%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP404_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 : Tue Sep 29 11:39:34 AM UTC 2026
% Result : Theorem 1.34s 0.68s
% Output : Refutation 1.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP404_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 13:00:07 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 1.34/0.68 % (3511483)Will run a generic schedule for satisfiability detection.
% 1.34/0.68 % (3511493)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3275195618:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.34/0.68 % (3511489)% WARNING: option uhcvi not known.
% 1.34/0.68 % (3511488)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3473128283_2999 on theBenchmark for (2999ds/0Mi)
% 1.34/0.68 % (3511492)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3729935304:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.34/0.68 % (3511491)dis+10_1_sil=32000:sp=arity:random_seed=1054570172:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.34/0.68 % (3511489)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=861176915:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.34/0.68 % (3511490)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4084853917:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.34/0.68 % (3511494)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1674787195:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.34/0.68 % (3511488)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.34/0.68 % (3511488)Terminated due to inappropriate strategy.
% 1.34/0.68 % (3511488)------------------------------
% 1.34/0.68 % (3511488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511488)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511488)Termination reason: Inappropriate
% 1.34/0.68 % (3511488)Time elapsed: 0.032 s
% 1.34/0.68 % (3511488)Peak memory usage: 12 MB
% 1.34/0.68 % (3511488)Instructions burned: 66 (million)
% 1.34/0.68 % (3511488)------------------------------
% 1.34/0.68 % (3511488)------------------------------
% 1.34/0.68 % (3511493)Instruction limit reached!
% 1.34/0.68 % (3511493)------------------------------
% 1.34/0.68 % (3511493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511493)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511493)Termination reason: Instruction limit
% 1.34/0.68 % (3511493)Termination phase: Saturation
% 1.34/0.68 % (3511493)Time elapsed: 0.041 s
% 1.34/0.68 % (3511493)Peak memory usage: 14 MB
% 1.34/0.68 % (3511493)Instructions burned: 132 (million)
% 1.34/0.68 % (3511503)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1334029419:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.34/0.68 % (3511504)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=572762781:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.34/0.68 % (3511491)Instruction limit reached!
% 1.34/0.68 % (3511491)------------------------------
% 1.34/0.68 % (3511491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511491)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511491)Termination reason: Instruction limit
% 1.34/0.68 % (3511491)Termination phase: Saturation
% 1.34/0.68 % (3511491)Time elapsed: 0.058 s
% 1.34/0.68 % (3511491)Peak memory usage: 14 MB
% 1.34/0.68 % (3511491)Instructions burned: 103 (million)
% 1.34/0.68 % (3511492)Instruction limit reached!
% 1.34/0.68 % (3511492)------------------------------
% 1.34/0.68 % (3511492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511492)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511492)Termination reason: Instruction limit
% 1.34/0.68 % (3511492)Termination phase: Saturation
% 1.34/0.68 % (3511492)Time elapsed: 0.059 s
% 1.34/0.68 % (3511492)Peak memory usage: 14 MB
% 1.34/0.68 % (3511492)Instructions burned: 116 (million)
% 1.34/0.68 % (3511503)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.34/0.68 % (3511503)Terminated due to inappropriate strategy.
% 1.34/0.68 % (3511503)------------------------------
% 1.34/0.68 % (3511503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511503)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511503)Termination reason: Inappropriate
% 1.34/0.68 % (3511503)Time elapsed: 0.042 s
% 1.34/0.68 % (3511503)Peak memory usage: 12 MB
% 1.34/0.68 % (3511503)Instructions burned: 56 (million)
% 1.34/0.68 % (3511503)------------------------------
% 1.34/0.68 % (3511503)------------------------------
% 1.34/0.68 % (3511516)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1891283567:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.34/0.68 % (3511510)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=2705716812:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.34/0.68 % (3511511)ott-21_1_sil=16000:fs=off:random_seed=2541778379:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.34/0.68 % (3511494)Instruction limit reached!
% 1.34/0.68 % (3511494)------------------------------
% 1.34/0.68 % (3511494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511494)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511494)Termination reason: Instruction limit
% 1.34/0.68 % (3511494)Termination phase: Saturation
% 1.34/0.68 % (3511494)Time elapsed: 0.120 s
% 1.34/0.68 % (3511494)Peak memory usage: 15 MB
% 1.34/0.68 % (3511494)Instructions burned: 159 (million)
% 1.34/0.68 % (3511504)Instruction limit reached!
