%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM178^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 07:46:30 AM UTC 2026
% Result : Theorem 1.35s 0.36s
% Output : Refutation 1.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COM178^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 17:48:49 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.12 Running first-order model finding
% 0.09/0.12 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.35/0.36 % (454294)Will run a generic schedule for satisfiability detection.
% 1.35/0.36 % (454300)% WARNING: option uhcvi not known.
% 1.35/0.36 % (454303)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3018862242:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.35/0.36 % (454302)dis+10_1_sil=32000:sp=arity:random_seed=1268495839:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.35/0.36 % (454299)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=492227200_2999 on theBenchmark for (2999ds/0Mi)
% 1.35/0.36 % (454301)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=287652910:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.35/0.36 % (454300)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=213468047:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.35/0.36 % (454304)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=738410177:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.35/0.36 % (454305)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=156971264:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.35/0.36 % (454300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.35/0.36 % (454303)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.35/0.36 % (454302)Instruction limit reached!
% 1.35/0.36 % (454302)------------------------------
% 1.35/0.36 % (454302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454302)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454302)Termination reason: Instruction limit
% 1.35/0.36 % (454302)Termination phase: Property scanning
% 1.35/0.36 % (454302)Time elapsed: 0.024 s
% 1.35/0.36 % (454302)Peak memory usage: 11 MB
% 1.35/0.36 % (454302)Instructions burned: 107 (million)
% 1.35/0.36 % Exception at run slice level% (454300)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.35/0.36
% 1.35/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.35/0.36 % (454303)Instruction limit reached!
% 1.35/0.36 % (454303)------------------------------
% 1.35/0.36 % (454303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454303)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454303)Termination reason: Instruction limit
% 1.35/0.36 % (454303)Termination phase: Saturation
% 1.35/0.36 % (454303)Time elapsed: 0.026 s
% 1.35/0.36 % (454303)Peak memory usage: 12 MB
% 1.35/0.36 % (454303)Instructions burned: 117 (million)
% 1.35/0.36 % (454304)Instruction limit reached!
% 1.35/0.36 % (454304)------------------------------
% 1.35/0.36 % (454304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454304)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454304)Termination reason: Instruction limit
% 1.35/0.36 % (454304)Termination phase: Saturation
% 1.35/0.36 % (454304)Time elapsed: 0.031 s
% 1.35/0.36 % (454304)Peak memory usage: 12 MB
% 1.35/0.36 % (454304)Instructions burned: 134 (million)
% 1.35/0.36 % (454313)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1033146213:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.35/0.36 % (454314)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3101273932:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.35/0.36 % (454315)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=2249878940:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.35/0.36 % (454305)Instruction limit reached!
% 1.35/0.36 % (454305)------------------------------
% 1.35/0.36 % (454305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454305)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454305)Termination reason: Instruction limit
% 1.35/0.36 % (454305)Termination phase: Saturation
% 1.35/0.36 % (454305)Time elapsed: 0.037 s
% 1.35/0.36 % (454305)Peak memory usage: 13 MB
% 1.35/0.36 % (454305)Instructions burned: 162 (million)
% 1.35/0.36 % (454316)ott-21_1_sil=16000:fs=off:random_seed=664584198:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.35/0.36 % (454315)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.35/0.36 % (454320)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4116443891:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.35/0.36 % Exception at run slice level
% 1.35/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.35/0.36 % (454315)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.35/0.36 % (454323)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2810993069:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.35/0.36 % (454316)Instruction limit reached!
% 1.35/0.36 % (454316)------------------------------
% 1.35/0.36 % (454316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454316)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454316)Termination reason: Instruction limit
% 1.35/0.36 % (454316)Termination phase: Saturation
% 1.35/0.36 % (454316)Time elapsed: 0.041 s
% 1.35/0.36 % (454316)Peak memory usage: 13 MB
% 1.35/0.36 % (454316)Instructions burned: 180 (million)
% 1.35/0.36 % (454314)Instruction limit reached!
