%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT152^1 : 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 : n003.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 07:48:58 AM UTC 2026
% Result : Theorem 3.58s 0.83s
% Output : Refutation 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT152^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n003.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 18:03:59 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.22 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
% 3.58/0.83 % (2858500)Will run a generic schedule for satisfiability detection.
% 3.58/0.83 % (2858508)dis+10_1_sil=32000:sp=arity:random_seed=1680254516:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.58/0.83 % (2858506)% WARNING: option uhcvi not known.
% 3.58/0.83 % (2858505)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2752813536_2999 on theBenchmark for (2999ds/0Mi)
% 3.58/0.83 % (2858506)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1143120966:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.58/0.83 % (2858507)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2103470076:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.58/0.83 % (2858509)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1467596077:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.58/0.83 % (2858511)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3574617051:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.58/0.83 % (2858510)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=666300315:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.58/0.83 % (2858506)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.58/0.83 % (2858509)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.58/0.83 % (2858508)Instruction limit reached!
% 3.58/0.83 % (2858508)------------------------------
% 3.58/0.83 % (2858508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858508)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858508)Termination reason: Instruction limit
% 3.58/0.83 % (2858508)Termination phase: Saturation
% 3.58/0.83 % (2858508)Time elapsed: 0.024 s
% 3.58/0.83 % (2858508)Peak memory usage: 12 MB
% 3.58/0.83 % (2858508)Instructions burned: 103 (million)
% 3.58/0.83 % (2858519)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=934527143:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858506)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858509)Instruction limit reached!
% 3.58/0.83 % (2858509)------------------------------
% 3.58/0.83 % (2858509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858509)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858509)Termination reason: Instruction limit
% 3.58/0.83 % (2858509)Termination phase: Saturation
% 3.58/0.83 % (2858509)Time elapsed: 0.051 s
% 3.58/0.83 % (2858509)Peak memory usage: 13 MB
% 3.58/0.83 % (2858509)Instructions burned: 118 (million)
% 3.58/0.83 % (2858521)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3589307854:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.58/0.83 % (2858522)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=2026546923:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.58/0.83 % (2858522)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.58/0.83 % (2858523)ott-21_1_sil=16000:fs=off:random_seed=2141869517:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.58/0.83 % (2858511)Instruction limit reached!
% 3.58/0.83 % (2858511)------------------------------
% 3.58/0.83 % (2858511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858511)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858511)Termination reason: Instruction limit
% 3.58/0.83 % (2858511)Termination phase: Saturation
% 3.58/0.83 % (2858511)Time elapsed: 0.073 s
% 3.58/0.83 % (2858511)Peak memory usage: 14 MB
% 3.58/0.83 % (2858511)Instructions burned: 159 (million)
% 3.58/0.83 % (2858522)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.58/0.83 % (2858527)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2531708417:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.58/0.83 % (2858521)Instruction limit reached!
% 3.58/0.83 % (2858521)------------------------------
% 3.58/0.83 % (2858521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858521)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858521)Termination reason: Instruction limit
% 3.58/0.83 % (2858521)Termination phase: Saturation
% 3.58/0.83 % (2858521)Time elapsed: 0.059 s
% 3.58/0.83 % (2858521)Peak memory usage: 13 MB
% 3.58/0.83 % (2858521)Instructions burned: 131 (million)
% 3.58/0.83 % (2858510)Instruction limit reached!
% 3.58/0.83 % (2858510)------------------------------
% 3.58/0.83 % (2858510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858510)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858510)Termination reason: Instruction limit
% 3.58/0.83 % (2858510)Termination phase: Saturation
% 3.58/0.83 % (2858510)Time elapsed: 0.107 s
% 3.58/0.83 % (2858510)Peak memory usage: 13 MB
% 3.58/0.83 % (2858510)Instructions burned: 132 (million)
% 3.58/0.83 % (2858529)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3147034691:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.58/0.83 % (2858530)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1829200495:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.58/0.83 % (2858523)Instruction limit reached!
% 3.58/0.83 % (2858523)------------------------------
% 3.58/0.83 % (2858523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858523)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858523)Termination reason: Instruction limit
% 3.58/0.83 % (2858523)Termination phase: Saturation
% 3.58/0.83 % (2858523)Time elapsed: 0.080 s
% 3.58/0.83 % (2858523)Peak memory usage: 13 MB
% 3.58/0.83 % (2858523)Instructions burned: 180 (million)
% 3.58/0.83 % (2858533)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=841951007:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858535)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=1872416730: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)
% 3.58/0.83 % (2858535)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858522)Instruction limit reached!