% 1.34/0.68 % (3511504)------------------------------
% 1.34/0.68 % (3511504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511504)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511504)Termination reason: Instruction limit
% 1.34/0.68 % (3511504)Termination phase: Saturation
% 1.34/0.68 % (3511504)Time elapsed: 0.116 s
% 1.34/0.68 % (3511504)Peak memory usage: 14 MB
% 1.34/0.68 % (3511504)Instructions burned: 131 (million)
% 1.34/0.68 % (3511520)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4119583017:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.34/0.68 % (3511522)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=84928606:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.34/0.68 % (3511520)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.34/0.68 % (3511520)Terminated due to inappropriate strategy.
% 1.34/0.68 % (3511520)------------------------------
% 1.34/0.68 % (3511520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.68 % (3511520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.68 % (3511520)CaDiCaL version: 2.1.3
% 1.34/0.68 % (3511520)Termination reason: Inappropriate
% 1.34/0.68 % (3511520)Time elapsed: 0.032 s
% 1.34/0.68 % (3511520)Peak memory usage: 12 MB
% 1.34/0.68 % (3511520)Instructions burned: 56 (million)
% 1.34/0.68 % (3511520)------------------------------
% 1.34/0.68 % (3511520)------------------------------
% 1.34/0.68 % (3511510) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3511483-3511510"...
% 1.34/0.68 % (3511510)...printing done.
% 1.34/0.68 % (3511510)Refutation found. Thanks to Tanya!
% 1.34/0.68 % SZS status Theorem for theBenchmark
% 1.34/0.68 % SZS output start Proof for theBenchmark
% 1.34/0.68 tff(type_def_5, type, 'Nat_set_set$': $tType).
% 1.34/0.68 tff(type_def_6, type, 'Nat_int_set_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_7, type, 'Int_bool_fun$': $tType).
% 1.34/0.68 tff(type_def_8, type, 'Nat_nat_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_9, type, 'Int_set_set_bool_fun$': $tType).
% 1.34/0.68 tff(type_def_10, type, 'Clock$': $tType).
% 1.34/0.68 tff(type_def_11, type, 'Int_set_set_set$': $tType).
% 1.34/0.68 tff(type_def_12, type, 'Int_set$': $tType).
% 1.34/0.68 tff(type_def_13, type, 'Int_int_fun$': $tType).
% 1.34/0.68 tff(type_def_14, type, 'Int_set_set$': $tType).
% 1.34/0.68 tff(type_def_15, type, 'Nat_bool_fun_set$': $tType).
% 1.34/0.68 tff(type_def_16, type, 'Nat_set_nat_set_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_17, type, 'Int_int_set_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_18, type, 'A_run$': $tType).
% 1.34/0.68 tff(type_def_19, type, 'Nat_nat_fun$': $tType).
% 1.34/0.68 tff(type_def_20, type, 'Nat$': $tType).
% 1.34/0.68 tff(type_def_21, type, tlbool: $tType).
% 1.34/0.68 tff(type_def_22, type, 'Nat_set_bool_fun$': $tType).
% 1.34/0.68 tff(type_def_23, type, 'Nat_nat_set_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_24, type, 'Nat_set_set_set$': $tType).
% 1.34/0.68 tff(type_def_25, type, 'Int_set_bool_fun$': $tType).
% 1.34/0.68 tff(type_def_26, type, 'Int_set_int_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_27, type, 'Nat_set_set_bool_fun$': $tType).
% 1.34/0.68 tff(type_def_28, type, 'Int_int_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_29, type, 'Nat_bool_fun$': $tType).
% 1.34/0.68 tff(type_def_30, type, 'Int_set_nat_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_31, type, 'Nat_set$': $tType).
% 1.34/0.68 tff(type_def_32, type, 'Nat_int_fun$': $tType).
% 1.34/0.68 tff(type_def_33, type, 'Int_nat_set_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_34, type, 'Nat_int_bool_fun_fun$': $tType).
% 1.34/0.68 tff(type_def_35, type, 'Int_nat_bool_fun_fun$': $tType).