% 1.35/0.36 % (454314)------------------------------
% 1.35/0.36 % (454314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454314)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454314)Termination reason: Instruction limit
% 1.35/0.36 % (454314)Termination phase: Saturation
% 1.35/0.36 % (454314)Time elapsed: 0.050 s
% 1.35/0.36 % (454314)Peak memory usage: 13 MB
% 1.35/0.36 % (454314)Instructions burned: 131 (million)
% 1.35/0.36 % (454325)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1178961362:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.35/0.36 % (454326)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3729553750:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.35/0.36 % Exception at run slice level
% 1.35/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.35/0.36 % (454329)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=641979312:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.35/0.36 % (454329)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.35/0.36 % Exception at run slice level
% 1.35/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.35/0.36 % (454331)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4114425536:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 1.35/0.36 % (454331)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.35/0.36 % (454320)Instruction limit reached!
% 1.35/0.36 % (454320)------------------------------
% 1.35/0.36 % (454320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454320)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454320)Termination reason: Instruction limit
% 1.35/0.36 % (454320)Termination phase: Saturation
% 1.35/0.36 % (454320)Time elapsed: 0.125 s
% 1.35/0.36 % (454320)Peak memory usage: 15 MB
% 1.35/0.36 % (454320)Instructions burned: 478 (million)
% 1.35/0.36 % (454333)fmb+10_1_sil=64000:random_seed=2081672587:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 1.35/0.36 % (454325) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-454294-454325"...
% 1.35/0.36 % (454325)...printing done.
% 1.35/0.36 % (454325)Refutation found. Thanks to Tanya!
% 1.35/0.36 % SZS status Theorem for theBenchmark
% 1.35/0.36 % SZS output start Proof for theBenchmark
% 1.35/0.36 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 1.35/0.36 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 1.35/0.36 thf(type_def_7, type, set: $tType > $tType).
% 1.35/0.36 thf(type_def_8, type, itself: $tType > $tType).
% 1.35/0.36 thf(type_def_9, type, node: $tType).
% 1.35/0.36 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 1.35/0.36 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.35/0.36 thf(func_def_1, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 1.35/0.36 thf(func_def_2, type, coindu328551480prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_3, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 1.35/0.36 thf(func_def_4, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_5, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_6, type, coindu218763757pWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_7, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_8, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_9, type, coinductive_llexord: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_10, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_11, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 1.35/0.36 thf(func_def_12, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0))).
% 1.35/0.36 thf(func_def_13, type, coinductive_lhd: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_14, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_15, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 1.35/0.36 thf(func_def_16, type, coinductive_ltl: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_17, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_18, type, coinductive_lprefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_19, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_20, type, coindu501562517eWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_21, type, coinductive_lzip: !>[X0: $tType, X1: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X1 > coinductive_llist @ product_prod @ X0 @ X1))).
% 1.35/0.36 thf(func_def_22, type, coinductive_lsorted: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_23, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 1.35/0.36 thf(func_def_24, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_25, type, koenig793108494nected: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 1.35/0.36 thf(func_def_26, type, bot_bot: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 1.35/0.36 thf(func_def_28, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.35/0.36 thf(func_def_29, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.35/0.36 thf(func_def_30, type, type2: !>[X0: $tType]:(itself @ X0)).
% 1.35/0.36 thf(func_def_31, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 1.35/0.36 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.35/0.36 thf(func_def_33, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 1.35/0.36 thf(func_def_34, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.35/0.36 thf(func_def_35, type, f: (product_prod @ node @ set @ node > coinductive_llist @ node)).
% 1.35/0.36 thf(func_def_36, type, graph: (node > node > $o)).
% 1.35/0.36 thf(func_def_37, type, n: node).
% 1.35/0.36 thf(func_def_38, type, ns: set @ node).
% 1.35/0.36 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.35/0.36 thf(func_def_43, type, vAND: ($o > $o > $o)).
% 1.35/0.36 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.35/0.36 thf(func_def_45, type, vNOT: ($o > $o)).
% 1.35/0.36 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_47, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.35/0.36 thf(func_def_48, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.35/0.36 thf(func_def_49, type, vIMP: ($o > $o > $o)).
% 1.35/0.36 thf(func_def_50, type, vOR: ($o > $o > $o)).
% 1.35/0.36 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_52, type, db1: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_53, type, db3: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_54, type, db4: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_55, type, db5: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_56, type, db6: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_57, type, sP0: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > $o))).
