%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT197^1 : 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 07:49:01 AM UTC 2026
% Result : Theorem 1.42s 0.54s
% Output : Refutation 1.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT197^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:08:24 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
% 1.42/0.54 % (3520716)Will run a generic schedule for satisfiability detection.
% 1.42/0.54 % (3520721)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1493102912_2999 on theBenchmark for (2999ds/0Mi)
% 1.42/0.54 % (3520722)% WARNING: option uhcvi not known.
% 1.42/0.54 % (3520723)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4135565525:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.42/0.54 % (3520722)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=127758630:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.42/0.54 % (3520724)dis+10_1_sil=32000:sp=arity:random_seed=3378027174:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.42/0.54 % (3520725)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2451055282:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.42/0.54 % (3520726)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1461023478:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.42/0.54 % (3520727)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=888003264:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.42/0.54 % Exception at run slice level
% 1.42/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.54 % (3520722)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.42/0.54 % (3520725)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.42/0.54 % (3520735)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3031634186:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.42/0.54 % (3520724)Instruction limit reached!
% 1.42/0.54 % (3520724)------------------------------
% 1.42/0.54 % (3520724)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520724)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520724)Termination reason: Instruction limit
% 1.42/0.54 % (3520724)Termination phase: Function definition elimination
% 1.42/0.54 % (3520724)Time elapsed: 0.045 s
% 1.42/0.54 % (3520724)Peak memory usage: 11 MB
% 1.42/0.54 % (3520724)Instructions burned: 103 (million)
% 1.42/0.54 % (3520725)Instruction limit reached!
% 1.42/0.54 % (3520725)------------------------------
% 1.42/0.54 % (3520725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520725)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520725)Termination reason: Instruction limit
% 1.42/0.54 % (3520725)Termination phase: Property scanning
% 1.42/0.54 % (3520725)Time elapsed: 0.051 s
% 1.42/0.54 % (3520725)Peak memory usage: 11 MB
% 1.42/0.54 % (3520725)Instructions burned: 117 (million)
% 1.42/0.54 % (3520726)Instruction limit reached!
% 1.42/0.54 % (3520726)------------------------------
% 1.42/0.54 % (3520726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520726)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520726)Termination reason: Instruction limit
% 1.42/0.54 % (3520726)Termination phase: Property scanning
% 1.42/0.54 % (3520726)Time elapsed: 0.057 s
% 1.42/0.54 % (3520726)Peak memory usage: 11 MB
% 1.42/0.54 % (3520726)Instructions burned: 133 (million)
% 1.42/0.54 % (3520737)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2298344265:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.42/0.54 % Exception at run slice level
% 1.42/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.54 % (3520727)Instruction limit reached!
% 1.42/0.54 % (3520727)------------------------------
% 1.42/0.54 % (3520727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520727)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520727)Termination reason: Instruction limit
% 1.42/0.54 % (3520727)Termination phase: Saturation
% 1.42/0.54 % (3520727)Time elapsed: 0.070 s
% 1.42/0.54 % (3520727)Peak memory usage: 13 MB
% 1.42/0.54 % (3520727)Instructions burned: 160 (million)
% 1.42/0.54 % (3520738)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=1646356571:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.42/0.54 % (3520739)ott-21_1_sil=16000:fs=off:random_seed=3800537333:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.42/0.54 % (3520741)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3131347365:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.42/0.54 % (3520722)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.42/0.54 % (3520738)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.42/0.54 % (3520742)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=588590952:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.42/0.54 % (3520738)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.42/0.54 % (3520737)Instruction limit reached!
% 1.42/0.54 % (3520737)------------------------------
% 1.42/0.54 % (3520737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520737)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520737)Termination reason: Instruction limit
% 1.42/0.54 % (3520737)Termination phase: Property scanning
% 1.42/0.54 % (3520737)Time elapsed: 0.080 s
% 1.42/0.54 % (3520737)Peak memory usage: 11 MB
% 1.42/0.54 % (3520737)Instructions burned: 131 (million)
% 1.42/0.54 % (3520739)Instruction limit reached!