% 3.58/0.83 % (2858522)------------------------------
% 3.58/0.83 % (2858522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858522)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858522)Termination reason: Instruction limit
% 3.58/0.83 % (2858522)Termination phase: Saturation
% 3.58/0.83 % (2858522)Time elapsed: 0.173 s
% 3.58/0.83 % (2858522)Peak memory usage: 16 MB
% 3.58/0.83 % (2858522)Instructions burned: 687 (million)
% 3.58/0.83 % (2858537)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4083522979:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.58/0.83 % (2858538)fmb+10_1_sil=64000:random_seed=1401525362:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.58/0.83 % (2858537)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.58/0.83 % (2858538)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858541)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2370541183:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858543)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1004130:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 3.58/0.83 % (2858527)Instruction limit reached!
% 3.58/0.83 % (2858527)------------------------------
% 3.58/0.83 % (2858527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858527)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858527)Termination reason: Instruction limit
% 3.58/0.83 % (2858527)Termination phase: Saturation
% 3.58/0.83 % (2858527)Time elapsed: 0.221 s
% 3.58/0.83 % (2858527)Peak memory usage: 14 MB
% 3.58/0.83 % (2858527)Instructions burned: 479 (million)
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858546)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1933970292:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.58/0.83 % (2858545)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=165702289:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.58/0.83 % (2858546)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.58/0.83 % (2858545)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.58/0.83 % (2858546)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.58/0.83 % (2858535)Instruction limit reached!
% 3.58/0.83 % (2858535)------------------------------
% 3.58/0.83 % (2858535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858535)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858535)Termination reason: Instruction limit
% 3.58/0.83 % (2858535)Termination phase: Saturation
% 3.58/0.83 % (2858535)Time elapsed: 0.309 s
% 3.58/0.83 % (2858535)Peak memory usage: 15 MB
% 3.58/0.83 % (2858535)Instructions burned: 694 (million)
% 3.58/0.83 % (2858549)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1431882299:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.58/0.83 % (2858506) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2858500-2858506"...
% 3.58/0.83 % Exception at run slice level
% 3.58/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.58/0.83 % (2858506)...printing done.
% 3.58/0.83 % (2858506)Refutation found. Thanks to Tanya!
% 3.58/0.83 % SZS status Theorem for theBenchmark
% 3.58/0.83 % SZS output start Proof for theBenchmark
% 3.58/0.83 thf(type_def_5, type, extended_enat: $tType).
% 3.58/0.83 thf(type_def_6, type, stream: $tType > $tType).
% 3.58/0.83 thf(type_def_7, type, set: $tType > $tType).
% 3.58/0.83 thf(type_def_8, type, nat: $tType).
% 3.58/0.83 thf(type_def_9, type, itself: $tType > $tType).
% 3.58/0.83 thf(type_def_10, type, a: $tType).
% 3.58/0.83 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 3.58/0.83 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_1, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_2, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_3, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_4, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_5, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_6, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_7, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_8, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_9, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_10, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_11, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_12, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_13, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 3.58/0.83 thf(func_def_14, type, coindu1365464361scount: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > extended_enat))).
% 3.58/0.83 thf(func_def_15, type, extended_enat2: (nat > extended_enat)).
% 3.58/0.83 thf(func_def_16, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 3.58/0.83 thf(func_def_17, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 3.58/0.83 thf(func_def_18, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 3.58/0.83 thf(func_def_19, type, finite_card: !>[X0: $tType]:((set @ X0 > nat))).
% 3.58/0.83 thf(func_def_20, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 3.58/0.83 thf(func_def_21, type, linear1386806755on_alw: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > $o))).
% 3.58/0.83 thf(func_def_22, type, linear505997466_on_ev: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > $o))).
% 3.58/0.83 thf(func_def_23, type, linear1494993505on_nxt: !>[X0: $tType, X1: $tType]:(((stream @ X0 > X1) > stream @ X0 > X1))).
% 3.58/0.83 thf(func_def_24, type, linear1335279038n_wait: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_25, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.58/0.83 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.58/0.83 thf(func_def_27, type, type2: !>[X0: $tType]:(itself @ X0)).
% 3.58/0.83 thf(func_def_28, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.58/0.83 thf(func_def_29, type, sdrop: !>[X0: $tType]:((nat > stream @ X0 > stream @ X0))).
% 3.58/0.83 thf(func_def_30, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.58/0.83 thf(func_def_31, type, p: (stream @ a > $o)).