% 1.35/0.36 thf(func_def_58, type, sP1: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 1.35/0.36 thf(func_def_59, type, sK2: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.35/0.36 thf(func_def_60, type, sK3: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.35/0.36 thf(func_def_61, type, sK4: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_62, type, sK5: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_63, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 1.35/0.36 thf(func_def_64, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 1.35/0.36 thf(func_def_65, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 1.35/0.36 thf(func_def_66, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 1.35/0.36 thf(func_def_67, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 1.35/0.36 thf(func_def_68, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 1.35/0.36 thf(func_def_69, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 1.35/0.36 thf(func_def_70, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 1.35/0.36 thf(func_def_71, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 1.35/0.36 thf(func_def_72, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 1.35/0.36 thf(func_def_73, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 1.35/0.36 thf(func_def_74, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 1.35/0.36 thf(func_def_75, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 1.35/0.36 thf(func_def_76, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 1.35/0.36 thf(func_def_77, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 1.35/0.36 thf(func_def_78, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 1.35/0.36 thf(func_def_79, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 1.35/0.36 thf(func_def_80, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 1.35/0.36 thf(func_def_81, type, sK24: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_82, type, sK25: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_83, type, sK26: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.35/0.36 thf(func_def_84, type, sK27: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.35/0.36 thf(func_def_85, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 1.35/0.36 thf(func_def_86, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 1.35/0.36 thf(func_def_87, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 1.35/0.36 thf(func_def_88, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.35/0.36 thf(func_def_89, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.35/0.36 thf(func_def_90, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_91, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_92, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 1.35/0.36 thf(func_def_93, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 1.35/0.36 thf(func_def_94, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.35/0.36 thf(func_def_95, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.35/0.36 thf(func_def_96, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_97, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_98, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 1.35/0.36 thf(func_def_99, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.35/0.36 thf(func_def_100, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.35/0.36 thf(func_def_101, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_102, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_103, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.35/0.36 thf(func_def_104, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.35/0.36 thf(func_def_105, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_106, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_107, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.35/0.36 thf(func_def_108, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.35/0.36 thf(func_def_109, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_110, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 1.35/0.36 thf(func_def_111, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 1.35/0.36 thf(func_def_112, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 1.35/0.36 thf(func_def_113, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 1.35/0.36 thf(func_def_114, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 1.35/0.36 thf(func_def_115, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 1.35/0.36 thf(func_def_116, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 1.35/0.36 thf(func_def_117, type, sK60: !>[X0: $tType]:((set @ X0 > X0))).
% 1.35/0.36 thf(func_def_118, type, sK61: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_119, type, sK62: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.35/0.36 thf(func_def_120, type, sK63: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_121, type, sK64: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_122, type, sK65: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_123, type, sK66: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_124, type, sK67: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_125, type, sK68: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_126, type, sK69: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_127, type, sK70: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_128, type, sK71: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_129, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_130, type, sK73: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_131, type, sK74: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_132, type, sK75: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_133, type, sK76: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 1.35/0.36 thf(func_def_134, type, sK77: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_135, type, sK78: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_136, type, sK79: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 1.35/0.36 thf(func_def_137, type, sK80: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_138, type, sK81: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_139, type, sK82: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_140, type, sK83: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_141, type, sK84: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_142, type, sK85: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_143, type, sK86: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_144, type, sK87: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_145, type, sK88: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_146, type, sK89: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_147, type, sK90: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_148, type, sK91: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_149, type, sK92: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_150, type, sK93: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_151, type, sK94: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_152, type, sK95: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_153, type, sK96: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_154, type, sK97: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_155, type, sK98: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_156, type, sK99: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_157, type, sK100: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_158, type, sK101: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_159, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_160, type, sK103: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_161, type, sK104: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_162, type, sK105: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_163, type, sK106: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_164, type, sK107: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_165, type, sK108: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_166, type, sK109: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_167, type, sK110: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_168, type, sK111: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_169, type, sK112: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_170, type, sK113: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_171, type, sK114: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_172, type, sK115: !>[X0: $tType]:(((X0 > X0 > $o) > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_173, type, sK116: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_174, type, sK117: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_175, type, sK118: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_176, type, sK119: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_177, type, sK120: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_178, type, sK121: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_179, type, sK122: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_180, type, sK123: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_181, type, sK124: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_182, type, sK125: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_183, type, sK126: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_184, type, sK127: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_185, type, sK128: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_186, type, sK129: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_187, type, sK130: !>[X0: $tType]:((set @ product_prod @ coinductive_llist @ X0 @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_188, type, sK131: !>[X0: $tType]:((set @ product_prod @ coinductive_llist @ X0 @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_189, type, sK132: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_190, type, sK133: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_191, type, sK134: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_192, type, sK135: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_193, type, sK136: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_194, type, sK137: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_195, type, sK138: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_196, type, sK139: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_197, type, sF140: set @ node).