% 1.42/0.54 % (3520739)------------------------------
% 1.42/0.54 % (3520739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520739)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520739)Termination reason: Instruction limit
% 1.42/0.54 % (3520739)Termination phase: Saturation
% 1.42/0.54 % (3520739)Time elapsed: 0.078 s
% 1.42/0.54 % (3520739)Peak memory usage: 13 MB
% 1.42/0.54 % (3520739)Instructions burned: 180 (million)
% 1.42/0.54 % (3520748)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=153047971:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.42/0.54 % Exception at run slice level
% 1.42/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.42/0.54 % (3520747)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=968658985:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.42/0.54 % (3520750)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=4284464536: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)
% 1.42/0.54 % (3520741)Instruction limit reached!
% 1.42/0.54 % (3520741)------------------------------
% 1.42/0.54 % (3520741)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520741)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520741)Termination reason: Instruction limit
% 1.42/0.54 % (3520741)Termination phase: Saturation
% 1.42/0.54 % (3520741)Time elapsed: 0.129 s
% 1.42/0.54 % (3520741)Peak memory usage: 15 MB
% 1.42/0.54 % (3520741)Instructions burned: 477 (million)
% 1.42/0.54 % (3520753)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2788613270:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.42/0.54 % (3520722) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3520716-3520722"...
% 1.42/0.54 % (3520750)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.42/0.54 % (3520722)...printing done.
% 1.42/0.54 % (3520722)Refutation found. Thanks to Tanya!
% 1.42/0.54 % SZS status Theorem for theBenchmark
% 1.42/0.54 % SZS output start Proof for theBenchmark
% 1.42/0.54 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 1.42/0.54 thf(type_def_6, type, code_natural: $tType).
% 1.42/0.54 thf(type_def_7, type, extended_enat: $tType).
% 1.42/0.54 thf(type_def_8, type, set: $tType > $tType).
% 1.42/0.54 thf(type_def_9, type, nat: $tType).
% 1.42/0.54 thf(type_def_10, type, itself: $tType > $tType).
% 1.42/0.54 thf(type_def_11, type, b: $tType).
% 1.42/0.54 thf(type_def_12, type, a: $tType).
% 1.42/0.54 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 1.42/0.54 thf(func_def_0, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_1, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_2, type, monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_3, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_4, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_5, type, comm_monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_6, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_7, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_8, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_9, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_10, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_11, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_12, type, semiri456707255roduct: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.42/0.54 thf(func_def_13, type, bNF_rel_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1 > $o) > (X2 > X3 > $o) > (X0 > X2) > (X1 > X3) > $o))).
% 1.42/0.54 thf(func_def_14, type, code_case_natural: !>[X0: $tType]:((X0 > (code_natural > X0) > code_natural > X0))).
% 1.42/0.54 thf(func_def_15, type, code_rec_natural: !>[X0: $tType]:((X0 > (code_natural > X0 > X0) > code_natural > X0))).
% 1.42/0.54 thf(func_def_16, type, code_size_natural: (code_natural > nat)).
% 1.42/0.54 thf(func_def_17, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.42/0.54 thf(func_def_18, type, coindu246717305length: !>[X0: $tType]:((nat > coinductive_llist @ X0 > extended_enat))).
% 1.42/0.54 thf(func_def_19, type, coinductive_iterates: !>[X0: $tType]:(((X0 > X0) > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_20, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_21, type, coinductive_ldrop: !>[X0: $tType]:((extended_enat > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_22, type, coindu218763757pWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_23, type, coinductive_lfilter: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_24, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 1.42/0.54 thf(func_def_25, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_26, type, coinductive_llcp: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > extended_enat))).
% 1.42/0.54 thf(func_def_27, type, coinductive_llength: !>[X0: $tType]:((coinductive_llist @ X0 > extended_enat))).
% 1.42/0.54 thf(func_def_28, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_29, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0))).
% 1.42/0.54 thf(func_def_30, type, coindu1259883913_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coinductive_llist @ X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 1.42/0.54 thf(func_def_31, type, coindu1486289336t_all2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coinductive_llist @ X0 > coinductive_llist @ X1 > $o))).
% 1.42/0.54 thf(func_def_32, type, coinductive_lmap: !>[X0: $tType, X1: $tType]:(((X0 > X1) > coinductive_llist @ X0 > coinductive_llist @ X1))).
% 1.42/0.54 thf(func_def_33, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 1.42/0.54 thf(func_def_34, type, coindu543516966_llist: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > $o))).