% 3.58/0.83 thf(func_def_32, type, omega: stream @ a).
% 3.58/0.83 thf(func_def_34, type, vNOT: ($o > $o)).
% 3.58/0.83 thf(func_def_35, type, db0: !>[X0: $tType]:(X0)).
% 3.58/0.83 thf(func_def_36, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.58/0.83 thf(func_def_39, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.58/0.83 thf(func_def_40, type, vAND: ($o > $o > $o)).
% 3.58/0.83 thf(func_def_41, type, vIMP: ($o > $o > $o)).
% 3.58/0.83 thf(func_def_42, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.58/0.83 thf(func_def_43, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.58/0.83 thf(func_def_44, type, db1: !>[X0: $tType]:(X0)).
% 3.58/0.83 thf(func_def_45, type, vOR: ($o > $o > $o)).
% 3.58/0.83 thf(func_def_46, type, db2: !>[X0: $tType]:(X0)).
% 3.58/0.83 thf(func_def_47, type, sP0: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_48, type, sP1: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_49, type, sP2: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_50, type, sP3: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_51, type, sP4: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_52, type, sP5: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_53, type, sP6: (extended_enat > extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_54, type, sP7: (extended_enat > extended_enat > $o)).
% 3.58/0.83 thf(func_def_55, type, sP8: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.58/0.83 thf(func_def_56, type, sP9: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.58/0.83 thf(func_def_57, type, sP10: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.58/0.83 thf(func_def_58, type, sK11: ((extended_enat > $o) > nat)).
% 3.58/0.83 thf(func_def_59, type, sK12: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_60, type, sK13: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_61, type, sK14: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_62, type, sK15: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_63, type, sK16: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_64, type, sK17: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_65, type, sK18: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_66, type, sK19: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_67, type, sK20: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_68, type, sK21: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_69, type, sK22: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_70, type, sK23: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_71, type, sK24: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_72, type, sK25: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_73, type, sK26: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_74, type, sK27: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_75, type, sK28: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_76, type, sK29: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_77, type, sK30: !>[X0: $tType]:((nat > (X0 > extended_enat) > X0))).
% 3.58/0.83 thf(func_def_78, type, sK31: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 3.58/0.83 thf(func_def_79, type, sK32: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0))).
% 3.58/0.83 thf(func_def_80, type, sK33: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 3.58/0.83 thf(func_def_81, type, sK34: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 3.58/0.83 thf(func_def_82, type, sK35: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 3.58/0.83 thf(func_def_83, type, sK36: ((extended_enat > $o) > extended_enat)).
% 3.58/0.83 thf(func_def_84, type, sK37: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_85, type, sK38: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_86, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_87, type, sK40: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 3.58/0.83 thf(func_def_88, type, sK41: !>[X0: $tType]:((X0 > X0))).
% 3.58/0.83 thf(func_def_89, type, sK42: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0))).
% 3.58/0.83 thf(func_def_90, type, sK43: (nat > extended_enat > nat)).
% 3.58/0.83 thf(func_def_91, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1 > X0))).
% 3.58/0.83 thf(func_def_92, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > X1))).
% 3.58/0.83 thf(func_def_93, type, sK46: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 3.58/0.83 thf(func_def_94, type, sK47: (nat > set @ nat > nat)).
% 3.58/0.83 thf(func_def_95, type, sK48: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_96, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 3.58/0.83 thf(func_def_97, type, sK50: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 3.58/0.83 thf(func_def_98, type, sK51: (set @ nat > nat > nat)).
% 3.58/0.83 thf(func_def_99, type, sK52: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 3.58/0.83 thf(func_def_100, type, sK53: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_101, type, sK54: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 3.58/0.83 thf(func_def_102, type, sK55: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 3.58/0.83 thf(func_def_103, type, sK56: ((nat > nat) > nat)).
% 3.58/0.83 thf(func_def_104, type, sK57: !>[X0: $tType]:((nat > set @ X0 > set @ X0))).
% 3.58/0.83 thf(func_def_105, type, sK58: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_106, type, sK59: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_107, type, sK60: ((nat > nat) > nat)).
% 3.58/0.83 thf(func_def_108, type, sK61: ((nat > nat) > nat)).
% 3.58/0.83 thf(func_def_109, type, sK62: (nat > set @ extended_enat > extended_enat)).