% 1.35/0.36 thf(func_def_198, type, sF141: product_prod @ node @ set @ node).
% 1.35/0.36 thf(func_def_199, type, sF142: coinductive_llist @ node).
% 1.35/0.36 thf(func_def_200, type, sF143: set @ node).
% 1.35/0.36 thf(func_def_201, type, sF144: $o).
% 1.35/0.36 thf(func_def_202, type, sK145: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_203, type, sK146: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_204, type, sK147: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_205, type, sK148: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_206, type, sK149: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_207, type, sK150: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_208, type, sK151: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_209, type, sK152: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_210, type, sK153: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_211, type, sK154: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_212, type, sK155: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_213, type, sK156: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_214, type, sK157: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_215, type, sK158: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_216, type, sK159: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_217, type, sK160: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_218, type, sK161: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_219, type, sK162: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_220, type, sK163: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_221, type, sK164: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_222, type, sK165: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_223, type, sK166: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_224, type, sK167: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_225, type, sK168: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_226, type, sK169: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_227, type, sK170: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_228, type, sK171: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_229, type, sK172: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_230, type, sK173: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_231, type, sK174: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_232, type, sK175: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_233, type, sK176: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_234, type, sK177: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_235, type, sK178: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_236, type, sK179: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_237, type, sK180: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_238, type, sK181: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_239, type, sK182: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_240, type, sK183: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_241, type, sK184: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_242, type, sK185: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_243, type, sK186: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_244, type, sK187: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_245, type, sK188: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_246, type, sK189: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_247, type, sK190: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_248, type, sK191: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_249, type, sK192: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_250, type, sK193: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_251, type, sK194: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_252, type, sK195: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_253, type, sK196: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_254, type, sK197: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_255, type, sK198: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_256, type, sK199: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_257, type, sK200: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_258, type, sK201: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_259, type, sK202: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0))).
% 1.35/0.36 thf(func_def_260, type, sK203: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_261, type, sK204: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_262, type, sK205: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_263, type, sK206: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_264, type, sK207: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_265, type, sK208: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_266, type, sK209: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_267, type, sK210: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_268, type, sK211: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_269, type, sK212: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_270, type, sK213: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_271, type, sK214: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_272, type, sK215: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_273, type, sK216: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_274, type, sK217: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_275, type, sK218: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_276, type, sK219: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_277, type, sK220: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_278, type, sK221: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_279, type, sK222: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_280, type, sK223: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_281, type, sK224: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_282, type, sK225: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_283, type, sK226: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_284, type, sK227: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_285, type, sK228: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_286, type, sK229: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_287, type, sK230: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_288, type, sK231: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_289, type, sK232: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_290, type, sK233: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_291, type, sK234: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_292, type, sK235: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_293, type, sK236: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_294, type, sK237: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_295, type, sK238: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_296, type, sK239: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_297, type, sK240: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_298, type, sK241: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_299, type, sK242: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_300, type, sK243: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_301, type, sK244: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_302, type, sK245: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_303, type, sK246: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_304, type, sK247: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_305, type, sK248: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_306, type, sK249: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_307, type, sK250: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_308, type, sK251: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_309, type, sK252: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_310, type, sK253: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_311, type, sK254: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_312, type, sK255: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_313, type, sK256: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_314, type, sK257: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_315, type, sK258: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_316, type, sK259: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_317, type, sK260: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_318, type, sK261: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_319, type, sK262: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_320, type, sK263: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_321, type, sK264: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_322, type, sK265: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_323, type, sK266: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_324, type, sK267: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_325, type, sK268: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_326, type, sK269: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_327, type, sK270: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_328, type, sK271: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_329, type, sK272: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_330, type, sK273: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_331, type, sK274: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_332, type, sK275: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_333, type, sK276: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_334, type, sK277: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_335, type, sK278: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_336, type, sK279: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_337, type, sK280: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_338, type, sK281: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_339, type, sK282: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_340, type, sK283: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_341, type, sK284: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_342, type, sK285: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_343, type, sK286: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_344, type, sK287: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_345, type, sK288: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_346, type, sK289: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_347, type, sK290: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_348, type, sK291: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_349, type, sK292: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_350, type, sK293: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_351, type, sK294: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_352, type, sK295: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_353, type, sK296: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_354, type, sK297: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_355, type, sK298: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_356, type, sK299: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_357, type, sK300: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_358, type, db11: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_359, type, db10: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_360, type, db9: !>[X0: $tType]:(X0)).