% 1.42/0.54 thf(func_def_35, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 1.42/0.54 thf(func_def_36, type, coinductive_lprefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.42/0.54 thf(func_def_37, type, coinductive_ltake: !>[X0: $tType]:((extended_enat > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_38, type, coindu501562517eWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_39, type, coindu780009021istsum: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_40, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 1.42/0.54 thf(func_def_41, type, map_fun: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > (X1 > X2) > X0 > X3))).
% 1.42/0.54 thf(func_def_42, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.42/0.54 thf(func_def_43, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.42/0.54 thf(func_def_44, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.42/0.54 thf(func_def_45, type, lMirro999291890or_aux: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_46, type, case_nat: !>[X0: $tType]:((X0 > (nat > X0) > nat > X0))).
% 1.42/0.54 thf(func_def_47, type, rec_nat: !>[X0: $tType]:((X0 > (nat > X0 > X0) > nat > X0))).
% 1.42/0.54 thf(func_def_48, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 1.42/0.54 thf(func_def_49, type, type: !>[X0: $tType]:(itself @ X0)).
% 1.42/0.54 thf(func_def_50, type, bex1_rel: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > $o))).
% 1.42/0.54 thf(func_def_51, type, quotient3: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > (X1 > X0) > $o))).
% 1.42/0.54 thf(func_def_52, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.42/0.54 thf(func_def_53, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.42/0.54 thf(func_def_54, type, p: (a > b > $o)).
% 1.42/0.54 thf(func_def_55, type, acc_a: coinductive_llist @ b).
% 1.42/0.54 thf(func_def_56, type, acca: coinductive_llist @ a).
% 1.42/0.54 thf(func_def_57, type, xs_a: coinductive_llist @ b).
% 1.42/0.54 thf(func_def_58, type, xsa: coinductive_llist @ a).
% 1.42/0.54 thf(func_def_62, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.42/0.54 thf(func_def_63, type, db1: !>[X0: $tType]:(X0)).
% 1.42/0.54 thf(func_def_64, type, db0: !>[X0: $tType]:(X0)).
% 1.42/0.54 thf(func_def_65, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.42/0.54 thf(func_def_66, type, vAND: ($o > $o > $o)).
% 1.42/0.54 thf(func_def_67, type, vIMP: ($o > $o > $o)).
% 1.42/0.54 thf(func_def_68, type, vNOT: ($o > $o)).
% 1.42/0.54 thf(func_def_69, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.54 thf(func_def_70, type, db2: !>[X0: $tType]:(X0)).
% 1.42/0.54 thf(func_def_71, type, db3: !>[X0: $tType]:(X0)).
% 1.42/0.54 thf(func_def_72, type, db4: !>[X0: $tType]:(X0)).
% 1.42/0.54 thf(func_def_73, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.42/0.54 thf(func_def_74, type, vOR: ($o > $o > $o)).
% 1.42/0.54 thf(func_def_75, type, sK0: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_76, type, sK1: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_77, type, sK2: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_78, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_79, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_80, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_81, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_82, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_83, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_84, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X3 > X2) > (X0 > X1) > (X1 > X2 > $o) > (X0 > X3 > $o) > X0))).
% 1.42/0.54 thf(func_def_85, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X3 > X2) > (X0 > X1) > (X1 > X2 > $o) > (X0 > X3 > $o) > X3))).
% 1.42/0.54 thf(func_def_86, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_87, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_88, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_89, type, sK14: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_90, type, sK15: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_91, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_92, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_94, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_97, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_98, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 1.42/0.54 thf(func_def_100, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_101, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_102, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_103, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_104, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_105, type, sK30: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_106, type, sK31: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_107, type, sK32: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_108, type, sK33: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_109, type, sK34: !>[X0: $tType]:(((X0 > X0) > (X0 > coinductive_llist @ X0) > X0))).
% 1.42/0.54 thf(func_def_110, type, sK35: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_111, type, sK36: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_112, type, sK37: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_113, type, sK38: ((nat > nat > $o) > nat)).
% 1.42/0.54 thf(func_def_114, type, sK39: ((nat > nat > $o) > nat)).
% 1.42/0.54 thf(func_def_115, type, sK40: ((nat > nat > $o) > nat)).
% 1.42/0.54 thf(func_def_116, type, sK41: ((nat > nat > $o) > nat)).
% 1.42/0.54 thf(func_def_117, type, sK42: ((nat > nat > $o) > nat)).