% 3.58/0.83 thf(func_def_110, type, sK63: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_111, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_112, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_113, type, sK66: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_114, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_115, type, sK68: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_116, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_117, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_118, type, sK71: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_119, type, sK72: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_120, type, sK73: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_121, type, sK74: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_122, type, sK75: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_123, type, sK76: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_124, type, sK77: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_125, type, sK78: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.58/0.83 thf(func_def_126, type, sK79: !>[X0: $tType]:((X0 > X0))).
% 3.58/0.83 thf(func_def_127, type, sK80: !>[X0: $tType]:((X0 > X0))).
% 3.58/0.83 thf(func_def_128, type, sK81: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_129, type, sK82: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_130, type, sK83: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_131, type, sK84: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_132, type, sK85: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_133, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_134, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_135, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_136, type, sK89: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_137, type, sK90: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 3.58/0.83 thf(func_def_138, type, sK91: ((nat > $o) > nat)).
% 3.58/0.83 thf(func_def_139, type, sK92: ((nat > $o) > nat)).
% 3.58/0.83 thf(func_def_140, type, sK93: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 3.58/0.83 thf(func_def_141, type, sK94: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_142, type, sK95: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 3.58/0.83 thf(func_def_143, type, sK96: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 3.58/0.83 thf(func_def_144, type, sK97: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.58/0.83 thf(func_def_145, type, sK98: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.58/0.83 thf(func_def_146, type, sK99: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_147, type, sK100: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.58/0.83 thf(func_def_148, type, sK101: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_149, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.58/0.83 thf(func_def_150, type, sK103: nat).
% 3.58/0.83 thf(func_def_151, type, sK104: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.58/0.83 thf(func_def_152, type, sK105: (nat > set @ nat > nat)).
% 3.58/0.83 thf(func_def_153, type, sK106: (set @ nat > nat)).
% 3.58/0.83 thf(func_def_154, type, sK107: (nat > set @ nat > nat)).
% 3.58/0.83 thf(func_def_155, type, sK108: (set @ nat > nat)).
% 3.58/0.83 thf(func_def_156, type, sK109: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_157, type, db3: !>[X0: $tType]:(X0)).
% 3.58/0.83 thf(func_def_158, type, sK110: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_159, type, sK111: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_160, type, sK112: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_161, type, sK113: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_162, type, sK114: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_163, type, sK115: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_164, type, sK116: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_165, type, sK117: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_166, type, sK118: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_167, type, sK119: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_168, type, sK120: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat > nat))).
% 3.58/0.83 thf(func_def_169, type, sK121: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat > nat))).
% 3.58/0.83 thf(func_def_170, type, sK122: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_171, type, sK123: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_172, type, sK124: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_173, type, sK125: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_174, type, sK126: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_175, type, sK127: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_176, type, sK128: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_177, type, sK129: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_178, type, sK130: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_179, type, sK131: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_180, type, sK132: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_181, type, sK133: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_182, type, sK134: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_183, type, sK135: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_184, type, sK136: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_185, type, sK137: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_186, type, sK138: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_187, type, sK139: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_188, type, sK140: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_189, type, sK141: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_190, type, sK142: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_191, type, sK143: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_192, type, sK144: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_193, type, sK145: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_194, type, sK146: nat).
% 3.58/0.83 thf(func_def_195, type, sK147: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat > nat))).
% 3.58/0.83 thf(func_def_196, type, sK148: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat > nat))).
% 3.58/0.83 thf(func_def_197, type, sK149: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_198, type, sK150: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_199, type, sK151: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_200, type, sK152: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_201, type, sK153: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_202, type, sK154: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_203, type, sK155: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_204, type, sK156: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_205, type, sK157: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_206, type, sK158: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_207, type, sK159: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_208, type, sK160: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_209, type, sK161: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_210, type, sK162: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_211, type, sK163: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_212, type, sK164: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_213, type, sK165: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_214, type, sK166: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_215, type, sK167: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_216, type, sK168: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_217, type, sK169: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_218, type, sK170: (extended_enat > nat)).
% 3.58/0.83 thf(func_def_219, type, sK171: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_220, type, sK172: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_221, type, sK173: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat))).
% 3.58/0.83 thf(func_def_222, type, sK174: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_223, type, sK175: !>[X0: $tType]:(((stream @ X0 > $o) > (stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_224, type, sK176: !>[X0: $tType]:((stream @ X0 > (stream @ X0 > $o) > nat > nat))).
% 3.58/0.83 thf(func_def_225, type, sK177: !>[X0: $tType]:(((stream @ X0 > $o) > nat > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_226, type, sK178: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_227, type, sK179: !>[X0: $tType]:(((stream @ X0 > $o) > stream @ X0 > nat))).