% 1.35/0.36 thf(func_def_361, type, sK301: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_362, type, sK302: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_363, type, sK303: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_364, type, sK304: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_365, type, sK305: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_366, type, sK306: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_367, type, sK307: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_368, type, sK308: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_369, type, sK309: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_370, type, sK310: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_371, type, sK311: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_372, type, sK312: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_373, type, sK313: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_374, type, sK314: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_375, type, sK315: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_376, type, sK316: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_377, type, sK317: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_378, type, sK318: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_379, type, sK319: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_380, type, sK320: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_381, type, sK321: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_382, type, sK322: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_383, type, sK323: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_384, type, sK324: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_385, type, sK325: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_386, type, sK326: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_387, type, sK327: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_388, type, sK328: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_389, type, sK329: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_390, type, sK330: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_391, type, sK331: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_392, type, sK332: !>[X0: $tType]:(((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_393, type, sK333: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_394, type, sK334: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_395, type, sK335: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_396, type, sK336: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_397, type, sK337: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_398, type, sK338: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_399, type, sK339: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_400, type, sK340: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_401, type, sK341: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_402, type, sK342: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_403, type, sK343: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_404, type, sK344: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_405, type, sK345: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_406, type, sK346: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_407, type, sK347: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_408, type, sK348: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_409, type, sK349: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_410, type, sK350: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_411, type, sK351: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_412, type, sK352: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_413, type, sK353: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_414, type, sK354: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_415, type, sK355: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_416, type, sK356: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_417, type, sK357: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_418, type, sK358: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X1 @ X0 > coinductive_llist @ X0 > product_prod @ X1 @ X0 > coinductive_llist @ X1 > coinductive_llist @ X0))).
% 1.35/0.36 thf(func_def_419, type, sK359: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X1 @ X0 > product_prod @ X1 @ X0 > coinductive_llist @ X0 > coinductive_llist @ X1 > X0))).
% 1.35/0.36 thf(func_def_420, type, sK360: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X1 @ X0 > product_prod @ X1 @ X0 > coinductive_llist @ X0 > coinductive_llist @ X1 > coinductive_llist @ X1))).
% 1.35/0.36 thf(func_def_421, type, sK361: !>[X0: $tType, X1: $tType]:((coinductive_llist @ product_prod @ X1 @ X0 > product_prod @ X1 @ X0 > coinductive_llist @ X0 > coinductive_llist @ X1 > X1))).
% 1.35/0.36 thf(func_def_422, type, sK362: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 1.35/0.36 thf(func_def_423, type, sK363: !>[X0: $tType]:((set @ X0 > X0))).
% 1.35/0.36 thf(func_def_424, type, sK364: !>[X0: $tType]:(((X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_425, type, sK365: !>[X0: $tType]:(((X0 > $o) > X0))).
% 1.35/0.36 thf(func_def_426, type, sK366: !>[X0: $tType]:((set @ X0 > X0))).
% 1.35/0.36 thf(f1,axiom,(
% 1.35/0.36 (member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 1.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062lhd_A_If_A_In_M_Ans_J_J_A_092_060in_062_Alset_A_If_A_In_M_Ans_J_J_092_060close_062)).
% 1.35/0.36 thf(f2,axiom,(
% 1.35/0.36 (ns = bot_bot @ set @ node)),
% 1.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_ns__def)).
% 1.35/0.36 thf(f3,axiom,(
% 1.35/0.36 ! [X0 : node,X1 : set @ node] : (((coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) = X0)),
% 1.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_f__simps_I2_J)).
% 1.35/0.36 thf(f42,axiom,(
% 1.35/0.36 ! [X0 : $tType] : (coinductive_lset @ X0 = ((coinductive_gen_lset @ X0 @ bot_bot @ set @ X0)))),
% 1.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_lset__code)).
% 1.35/0.36 thf(f261,conjecture,(
% 1.35/0.36 (member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 1.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.35/0.36 thf(f262,negated_conjecture,(
% 1.35/0.36 ~(member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 1.35/0.36 inference(negated_conjecture,[status(cth)],[f261])).