% 1.42/0.54 thf(func_def_118, type, sK43: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_119, type, sK44: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_120, type, sK45: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_121, type, sK46: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_122, type, sK47: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > (X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_123, type, sK48: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_124, type, sK49: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_125, type, sK50: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_126, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > coinductive_llist @ X1 > X1))).
% 1.42/0.54 thf(func_def_127, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > coinductive_llist @ X1 > X1))).
% 1.42/0.54 thf(func_def_128, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > X1))).
% 1.42/0.54 thf(func_def_129, type, sK54: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > coinductive_llist @ X1 > X1))).
% 1.42/0.54 thf(func_def_130, type, sK55: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_131, type, sK56: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_132, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_133, type, sK58: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > coinductive_llist @ X1 > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_134, type, sK59: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > coinductive_llist @ X1 > coinductive_llist @ X0 > X1))).
% 1.42/0.54 thf(func_def_135, type, sK60: !>[X0: $tType, X1: $tType]:((X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_136, type, sK61: !>[X0: $tType, X1: $tType]:((X0 > coinductive_llist @ X1 > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_137, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_138, type, sK63: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 1.42/0.54 thf(func_def_139, type, sK64: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_140, type, sK65: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_141, type, sK66: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 1.42/0.54 thf(func_def_142, type, sK67: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_143, type, sK68: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_144, type, sK69: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 1.42/0.54 thf(func_def_145, type, sK70: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_146, type, sK71: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_147, type, sK72: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 1.42/0.54 thf(func_def_148, type, sK73: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_149, type, sK74: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_150, type, sK75: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_151, type, sK76: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_152, type, sK77: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_153, type, sK78: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_154, type, sK79: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_155, type, sK80: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_156, type, sK81: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_157, type, sK82: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_158, type, sK83: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_159, type, sK84: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_160, type, sK85: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_161, type, sK86: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_162, type, sK87: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.42/0.54 thf(func_def_163, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0) > coinductive_llist @ X1 > X0 > coinductive_llist @ X0 > coinductive_llist @ X1))).
% 1.42/0.54 thf(func_def_164, type, sK89: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X1 > X0 > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_165, type, sK90: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X1 > X0 > (X1 > X0 > $o) > coinductive_llist @ X1))).
% 1.42/0.54 thf(func_def_166, type, sK91: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X1 > (X1 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_167, type, sK92: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X1 > coinductive_llist @ X0 > X0 > (X0 > X1 > $o) > coinductive_llist @ X1))).
% 1.42/0.54 thf(func_def_168, type, sK93: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X1 > coinductive_llist @ X0 > X0 > (X0 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_169, type, sK94: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.42/0.54 thf(func_def_170, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_171, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_172, type, sK97: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_173, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_174, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_175, type, sK100: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_176, type, sK101: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_177, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_178, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_179, type, sK104: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_180, type, sK105: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 1.42/0.54 thf(func_def_181, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_182, type, sK107: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_183, type, sK108: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_184, type, sK109: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 1.42/0.54 thf(func_def_185, type, sK110: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_186, type, sK111: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_187, type, sK112: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_188, type, sK113: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_189, type, sK114: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_190, type, sK115: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_191, type, sK116: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_192, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_193, type, sK118: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_194, type, sK119: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_195, type, sK120: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_196, type, sK121: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_197, type, sK122: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_198, type, sK123: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_199, type, sK124: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_200, type, sK125: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_201, type, sK126: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_202, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_203, type, sK128: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_204, type, sK129: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_205, type, sK130: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_206, type, sK131: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_207, type, sK132: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_208, type, sK133: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_209, type, sK134: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_210, type, sK135: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_211, type, sK136: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_212, type, sK137: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_213, type, sK138: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_214, type, sK139: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_215