% 3.58/0.83 thf(func_def_228, type, sK180: (nat > nat)).
% 3.58/0.83 thf(func_def_230, type, sK182: ((extended_enat > $o) > nat)).
% 3.58/0.83 thf(func_def_231, type, sK183: ((extended_enat > $o) > extended_enat)).
% 3.58/0.83 thf(f1,axiom,(
% 3.58/0.83 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X4 : stream @ a] : (~(p @ X4)))) @ omega) => (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[X5 : nat] : ((p @ (sdrop @ a @ X5 @ omega)))))))))),
% 3.58/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062ev_A_Ialw_A_I_092_060lambda_062xs_O_A_092_060not_062_AP_Axs_J_J_A_092_060omega_062_A_092_060Longrightarrow_062_Ascount_AP_A_092_060omega_062_A_061_Aenat_A_Icard_A_123i_O_AP_A_Isdrop_Ai_A_092_060omega_062_J_125_J_092_060close_062)).
% 3.58/0.83 thf(f26,axiom,(
% 3.58/0.83 ! [X0 : $tType] : (linear1386806755on_alw @ X0 = (^[X1 : (stream @ X0 > $o), X2 : stream @ X0] : (! [X3 : nat] : (X1 @ (sdrop @ X0 @ X3 @ X2)))))),
% 3.58/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_alw__iff__sdrop)).
% 3.58/0.83 thf(f27,axiom,(
% 3.58/0.83 ! [X0 : $tType] : (linear505997466_on_ev @ X0 = (^[X1 : (stream @ X0 > $o), X2 : stream @ X0] : (? [X3 : nat] : (X1 @ (sdrop @ X0 @ X3 @ X2)))))),
% 3.58/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_ev__iff__sdrop)).
% 3.58/0.83 thf(f39,axiom,(
% 3.58/0.83 ! [X0 : nat] : (ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)),
% 3.58/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_enat__ord__code_I4_J)).
% 3.58/0.83 thf(f283,axiom,(
% 3.58/0.83 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X0 : stream @ a] : (~(p @ X0)))) @ omega)),
% 3.58/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 3.58/0.83 thf(f284,conjecture,(
% 3.58/0.83 (ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)),
% 3.58/0.83 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 3.58/0.83 thf(f285,negated_conjecture,(
% 3.58/0.83 ~(ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)),
% 3.58/0.83 inference(negated_conjecture,[status(cth)],[f284])).
% 3.58/0.83 thf(f286,plain,(
% 3.58/0.83 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X0 : stream @ a] : (~(p @ X0)))) @ omega) => (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[X1 : nat] : ((p @ (sdrop @ a @ X1 @ omega)))))))))),
% 3.58/0.83 inference(rectify,[],[f1])).
% 3.58/0.83 thf(f287,plain,(
% 3.58/0.83 (((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)) = $true) => (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega))))))))),
% 3.58/0.83 inference(fool_elimination,[],[f286])).
% 3.58/0.83 thf(f318,plain,(
% 3.58/0.83 ! [X0 : $tType] : (linear1386806755on_alw @ X0 = (^[X1 : (stream @ X0 > $o), X2 : stream @ X0] : (! [X3 : nat] : (X1 @ (sdrop @ X0 @ X3 @ X2)))))),
% 3.58/0.83 inference(rectify,[],[f26])).
% 3.58/0.83 thf(f319,plain,(
% 3.58/0.83 ! [X0 : $tType] : (linear1386806755on_alw @ X0 = (^[Y0 : stream @ X0 > $o]: ((^[Y1 : stream @ X0]: (!! @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ X0 @ Y2 @ Y1))))))))),
% 3.58/0.83 inference(fool_elimination,[],[f318])).
% 3.58/0.83 thf(f320,plain,(
% 3.58/0.83 ! [X0 : $tType] : (linear505997466_on_ev @ X0 = (^[X1 : (stream @ X0 > $o), X2 : stream @ X0] : (? [X3 : nat] : (X1 @ (sdrop @ X0 @ X3 @ X2)))))),
% 3.58/0.83 inference(rectify,[],[f27])).
% 3.58/0.83 thf(f321,plain,(
% 3.58/0.83 ! [X0 : $tType] : (linear505997466_on_ev @ X0 = (^[Y0 : stream @ X0 > $o]: ((^[Y1 : stream @ X0]: (?? @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ X0 @ Y2 @ Y1))))))))),
% 3.58/0.83 inference(fool_elimination,[],[f320])).