% 1.34/0.68 tff(func_def_0, type, 'uvs$': 'Int_set_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_1, type, 'uminus$c': 'Int_bool_fun$' > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_2, type, 'collect$c': 'Int_bool_fun$' > 'Int_set$').
% 1.34/0.68 tff(func_def_3, type, 'less$': 'Nat_set$' > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_4, type, 'finite$b': 'Nat_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_5, type, 'uuw$': ('Nat_set$' * 'Nat_int_set_bool_fun_fun$') > 'Int_set_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_6, type, 'member$a': 'Int_set$' > 'Int_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_7, type, def_5: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_8, type, 'uvj$': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_9, type, 'uup$': 'Nat_set_set$' > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_10, type, 'uvr$': 'Nat_set$' > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_11, type, 'uuo$': 'Int_set_set$' > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_12, type, 'is_empty$': 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_13, type, 'collect$a': 'Int_set_bool_fun$' > 'Int_set_set$').
% 1.34/0.68 tff(func_def_14, type, 'uux$': ('Nat_set$' * 'Nat_nat_set_bool_fun_fun$' * 'Nat_set$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_15, type, 'uva$': ('Int_set_set$' * 'Int_set_nat_bool_fun_fun$') > 'Nat_int_set_bool_fun_fun$').
% 1.34/0.68 tff(func_def_16, type, 'ordering_top$a': ('Nat_nat_bool_fun_fun$' * 'Nat_nat_bool_fun_fun$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_17, type, 'uvo$': $int > 'Int_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_18, type, 'bot$e': 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_19, type, 'zero$': 'Nat$').
% 1.34/0.68 tff(func_def_20, type, 'tick_count_strict$': ('A_run$' * 'Clock$') > 'Nat_nat_fun$').
% 1.34/0.68 tff(func_def_21, type, 'uvd$': ('Nat_set_set$' * 'Nat_set_bool_fun$') > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_22, type, 'less$d': 'Int_set$' > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_23, type, 'uvi$': 'Nat_set_nat_set_bool_fun_fun$').
% 1.34/0.68 tff(func_def_24, type, 'uvm$': $int > 'Int_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_25, type, 'less_eq$a': 'Int_set_set$' > 'Int_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_26, type, 'uvl$': 'Int_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_27, type, 'bot$j': 'Nat$').
% 1.34/0.68 tff(func_def_28, type, 'member$': 'Nat_set$' > 'Nat_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_29, type, 'finite$c': 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_30, type, 'fun_app$m': ('Int_int_set_bool_fun_fun$' * $int) > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_31, type, 'g$': 'Nat_nat_fun$').
% 1.34/0.68 tff(func_def_32, type, 'bot$h': 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_33, type, 'n$': 'Nat$').
% 1.34/0.68 tff(func_def_34, type, 'uvp$': 'Nat_bool_fun$' > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_35, type, 'less$a': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_36, type, 'uvh$': 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_37, type, 'uuq$': 'Nat_set$' > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_38, type, 'fun_app$a': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_39, type, 'uus$': ('Nat_set$' * 'Nat_nat_bool_fun_fun$') > 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_40, type, def_7: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_41, type, 'fun_app$o': ('Int_set_nat_bool_fun_fun$' * 'Int_set$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_42, type, 'arg_min_on$a': ('Nat_int_fun$' * 'Nat_set$') > 'Nat$').
% 1.34/0.68 tff(func_def_43, type, 'less$b': 'Int_set_set$' > 'Int_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_44, type, 'collect$d': 'Int_set_set_bool_fun$' > 'Int_set_set_set$').
% 1.34/0.68 tff(func_def_45, type, 'of_nat$': 'Nat_int_fun$').
% 1.34/0.68 tff(func_def_46, type, 'bot$': 'Nat_set$').
% 1.34/0.68 tff(func_def_47, type, 'uuc$': ('Int_set_bool_fun$' * 'Int_set_bool_fun$') > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_48, type, 'of_int$': 'Int_int_fun$').
% 1.34/0.68 tff(func_def_49, type, 'uuk$': 'Int_set_set$' > 'Int_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_50, type, 'bot$b': 'Nat_set_set$').
% 1.34/0.68 tff(func_def_51, type, 'bot$a': 'Int_set_set$').