, type, sK140: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_216, type, sK141: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_217, type, sK142: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_218, type, sK143: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_219, type, sK144: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_220, type, sK145: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_221, type, sK146: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_222, type, sK147: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_223, type, sK148: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_224, type, sK149: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_225, type, sK150: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_226, type, sK151: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_227, type, sK152: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_228, type, sK153: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_229, type, sK154: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_230, type, sK155: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_231, type, sK156: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_232, type, sK157: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_233, type, sK158: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_234, type, sK159: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_235, type, sK160: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_236, type, sK161: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_237, type, sK162: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_238, type, sK163: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_239, type, sK164: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_240, type, sK165: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_241, type, sK166: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_242, type, sK167: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_243, type, sK168: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_244, type, sK169: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_245, type, sK170: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_246, type, sK171: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_247, type, sK172: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_248, type, sK173: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_249, type, sK174: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_250, type, sK175: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_251, type, sK176: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_252, type, sK177: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_253, type, sK178: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_254, type, sK179: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_255, type, sK180: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_256, type, sK181: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_257, type, sK182: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_258, type, sK183: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_259, type, sK184: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_260, type, sK185: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_261, type, sK186: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_262, type, sK187: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_263, type, sK188: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_264, type, sK189: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_265, type, sK190: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_266, type, sK191: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_267, type, sK192: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_268, type, sK193: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_269, type, sK194: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_270, type, sK195: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_271, type, sK196: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_272, type, sK197: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_273, type, sK198: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_274, type, sK199: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_275, type, sK200: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_276, type, sK201: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_277, type, sK202: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_278, type, sK203: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_279, type, sK204: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_280, type, sK205: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_281, type, sK206: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_282, type, sK207: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_283, type, sK208: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_284, type, sK209: !>[X0: $tType, X1: $tType]:(((X1 > X1 > $o) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_285, type, sK210: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X0 > $o) > X1))).
% 1.42/0.54 thf(func_def_286, type, sK211: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_287, type, sK212: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X1))).
% 1.42/0.54 thf(func_def_288, type, sK213: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_289, type, sK214: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0 > $o) > X0))).
% 1.42/0.54 thf(func_def_290, type, sK215: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_291, type, sK216: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X1 > $o) > X0))).
% 1.42/0.54 thf(func_def_292, type, sK217: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 1.42/0.54 thf(func_def_293, type, sK218: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1 > $o) > X1))).
% 1.42/0.54 thf(func_def_294, type, sK219: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((X0 > X1 > $o) > (X5 > X0 > X3) > (X5 > X2 > $o) > (X3 > X4 > $o) > (X2 > X1 > X4) > X2))).
% 1.42/0.54 thf(func_def_295, type, sK220: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((X0 > X1 > $o) > (X5 > X0 > X3) > (X5 > X2 > $o) > (X3 > X4 > $o) > (X2 > X1 > X4) > X5))).
% 1.42/0.54 thf(f1,axiom,(
% 1.42/0.54 (coindu1486289336t_all2 @ a @ b @ p @ acca @ acc_a)),
% 1.42/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_local_OLNil_I2_J)).
% 1.42/0.54 thf(f5,axiom,(
% 1.42/0.54 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > $o),X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => (((coinductive_llength @ X0 @ X3)) = ((coinductive_llength @ X1 @ X4))))),
% 1.42/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_llist__all2__llengthD)).
% 1.42/0.54 thf(f11,axiom,(
% 1.42/0.54 ! [X0 : $tType] : (coinductive_llength @ X0 = ((coindu246717305length @ X0 @ zero_zero @ nat)))),
% 1.42/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_llength__code)).
% 1.42/0.54 thf(f286,conjecture,(
% 1.42/0.54 (((coinductive_llength @ a @ acca)) = ((coinductive_llength @ b @ acc_a)))),
% 1.42/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.42/0.54 thf(f287,negated_conjecture,(
% 1.42/0.54 ~ (((coinductive_llength @ a @ acca)) = ((coinductive_llength @ b @ acc_a)))),
% 1.42/0.54 inference(negated_conjecture,[status(cth)],[f286])).
% 1.42/0.54 thf(f288,plain,(
% 1.42/0.54 (coindu1486289336t_all2 @ a @ b @ p @ acca @ acc_a)),
% 1.42/0.54 inference(rectify,[],[f1])).
% 1.42/0.54 thf(f289,plain,(
% 1.42/0.54 (((coindu1486289336t_all2 @ a @ b @ p @ acca @ acc_a)) = $true)),
% 1.42/0.54 inference(fool_elimination,[],[f288])).
% 1.42/0.54 thf(f294,plain,(
% 1.42/0.54 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > $o),X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => (((coinductive_llength @ X0 @ X3)) = ((coinductive_llength @ X1 @ X4))))),
% 1.42/0.54 inference(rectify,[],[f5])).
