
% 1.97/0.90 (((lList2228235758e_ll2f @ a @ t @ i)) = ((some @ a @ x)))),
% 1.97/0.90 inference(cnf_transformation,[],[f3])).
% 1.97/0.90 thf(f1128,plain,(
% 1.97/0.90 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : coinductive_llist @ X0] : ((((lList2228235758e_ll2f @ X0 @ X1 @ X2)) != none @ X0) | (((ord_less_eq @ nat @ X2 @ X3)) != $true) | (((lList2228235758e_ll2f @ X0 @ X1 @ X3)) = none @ X0)) )),
% 1.97/0.90 inference(cnf_transformation,[],[f829])).
% 1.97/0.90 thf(f1148,plain,(
% 1.97/0.90 ( ! [X0 : $tType] : ((is_none @ X0 = (^[Y0 : option @ X0]: (none @ X0 = Y0)))) )),
% 1.97/0.90 inference(cnf_transformation,[],[f411])).
% 1.97/0.90 thf(f1171,plain,(
% 1.97/0.90 ( ! [X0 : $tType,X1 : option @ X0] : ((((some @ X0 @ (sK45 @ X0 @ X1))) = X1) | (none @ X0 = X1)) )),
% 1.97/0.90 inference(cnf_transformation,[],[f1011])).
% 1.97/0.90 thf(f1174,plain,(
% 1.97/0.90 ( ! [X0 : $tType,X1 : X0] : ((((is_none @ X0 @ (some @ X0 @ X1))) != $true)) )),
% 1.97/0.90 inference(cnf_transformation,[],[f749])).
% 1.97/0.90 thf(f1396,plain,(
% 1.97/0.90 (q != $true)),
% 1.97/0.90 inference(cnf_transformation,[],[f757])).
% 1.97/0.90 thf(f1402,plain,(
% 1.97/0.90 ( ! [X0 : $tType,X1 : X0] : (($true != (((^[Y0 : option @ X0]: (none @ X0 = Y0)) @ (some @ X0 @ X1))))) )),
% 1.97/0.90 inference(definition_unfolding,[],[f1174,f1148])).
% 1.97/0.90 thf(f1917,plain,(
% 1.97/0.90 ( ! [X0 : $tType,X1 : X0] : (($true != ((none @ X0 = (some @ X0 @ X1))))) )),
% 1.97/0.90 inference(beta-eta_normalization,[],[f1402])).
% 1.97/0.90 thf(f1918,plain,(
% 1.97/0.90 ( ! [X0 : $tType,X1 : X0] : ((((some @ X0 @ X1)) != none @ X0)) )),
% 1.97/0.90 inference(equality_proxy_clausification,[],[f1917])).
% 1.97/0.90 thf(f2007,plain,(
% 1.97/0.90 ( ! [X0 : a] : ((((lList2228235758e_ll2f @ a @ t @ j)) != ((some @ a @ X0)))) )),
% 1.97/0.90 inference(forward_subsumption_resolution,[],[f1037,f1396])).
% 1.97/0.90 thf(f2284,plain,(
% 1.97/0.90 ( ! [X0 : option @ a] : ((((lList2228235758e_ll2f @ a @ t @ j)) != X0) | (none @ a = X0)) )),
% 1.97/0.90 inference(constrained_superposition,[],[f2007,f1171])).
% 1.97/0.90 thf(f2288,plain,(
% 1.97/0.90 (((lList2228235758e_ll2f @ a @ t @ j)) = none @ a)),
% 1.97/0.90 inference(equality_resolution,[],[f2284])).
% 1.97/0.90 thf(f8630,plain,(
% 1.97/0.90 ( ! [X0 : nat] : ((none @ a != none @ a) | ($true != ((ord_less_eq @ nat @ j @ X0))) | (none @ a = ((lList2228235758e_ll2f @ a @ t @ X0)))) )),
% 1.97/0.90 inference(constrained_superposition,[],[f1128,f2288])).
% 1.97/0.90 thf(f8638,plain,(
% 1.97/0.90 ( ! [X0 : nat] : (($true != ((ord_less_eq @ nat @ j @ X0))) | (none @ a = ((lList2228235758e_ll2f @ a @ t @ X0)))) )),
% 1.97/0.90 inference(trivial_inequality_removal,[],[f8630])).
% 1.97/0.90 thf(f9034,plain,(
% 1.97/0.90 ($true != $true) | (((lList2228235758e_ll2f @ a @ t @ i)) = none @ a)),
% 1.97/0.90 inference(constrained_superposition,[],[f8638,f1038])).
% 1.97/0.90 thf(f9035,plain,(
% 1.97/0.90 (((lList2228235758e_ll2f @ a @ t @ i)) = none @ a)),
% 1.97/0.90 inference(trivial_inequality_removal,[],[f9034])).
% 1.97/0.90 thf(f9316,plain,(
% 1.97/0.90 (((some @ a @ x)) = none @ a)),
% 1.97/0.90 inference(constrained_superposition,[],[f1039,f9035])).
% 1.97/0.90 thf(f9321,plain,(
% 1.97/0.90 $false),
% 1.97/0.90 inference(forward_subsumption_resolution,[],[f9316,f1918])).
% 1.97/0.90 % SZS output end Proof for theBenchmark
% 1.97/0.90 % (1621201)------------------------------
% 1.97/0.90 % (1621201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.97/0.90 % (1621201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.97/0.90 % (1621201)CaDiCaL version: 2.1.3
% 1.97/0.90 % (1621201)Termination reason: Refutation
% 1.97/0.90 % (1621201)Time elapsed: 0.448 s
% 1.97/0.90 % (1621201)Peak memory usage: 18 MB
% 1.97/0.90 % (1621201)Instructions burned: 938 (million)
% 1.97/0.90 % (1621170)Success in time 0.659 s
% 1.97/0.90 % Vampire exiting
%------------------------------------------------------------------------------