% 1.34/0.68 tff(func_def_52, type, 'uue$': ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_53, type, def_1: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_54, type, 'ordering_top$': ('Nat_set_nat_set_bool_fun_fun$' * 'Nat_set_nat_set_bool_fun_fun$') > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_55, type, 'uum$': 'Nat_set_nat_set_bool_fun_fun$').
% 1.34/0.68 tff(func_def_56, type, 'uminus$': 'Nat_set$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_57, type, 'fun_app$n': ('Nat_int_set_bool_fun_fun$' * 'Nat$') > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_58, type, 'uua$': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_59, type, 'finite$': 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_60, type, 'fun_app$s': ('Int_int_fun$' * $int) > $int).
% 1.34/0.68 tff(func_def_61, type, tltrue: tlbool).
% 1.34/0.68 tff(func_def_62, type, def_8: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_63, type, def_6: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_64, type, 'r$': 'A_run$').
% 1.34/0.68 tff(func_def_65, type, 'uminus$b': 'Int_set$' > 'Int_set$').
% 1.34/0.68 tff(func_def_66, type, 'fun_app$g': ('Nat_set_nat_set_bool_fun_fun$' * 'Nat_set$') > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_67, type, 'uuh$': ('Nat_set_bool_fun$' * 'Nat_set_bool_fun$') > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_68, type, 'uub$': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_69, type, 'collect$e': 'Nat_set_set_bool_fun$' > 'Nat_set_set_set$').
% 1.34/0.68 tff(func_def_70, type, 'uvb$': ('Int_set_set$' * 'Int_set_int_bool_fun_fun$') > 'Int_int_set_bool_fun_fun$').
% 1.34/0.68 tff(func_def_71, type, 'uvg$': 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_72, type, 'less$c': 'Nat_set_set$' > 'Nat_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_73, type, 'f$': 'Nat_nat_fun$').
% 1.34/0.68 tff(func_def_74, type, 'arg_min_on$': ('Int_int_fun$' * 'Int_set$') > $int).
% 1.34/0.68 tff(func_def_75, type, 'less_eq$d': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_76, type, 'collect$': 'Nat_bool_fun$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_77, type, 'sub$': 'A_run$').
% 1.34/0.68 tff(func_def_78, type, 'less_eq$c': 'Int_set$' > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_79, type, 'fun_app$l': ('Int_set_int_bool_fun_fun$' * 'Int_set$') > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_80, type, 'member$c': 'Int_int_set_bool_fun_fun$').
% 1.34/0.68 tff(func_def_81, type, 'uut$': ('Nat_set$' * 'Nat_int_bool_fun_fun$') > 'Int_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_82, type, 'fun_app$k': ('Nat_nat_set_bool_fun_fun$' * 'Nat$') > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_83, type, 'uuy$': ('Int_set$' * 'Int_int_set_bool_fun_fun$') > 'Int_set_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_84, type, 'less_eq$b': 'Nat_set$' > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_85, type, 'bot$g': 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_86, type, 'fun_app$c': ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_87, type, 'bot$d': 'Nat_bool_fun_set$').
% 1.34/0.68 tff(func_def_88, type, 'uvf$': ('Int_set$' * 'Int_bool_fun$') > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_89, type, 'less_eq$': 'Nat_set_set$' > 'Nat_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_90, type, 'bot$c': 'Int_set$').
% 1.34/0.68 tff(func_def_91, type, 'uuf$': ('Int_bool_fun$' * 'Int_bool_fun$') > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_92, type, def_4: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_93, type, 'fun_app$j': ('Int_int_bool_fun_fun$' * $int) > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_94, type, 'uminus$a': 'Nat_bool_fun$' > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_95, type, 'uug$': ('Int_set_bool_fun$' * 'Int_set_bool_fun$') > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_96, type, 'uuz$': ('Int_set$' * 'Int_nat_set_bool_fun_fun$' * 'Nat_set$') > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_97, type, 'dil_inverse$': 'Nat_nat_fun$' > 'Nat_nat_fun$').
% 1.34/0.68 tff(func_def_98, type, tlfalse: tlbool).
% 1.34/0.68 tff(func_def_99, type, 'nat$': $int > 'Nat$').