% 1.42/0.54 thf(f295,plain,(
% 1.42/0.54 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > $o),X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) = $true) => (((coinductive_llength @ X0 @ X3)) = ((coinductive_llength @ X1 @ X4))))),
% 1.42/0.54 inference(fool_elimination,[],[f294])).
% 1.42/0.54 thf(f771,plain,(
% 1.42/0.54 (((coinductive_llength @ a @ acca)) != ((coinductive_llength @ b @ acc_a)))),
% 1.42/0.54 inference(flattening,[],[f287])).
% 1.42/0.54 thf(f772,plain,(
% 1.42/0.54 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1 > $o),X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((((coinductive_llength @ X0 @ X3)) = ((coinductive_llength @ X1 @ X4))) | (((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) != $true))),
% 1.42/0.54 inference(ennf_transformation,[],[f295])).
% 1.42/0.54 thf(f1020,plain,(
% 1.42/0.54 (((coindu1486289336t_all2 @ a @ b @ p @ acca @ acc_a)) = $true)),
% 1.42/0.54 inference(cnf_transformation,[],[f289])).
% 1.42/0.54 thf(f1024,plain,(
% 1.42/0.54 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1 > $o),X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((((coinductive_llength @ X0 @ X3)) = ((coinductive_llength @ X1 @ X4))) | (((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) != $true)) )),
% 1.42/0.54 inference(cnf_transformation,[],[f772])).
% 1.42/0.54 thf(f1031,plain,(
% 1.42/0.54 ( ! [X0 : $tType] : ((coinductive_llength @ X0 = ((coindu246717305length @ X0 @ zero_zero @ nat)))) )),
% 1.42/0.54 inference(cnf_transformation,[],[f11])).
% 1.42/0.54 thf(f1367,plain,(
% 1.42/0.54 (((coinductive_llength @ a @ acca)) != ((coinductive_llength @ b @ acc_a)))),
% 1.42/0.54 inference(cnf_transformation,[],[f771])).
% 1.42/0.54 thf(f1372,plain,(
% 1.42/0.54 ( ! [X1 : $tType,X0 : $tType,X2 : (X0 > X1 > $o),X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) != $true) | (((coindu246717305length @ X0 @ zero_zero @ nat @ X3)) = ((coindu246717305length @ X1 @ zero_zero @ nat @ X4)))) )),
% 1.42/0.54 inference(definition_unfolding,[],[f1024,f1031,f1031])).
% 1.42/0.54 thf(f1442,plain,(
% 1.42/0.54 (((coindu246717305length @ a @ zero_zero @ nat @ acca)) != ((coindu246717305length @ b @ zero_zero @ nat @ acc_a)))),
% 1.42/0.54 inference(definition_unfolding,[],[f1367,f1031,f1031])).
% 1.42/0.54 thf(f5294,plain,(
% 1.42/0.54 ($true != $true) | (((coindu246717305length @ a @ zero_zero @ nat @ acca)) = ((coindu246717305length @ b @ zero_zero @ nat @ acc_a)))),
% 1.42/0.54 inference(constrained_superposition,[],[f1372,f1020])).
% 1.42/0.54 thf(f5295,plain,(
% 1.42/0.54 (((coindu246717305length @ a @ zero_zero @ nat @ acca)) = ((coindu246717305length @ b @ zero_zero @ nat @ acc_a)))),
% 1.42/0.54 inference(trivial_inequality_removal,[],[f5294])).
% 1.42/0.54 thf(f5297,plain,(
% 1.42/0.54 $false),
% 1.42/0.54 inference(forward_subsumption_resolution,[],[f5295,f1442])).
% 1.42/0.54 % SZS output end Proof for theBenchmark
% 1.42/0.54 % (3520722)------------------------------
% 1.42/0.54 % (3520722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.54 % (3520722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.54 % (3520722)CaDiCaL version: 2.1.3
% 1.42/0.54 % (3520722)Termination reason: Refutation
% 1.42/0.54 % (3520722)Time elapsed: 0.229 s
% 1.42/0.54 % (3520722)Peak memory usage: 15 MB
% 1.42/0.54 % (3520722)Instructions burned: 412 (million)
% 1.42/0.54 % (3520716)Success in time 0.289 s
% 1.42/0.54 % Vampire exiting
%------------------------------------------------------------------------------