% 3.58/0.83 thf(f344,plain,(
% 3.58/0.83 ! [X0 : nat] : (ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)),
% 3.58/0.83 inference(rectify,[],[f39])).
% 3.58/0.83 thf(f345,plain,(
% 3.58/0.83 ! [X0 : nat] : (((ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)) = $true)),
% 3.58/0.83 inference(fool_elimination,[],[f344])).
% 3.58/0.83 thf(f811,plain,(
% 3.58/0.83 (linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[X0 : stream @ a] : (~(p @ X0)))) @ omega)),
% 3.58/0.83 inference(rectify,[],[f283])).
% 3.58/0.83 thf(f812,plain,(
% 3.58/0.83 (((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)) = $true)),
% 3.58/0.83 inference(fool_elimination,[],[f811])).
% 3.58/0.83 thf(f813,plain,(
% 3.58/0.83 ~(ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)),
% 3.58/0.83 inference(rectify,[],[f285])).
% 3.58/0.83 thf(f814,plain,(
% 3.58/0.83 ~ (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) = $true)),
% 3.58/0.83 inference(fool_elimination,[],[f813])).
% 3.58/0.83 thf(f853,plain,(
% 3.58/0.83 (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) != $true)),
% 3.58/0.83 inference(flattening,[],[f814])).
% 3.58/0.83 thf(f854,plain,(
% 3.58/0.83 (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | (((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)) != $true)),
% 3.58/0.83 inference(ennf_transformation,[],[f287])).
% 3.58/0.83 thf(f1245,plain,(
% 3.58/0.83 (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | (((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)) != $true)),
% 3.58/0.83 inference(cnf_transformation,[],[f854])).
% 3.58/0.83 thf(f1302,plain,(
% 3.58/0.83 ( ! [X0 : $tType] : ((linear1386806755on_alw @ X0 = (^[Y0 : stream @ X0 > $o]: ((^[Y1 : stream @ X0]: (!! @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ X0 @ Y2 @ Y1))))))))) )),
% 3.58/0.83 inference(cnf_transformation,[],[f319])).
% 3.58/0.83 thf(f1303,plain,(
% 3.58/0.83 ( ! [X0 : $tType] : ((linear505997466_on_ev @ X0 = (^[Y0 : stream @ X0 > $o]: ((^[Y1 : stream @ X0]: (?? @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ X0 @ Y2 @ Y1))))))))) )),
% 3.58/0.83 inference(cnf_transformation,[],[f321])).
% 3.58/0.83 thf(f1319,plain,(
% 3.58/0.83 ( ! [X0 : nat] : ((((ord_less @ extended_enat @ (extended_enat2 @ X0) @ extend1396239628finity @ extended_enat)) = $true)) )),
% 3.58/0.83 inference(cnf_transformation,[],[f345])).
% 3.58/0.83 thf(f1632,plain,(
% 3.58/0.83 (((linear505997466_on_ev @ a @ (linear1386806755on_alw @ a @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)) = $true)),
% 3.58/0.83 inference(cnf_transformation,[],[f812])).
% 3.58/0.83 thf(f1633,plain,(
% 3.58/0.83 (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) != $true)),
% 3.58/0.83 inference(cnf_transformation,[],[f853])).
% 3.58/0.83 thf(f1635,definition,(
% 3.58/0.83 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.58/0.83 introduced(theory,[fool_exhaustiveness_axiom])).
% 3.58/0.83 thf(f1636,plain,(
% 3.58/0.83 (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($true != (((^[Y0 : stream @ a > $o]: ((^[Y1 : stream @ a]: (?? @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ a @ Y2 @ Y1))))))) @ ((^[Y0 : stream @ a > $o]: ((^[Y1 : stream @ a]: (!! @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ a @ Y2 @ Y1))))))) @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 3.58/0.83 inference(definition_unfolding,[],[f1245,f1303,f1302])).
% 3.58/0.83 thf(f1684,plain,(
% 3.58/0.83 ($true = (((^[Y0 : stream @ a > $o]: ((^[Y1 : stream @ a]: (?? @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ a @ Y2 @ Y1))))))) @ ((^[Y0 : stream @ a > $o]: ((^[Y1 : stream @ a]: (!! @ nat @ (^[Y2 : nat]: (Y0 @ (sdrop @ a @ Y2 @ Y1))))))) @ (^[Y0 : stream @ a]: (~ (p @ Y0)))) @ omega)))),
% 3.58/0.83 inference(definition_unfolding,[],[f1632,f1303,f1302])).