% 1.34/0.68 tff(func_def_100, type, 'fun_app$p': ('Int_nat_bool_fun_fun$' * $int) > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_101, type, 'uvn$': $int > 'Int_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_102, type, 'uvq$': 'Int_bool_fun$' > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_103, type, 'finite$a': 'Int_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_104, type, 'uun$': 'Int_set$' > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_105, type, 'uvk$': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_106, type, def_2: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_107, type, 'fun_app$q': ('Nat_int_bool_fun_fun$' * 'Nat$') > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_108, type, 'member$b': 'Nat_nat_set_bool_fun_fun$').
% 1.34/0.68 tff(func_def_109, type, 'uud$': ('Nat_set_bool_fun$' * 'Nat_set_bool_fun$') > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_110, type, 'uve$': ('Nat_set$' * 'Nat_bool_fun$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_111, type, 'collect$b': 'Nat_set_bool_fun$' > 'Nat_set_set$').
% 1.34/0.68 tff(func_def_112, type, 'fun_app$r': ('Int_nat_set_bool_fun_fun$' * $int) > 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_113, type, 'uuj$': ('Int_bool_fun$' * 'Int_bool_fun$') > 'Int_bool_fun$').
% 1.34/0.68 tff(func_def_114, type, 'uvc$': ('Int_set_set$' * 'Int_set_bool_fun$') > 'Int_set_bool_fun$').
% 1.34/0.68 tff(func_def_115, type, 'fun_app$b': ('Nat_int_fun$' * 'Nat$') > $int).
% 1.34/0.68 tff(func_def_116, type, 'uuu$': ('Int_set$' * 'Int_nat_bool_fun_fun$') > 'Nat_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_117, type, 'dbl_dec$': 'Int_int_fun$').
% 1.34/0.68 tff(func_def_118, type, 'uu$': 'Nat_nat_bool_fun_fun$').
% 1.34/0.68 tff(func_def_119, type, 'uur$': 'Int_set_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_120, type, def_3: ('Nat_bool_fun$' * 'Nat$') > tlbool).
% 1.34/0.68 tff(func_def_121, type, 'uul$': 'Nat_set_set$' > 'Nat_set_set_bool_fun$').
% 1.34/0.68 tff(func_def_122, type, 'uuv$': ('Int_set$' * 'Int_int_bool_fun_fun$') > 'Int_int_bool_fun_fun$').
% 1.34/0.68 tff(func_def_123, type, 'bot$i': 'Nat_set_bool_fun$').
% 1.34/0.68 tff(func_def_124, type, 'uui$': ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat_bool_fun$').
% 1.34/0.68 tff(func_def_129, type, sK0: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_130, type, sK1: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_131, type, sK2: ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_132, type, sK3: ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_133, type, sK4: 'Int_set_set_bool_fun$' > 'Int_set_set$').
% 1.34/0.68 tff(func_def_134, type, sK5: 'Nat_set_set_bool_fun$' > 'Nat_set_set$').
% 1.34/0.68 tff(func_def_135, type, sK6: 'Nat_set_bool_fun$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_136, type, sK7: 'Int_set_bool_fun$' > 'Int_set$').
% 1.34/0.68 tff(func_def_137, type, sK8: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_138, type, sK9: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_139, type, sK10: ('Int_set_bool_fun$' * 'Int_set_bool_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_140, type, sK11: ('Nat_set_bool_fun$' * 'Nat_set_bool_fun$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_141, type, sK12: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_142, type, sK13: ('Int_bool_fun$' * 'Int_bool_fun$') > $int).