% 1.35/0.36 thf(f263,plain,(
% 1.35/0.36 (member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 1.35/0.36 inference(rectify,[],[f1])).
% 1.35/0.36 thf(f264,plain,(
% 1.35/0.36 (((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 1.35/0.36 inference(fool_elimination,[],[f263])).
% 1.35/0.36 thf(f681,plain,(
% 1.35/0.36 ~(member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))),
% 1.35/0.36 inference(rectify,[],[f262])).
% 1.35/0.36 thf(f682,plain,(
% 1.35/0.36 ~ (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 1.35/0.36 inference(fool_elimination,[],[f681])).
% 1.35/0.36 thf(f747,plain,(
% 1.35/0.36 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) != $true)),
% 1.35/0.36 inference(flattening,[],[f682])).
% 1.35/0.36 thf(f1011,plain,(
% 1.35/0.36 (((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) = $true)),
% 1.35/0.36 inference(cnf_transformation,[],[f264])).
% 1.35/0.36 thf(f1012,plain,(
% 1.35/0.36 (ns = bot_bot @ set @ node)),
% 1.35/0.36 inference(cnf_transformation,[],[f2])).
% 1.35/0.36 thf(f1013,plain,(
% 1.35/0.36 ( ! [X0 : node,X1 : set @ node] : ((((coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) = X0)) )),
% 1.35/0.36 inference(cnf_transformation,[],[f3])).
% 1.35/0.36 thf(f1056,plain,(
% 1.35/0.36 ( ! [X0 : $tType] : ((coinductive_lset @ X0 = ((coinductive_gen_lset @ X0 @ bot_bot @ set @ X0)))) )),
% 1.35/0.36 inference(cnf_transformation,[],[f42])).
% 1.35/0.36 thf(f1392,plain,(
% 1.35/0.36 (((member @ node @ n @ (coinductive_lset @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))) != $true)),
% 1.35/0.36 inference(cnf_transformation,[],[f747])).
% 1.35/0.36 thf(f1397,plain,(
% 1.35/0.36 ($true = ((member @ node @ (coinductive_lhd @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))) @ (coinductive_gen_lset @ node @ bot_bot @ set @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))))),
% 1.35/0.36 inference(definition_unfolding,[],[f1011,f1056])).
% 1.35/0.36 thf(f1591,plain,(
% 1.35/0.36 ($true != ((member @ node @ n @ (coinductive_gen_lset @ node @ bot_bot @ set @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))))),
% 1.35/0.36 inference(definition_unfolding,[],[f1392,f1056])).
% 1.35/0.36 thf(f1605,definition,(
% 1.35/0.36 (sF140 = bot_bot @ set @ node)),
% 1.35/0.36 introduced(definition,[new_symbols(definition,[sF140])],[function_definition])).
% 1.35/0.36 thf(f1606,plain,(
% 1.35/0.36 (bot_bot @ set @ node = sF140)),
% 1.35/0.36 inference(reorient_equations,[],[f1605])).
% 1.35/0.36 thf(f1607,definition,(
% 1.35/0.36 (sF141 = ((product_Pair @ node @ set @ node @ n @ ns)))),
% 1.35/0.36 introduced(definition,[new_symbols(definition,[sF141])],[function_definition])).
% 1.35/0.36 thf(f1608,plain,(
% 1.35/0.36 (((product_Pair @ node @ set @ node @ n @ ns)) = sF141)),
% 1.35/0.36 inference(reorient_equations,[],[f1607])).
% 1.35/0.36 thf(f1609,definition,(
% 1.35/0.36 (sF142 = ((f @ sF141)))),
% 1.35/0.36 introduced(definition,[new_symbols(definition,[sF142])],[function_definition])).
% 1.35/0.36 thf(f1610,plain,(
% 1.35/0.36 (((f @ sF141)) = sF142)),
% 1.35/0.36 inference(reorient_equations,[],[f1609])).
% 1.35/0.36 thf(f1611,definition,(
% 1.35/0.36 (sF143 = ((coinductive_gen_lset @ node @ sF140 @ sF142)))),
% 1.35/0.36 introduced(definition,[new_symbols(definition,[sF143])],[function_definition])).
% 1.35/0.36 thf(f1612,plain,(
% 1.35/0.36 (((coinductive_gen_lset @ node @ sF140 @ sF142)) = sF143)),
% 1.35/0.36 inference(reorient_equations,[],[f1611])).