% 3.58/0.83 thf(f1711,plain,(
% 3.58/0.83 ($true = ((?? @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (~ (p @ (sdrop @ a @ Y1 @ (sdrop @ a @ Y0 @ omega))))))))))),
% 3.58/0.83 inference(beta-eta_normalization,[],[f1684])).
% 3.58/0.83 thf(f1712,plain,(
% 3.58/0.83 ($true = (((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (~ (p @ (sdrop @ a @ Y1 @ (sdrop @ a @ Y0 @ omega))))))) @ sK103)))),
% 3.58/0.83 inference(sigma_proxy_clausification,[],[f1711])).
% 3.58/0.83 thf(f1713,plain,(
% 3.58/0.83 ($true = ((!! @ nat @ (^[Y0 : nat]: (~ (p @ (sdrop @ a @ Y0 @ (sdrop @ a @ sK103 @ omega))))))))),
% 3.58/0.83 inference(beta-eta_normalization,[],[f1712])).
% 3.58/0.83 thf(f1714,plain,(
% 3.58/0.83 ( ! [X1 : nat] : (($true = (((^[Y0 : nat]: (~ (p @ (sdrop @ a @ Y0 @ (sdrop @ a @ sK103 @ omega))))) @ X1)))) )),
% 3.58/0.83 inference(pi_proxy_clausification,[],[f1713])).
% 3.58/0.83 thf(f1715,plain,(
% 3.58/0.83 ( ! [X1 : nat] : (($true = ((~ (p @ (sdrop @ a @ X1 @ (sdrop @ a @ sK103 @ omega))))))) )),
% 3.58/0.83 inference(beta-eta_normalization,[],[f1714])).
% 3.58/0.83 thf(f1716,plain,(
% 3.58/0.83 ( ! [X1 : nat] : (($false = ((p @ (sdrop @ a @ X1 @ (sdrop @ a @ sK103 @ omega)))))) )),
% 3.58/0.83 inference(not_proxy_clausification,[],[f1715])).
% 3.58/0.83 thf(f2173,plain,(
% 3.58/0.83 (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($true != ((?? @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (~ (p @ (sdrop @ a @ Y1 @ (sdrop @ a @ Y0 @ omega))))))))))),
% 3.58/0.83 inference(beta-eta_normalization,[],[f1636])).
% 3.58/0.83 thf(f2174,plain,(
% 3.58/0.83 ( ! [X1 : nat] : ((((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($false = (((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: (~ (p @ (sdrop @ a @ Y1 @ (sdrop @ a @ Y0 @ omega))))))) @ X1)))) )),
% 3.58/0.83 inference(pi_proxy_clausification,[],[f2173])).
% 3.58/0.83 thf(f2175,plain,(
% 3.58/0.83 ( ! [X1 : nat] : ((((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($false = ((!! @ nat @ (^[Y0 : nat]: (~ (p @ (sdrop @ a @ Y0 @ (sdrop @ a @ X1 @ omega))))))))) )),
% 3.58/0.83 inference(beta-eta_normalization,[],[f2174])).
% 3.58/0.83 thf(f2176,plain,(
% 3.58/0.83 ( ! [X1 : nat] : ((((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($false = (((^[Y0 : nat]: (~ (p @ (sdrop @ a @ Y0 @ (sdrop @ a @ X1 @ omega))))) @ (sK180 @ X1))))) )),
% 3.58/0.83 inference(sigma_proxy_clausification,[],[f2175])).
% 3.58/0.83 thf(f2177,plain,(
% 3.58/0.83 ( ! [X1 : nat] : ((((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($false = ((~ (p @ (sdrop @ a @ (sK180 @ X1) @ (sdrop @ a @ X1 @ omega))))))) )),
% 3.58/0.83 inference(beta-eta_normalization,[],[f2176])).
% 3.58/0.83 thf(f2178,plain,(
% 3.58/0.83 ( ! [X1 : nat] : ((((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ($true = ((p @ (sdrop @ a @ (sK180 @ X1) @ (sdrop @ a @ X1 @ omega)))))) )),
% 3.58/0.83 inference(not_proxy_clausification,[],[f2177])).
% 3.58/0.83 thf(f2188,definition,(
% 3.58/0.83 spl181_3 <=> ! [X1 : nat] : ($true = ((p @ (sdrop @ a @ (sK180 @ X1) @ (sdrop @ a @ X1 @ omega)))))),
% 3.58/0.83 introduced(definition,[new_symbols(definition,[spl181_3])],[avatar_definition])).