% 1.34/0.68 tff(func_def_143, type, sK14: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_144, type, sK15: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_145, type, sK16: ('Nat_set$' * 'Nat_set$' * 'Nat_nat_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_146, type, sK17: ('Nat_set$' * 'Nat_set$' * 'Nat_nat_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_147, type, sK18: ('Nat_set$' * 'Int_set$' * 'Nat_int_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_148, type, sK19: ('Nat_set$' * 'Int_set$' * 'Nat_int_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_149, type, sK20: ('Int_set$' * 'Nat_set$' * 'Int_nat_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_150, type, sK21: ('Int_set$' * 'Nat_set$' * 'Int_nat_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_151, type, sK22: ('Int_set$' * 'Int_set$' * 'Int_int_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_152, type, sK23: ('Int_set$' * 'Int_set$' * 'Int_int_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_153, type, sK24: ('Nat_set$' * 'Int_set_set$' * 'Nat_int_set_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_154, type, sK25: ('Nat_set$' * 'Int_set_set$' * 'Nat_int_set_bool_fun_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_155, type, sK26: ('Nat_set$' * 'Nat_set_set$' * 'Nat_nat_set_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_156, type, sK27: ('Nat_set$' * 'Nat_set_set$' * 'Nat_nat_set_bool_fun_fun$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_157, type, sK28: ('Int_set$' * 'Int_set_set$' * 'Int_int_set_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_158, type, sK29: ('Int_set$' * 'Int_set_set$' * 'Int_int_set_bool_fun_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_159, type, sK30: ('Int_set$' * 'Nat_set_set$' * 'Int_nat_set_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_160, type, sK31: ('Int_set$' * 'Nat_set_set$' * 'Int_nat_set_bool_fun_fun$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_161, type, sK32: ('Int_set_set$' * 'Nat_set$' * 'Int_set_nat_bool_fun_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_162, type, sK33: ('Int_set_set$' * 'Nat_set$' * 'Int_set_nat_bool_fun_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_163, type, sK34: ('Int_set_set$' * 'Int_set$' * 'Int_set_int_bool_fun_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_164, type, sK35: ('Int_set_set$' * 'Int_set$' * 'Int_set_int_bool_fun_fun$') > $int).
% 1.34/0.68 tff(func_def_165, type, sK36: 'Int_set_bool_fun$' > 'Int_set$').
% 1.34/0.68 tff(func_def_166, type, sK37: 'Nat_set_bool_fun$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_167, type, sK38: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_168, type, sK39: 'Int_bool_fun$' > $int).
% 1.34/0.68 tff(func_def_169, type, sK40: ('Int_set_set$' * 'Int_set$') > 'Int_set$').
% 1.34/0.68 tff(func_def_170, type, sK41: ('Nat_set_set$' * 'Nat_set$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_171, type, sK42: ('Nat_set$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_172, type, sK43: ('Int_set$' * $int) > $int).
% 1.34/0.68 tff(func_def_173, type, sK44: ('Int_set_set$' * 'Int_set$') > 'Int_set$').
% 1.34/0.68 tff(func_def_174, type, sK45: ('Nat_set_set$' * 'Nat_set$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_175, type, sK46: ('Nat_set$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_176, type, sK47: ('Int_set$' * $int) > $int).
% 1.34/0.68 tff(func_def_177, type, sK48: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_178, type, sK49: 'Nat_nat_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_179, type, sK50: 'Nat_nat_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_180, type, sK51: 'Int_set_set$' > 'Int_set$').
% 1.34/0.68 tff(func_def_181, type, sK52: 'Nat_set_set$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_182, type, sK53: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_183, type, sK54: 'Int_set$' > $int).
% 1.34/0.68 tff(func_def_184, type, sK55: 'Int_set_set$' > 'Int_set$').
% 1.34/0.68 tff(func_def_185, type, sK56: 'Nat_set_set$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_186, type, sK57: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_187, type, sK58: 'Int_set$' > $int).
% 1.34/0.68 tff(func_def_188, type, sK59: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_189, type, sK60: 'Int_set_set$' > 'Int_set$').
% 1.34/0.68 tff(func_def_190, type, sK61: 'Nat_set_set$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_191, type, sK62: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_192, type, sK63: 'Int_set$' > $int).
% 1.34/0.68 tff(func_def_193, type, sK64: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_194, type, sK65: 'Int_set$' > $int).
% 1.34/0.68 tff(func_def_195, type, sK66: 'Int_set_bool_fun$' > 'Int_set$').
% 1.34/0.68 tff(func_def_196, type, sK67: 'Nat_set_bool_fun$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_197, type, sK68: 'Int_bool_fun$' > $int).
% 1.34/0.68 tff(func_def_198, type, sK69: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_199, type, sK70: 'Int_set_bool_fun$' > 'Int_set$').
% 1.34/0.68 tff(func_def_200, type, sK71: 'Nat_set_bool_fun$' > 'Nat_set$').
% 1.34/0.68 tff(func_def_201, type, sK72: 'Int_bool_fun$' > $int).
% 1.34/0.68 tff(func_def_202, type, sK73: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_203, type, sK74: 'Int_set$' > $int).