% 1.35/0.36 thf(f1613,definition,(
% 1.35/0.36 (sF144 = ((member @ node @ n @ sF143)))),
% 1.35/0.36 introduced(definition,[new_symbols(definition,[sF144])],[function_definition])).
% 1.35/0.36 thf(f1614,plain,(
% 1.35/0.36 (((member @ node @ n @ sF143)) = sF144)),
% 1.35/0.36 inference(reorient_equations,[],[f1613])).
% 1.35/0.36 thf(f1615,plain,(
% 1.35/0.36 ($true != sF144)),
% 1.35/0.36 inference(definition_folding,[],[f1591,f1614,f1612,f1610,f1608,f1606])).
% 1.35/0.36 thf(f5453,plain,(
% 1.35/0.36 ($false = ((member @ node @ n @ sF143))) | ($true = sF144)),
% 1.35/0.36 inference(iff_proxy_clausification,[],[f1614])).
% 1.35/0.36 thf(f5456,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ (coinductive_gen_lset @ node @ bot_bot @ set @ node @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))))),
% 1.35/0.36 inference(forward_demodulation,[],[f1397,f1013])).
% 1.35/0.36 thf(f5457,plain,(
% 1.35/0.36 (sF141 = ((product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))),
% 1.35/0.36 inference(forward_demodulation,[],[f1608,f1012])).
% 1.35/0.36 thf(f5458,plain,(
% 1.35/0.36 ($false = ((member @ node @ n @ sF143)))),
% 1.35/0.36 inference(forward_subsumption_resolution,[],[f5453,f1615])).
% 1.35/0.36 thf(f5469,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ (coinductive_gen_lset @ node @ sF140 @ (f @ (product_Pair @ node @ set @ node @ n @ ns))))))),
% 1.35/0.36 inference(forward_demodulation,[],[f5456,f1606])).
% 1.35/0.36 thf(f5470,plain,(
% 1.35/0.36 (sF141 = ((product_Pair @ node @ set @ node @ n @ sF140)))),
% 1.35/0.36 inference(forward_demodulation,[],[f5457,f1606])).
% 1.35/0.36 thf(f5471,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ (coinductive_gen_lset @ node @ sF140 @ (f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))))))),
% 1.35/0.36 inference(forward_demodulation,[],[f5469,f1012])).
% 1.35/0.36 thf(f5472,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ (coinductive_gen_lset @ node @ sF140 @ (f @ (product_Pair @ node @ set @ node @ n @ sF140))))))),
% 1.35/0.36 inference(forward_demodulation,[],[f5471,f1606])).
% 1.35/0.36 thf(f5473,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ (coinductive_gen_lset @ node @ sF140 @ (f @ sF141)))))),
% 1.35/0.36 inference(forward_demodulation,[],[f5472,f5470])).
% 1.35/0.36 thf(f5474,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ (coinductive_gen_lset @ node @ sF140 @ sF142))))),
% 1.35/0.36 inference(forward_demodulation,[],[f5473,f1610])).
% 1.35/0.36 thf(f5475,plain,(
% 1.35/0.36 ($true = ((member @ node @ n @ sF143)))),
% 1.35/0.36 inference(forward_demodulation,[],[f5474,f1612])).
% 1.35/0.36 thf(f5476,plain,(
% 1.35/0.36 ($true = $false)),
% 1.35/0.36 inference(forward_demodulation,[],[f5475,f5458])).
% 1.35/0.36 thf(f5477,plain,(
% 1.35/0.36 $false),
% 1.35/0.36 inference(trivial_inequality_removal,[],[f5476])).
% 1.35/0.36 % SZS output end Proof for theBenchmark
% 1.35/0.36 % (454325)------------------------------
% 1.35/0.36 % (454325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.35/0.36 % (454325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.35/0.36 % (454325)CaDiCaL version: 2.1.3
% 1.35/0.36 % (454325)Termination reason: Refutation
% 1.35/0.36 % (454325)Time elapsed: 0.095 s
% 1.35/0.36 % (454325)Peak memory usage: 16 MB
% 1.35/0.36 % (454325)Instructions burned: 395 (million)
% 1.35/0.36 % (454294)Success in time 0.232 s
% 1.35/0.36 % Vampire exiting
%------------------------------------------------------------------------------