% 3.58/0.83 thf(f2189,plain,(
% 3.58/0.83 ( ! [X1 : nat] : (($true = ((p @ (sdrop @ a @ (sK180 @ X1) @ (sdrop @ a @ X1 @ omega)))))) ) | ~spl181_3),
% 3.58/0.83 inference(avatar_component_clause,[],[f2188])).
% 3.58/0.83 thf(f2191,definition,(
% 3.58/0.83 spl181_4 <=> (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega))))))))),
% 3.58/0.83 introduced(definition,[new_symbols(definition,[spl181_4])],[avatar_definition])).
% 3.58/0.83 thf(f2193,plain,(
% 3.58/0.83 (((coindu1365464361scount @ a @ p @ omega)) = ((extended_enat2 @ (finite_card @ nat @ (collect @ nat @ (^[Y0 : nat]: (p @ (sdrop @ a @ Y0 @ omega)))))))) | ~spl181_4),
% 3.58/0.83 inference(avatar_component_clause,[],[f2191])).
% 3.58/0.83 thf(f2194,plain,(
% 3.58/0.83 spl181_3 | spl181_4),
% 3.58/0.83 inference(avatar_split_clause,[],[f2178,f2191,f2188])).
% 3.58/0.83 thf(f2197,plain,(
% 3.58/0.83 ($true != $true) | (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) = $false)),
% 3.58/0.83 inference(constrained_superposition,[],[f1633,f1635])).
% 3.58/0.83 thf(f2199,plain,(
% 3.58/0.83 (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) = $false)),
% 3.58/0.83 inference(trivial_inequality_removal,[],[f2197])).
% 3.58/0.83 thf(f6585,plain,(
% 3.58/0.83 ($true = $false) | ~spl181_3),
% 3.58/0.83 inference(constrained_superposition,[],[f2189,f1716])).
% 3.58/0.83 thf(f6622,plain,(
% 3.58/0.83 $false | ~spl181_3),
% 3.58/0.83 inference(trivial_inequality_removal,[],[f6585])).
% 3.58/0.83 thf(f6623,plain,(
% 3.58/0.83 ~spl181_3),
% 3.58/0.83 inference(avatar_contradiction_clause,[],[f6622])).
% 3.58/0.83 thf(f9927,plain,(
% 3.58/0.83 (((ord_less @ extended_enat @ (coindu1365464361scount @ a @ p @ omega) @ extend1396239628finity @ extended_enat)) = $true) | ~spl181_4),
% 3.58/0.83 inference(constrained_superposition,[],[f1319,f2193])).
% 3.58/0.83 thf(f9952,plain,(
% 3.58/0.83 ($true = $false) | ~spl181_4),
% 3.58/0.83 inference(forward_demodulation,[],[f9927,f2199])).
% 3.58/0.83 thf(f9953,plain,(
% 3.58/0.83 $false | ~spl181_4),
% 3.58/0.83 inference(trivial_inequality_removal,[],[f9952])).
% 3.58/0.83 thf(f9954,plain,(
% 3.58/0.83 ~spl181_4),
% 3.58/0.83 inference(avatar_contradiction_clause,[],[f9953])).
% 3.58/0.83 cnf(s3, plain, spl181_3 | spl181_4, inference(sat_conversion,[],[f2194])).
% 3.58/0.83 cnf(s159, plain, ~spl181_3, inference(sat_conversion,[],[f6623])).
% 3.58/0.83 cnf(s249, plain, ~spl181_4, inference(sat_conversion,[],[f9954])).
% 3.58/0.83 cnf(s337, plain, $false, inference(rat,[],[s3,s249,s159])).
% 3.58/0.83 thf(f9958,plain,(
% 3.58/0.83 $false),
% 3.58/0.83 inference(avatar_sat_refutation,[],[s337])).
% 3.58/0.83 % SZS output end Proof for theBenchmark
% 3.58/0.83 % (2858506)------------------------------
% 3.58/0.83 % (2858506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.58/0.83 % (2858506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/0.83 % (2858506)CaDiCaL version: 2.1.3
% 3.58/0.83 % (2858506)Termination reason: Refutation
% 3.58/0.83 % (2858506)Time elapsed: 0.560 s
% 3.58/0.83 % (2858506)Peak memory usage: 20 MB
% 3.58/0.83 % (2858506)Instructions burned: 1119 (million)
% 3.58/0.83 % (2858500)Success in time 0.606 s
% 3.58/0.83 % Vampire exiting
%------------------------------------------------------------------------------