% 1.34/0.68 tff(func_def_204, type, sK75: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_205, type, sK76: ('Int_set$' * 'Int_set$') > $int).
% 1.34/0.68 tff(func_def_206, type, sK77: ('Nat_set$' * 'Nat_set$') > 'Nat$').
% 1.34/0.68 tff(func_def_207, type, sK78: ('Int_set$' * 'Int_set$') > $int).
% 1.34/0.68 tff(func_def_208, type, sK79: ('Nat_set$' * 'Nat_set$') > 'Nat$').
% 1.34/0.68 tff(func_def_209, type, sK80: ('Int_set$' * 'Int_set$') > $int).
% 1.34/0.68 tff(func_def_210, type, sK81: ('Nat_set$' * 'Nat_set$') > 'Nat$').
% 1.34/0.68 tff(func_def_211, type, sK82: ('Int_set_bool_fun$' * 'Int_set_bool_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_212, type, sK83: ('Nat_set_bool_fun$' * 'Nat_set_bool_fun$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_213, type, sK84: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_214, type, sK85: ('Int_bool_fun$' * 'Int_bool_fun$') > $int).
% 1.34/0.68 tff(func_def_215, type, sK86: ('Int_set_bool_fun$' * 'Int_set_bool_fun$') > 'Int_set$').
% 1.34/0.68 tff(func_def_216, type, sK87: ('Nat_set_bool_fun$' * 'Nat_set_bool_fun$') > 'Nat_set$').
% 1.34/0.68 tff(func_def_217, type, sK88: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_218, type, sK89: ('Int_bool_fun$' * 'Int_bool_fun$') > $int).
% 1.34/0.68 tff(func_def_219, type, sK100: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_220, type, sK101: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_221, type, sK102: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_222, type, sK103: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_223, type, sK104: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_224, type, sK105: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_225, type, sK106: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_226, type, sK107: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_227, type, sK108: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_228, type, sK109: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_229, type, sK110: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_230, type, sK111: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_231, type, sK112: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_232, type, sK113: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_233, type, sK114: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_234, type, sK115: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_235, type, sK116: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_236, type, sK117: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_237, type, sK118: $int > $int).
% 1.34/0.68 tff(func_def_238, type, sK119: $int > $int).
% 1.34/0.68 tff(func_def_239, type, sK120: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_240, type, sK121: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_241, type, sK122: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_242, type, sK123: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_243, type, sK124: 'Int_int_bool_fun_fun$' > $int).
% 1.34/0.68 tff(func_def_244, type, sK125: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_245, type, sK126: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_246, type, sK127: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_247, type, sK128: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_248, type, sK129: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_249, type, sK130: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_250, type, sK131: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_251, type, sK132: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_252, type, sK133: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_253, type, sK134: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_254, type, sK135: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_255, type, sK136: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_256, type, sK137: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_257, type, sK138: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_258, type, sK139: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_259, type, sK140: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_260, type, sK141: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_261, type, sK142: 'Int_int_fun$' > $int).
% 1.34/0.68 tff(func_def_262, type, sK143: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_263, type, sK144: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_264, type, sK145: 'Nat_set$' > 'Nat$').
% 1.34/0.68 tff(func_def_265, type, sK146: ('Nat_set$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_266, type, sK147: ('Int_set$' * 'Int_bool_fun$') > $int).
% 1.34/0.68 tff(func_def_267, type, sK148: ('Nat_set$' * 'Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_268, type, sK149: ('Int_set$' * 'Int_bool_fun$' * 'Int_bool_fun$') > $int).
% 1.34/0.68 tff(func_def_269, type, sK150: $int > 'Nat$').
% 1.34/0.68 tff(func_def_270, type, sK151: $int > 'Nat$').
% 1.34/0.68 tff(func_def_271, type, sK152: $int > 'Nat$').
% 1.34/0.68 tff(func_def_272, type, sK153: $int > 'Nat$').
% 1.34/0.68 tff(func_def_273, type, sK154: $int > 'Nat$').
% 1.34/0.68 tff(func_def_274, type, sK155: ('Nat_bool_fun$' * $int) > 'Nat$').
% 1.34/0.68 tff(func_def_275, type, sK156: $int > 'Nat$').
% 1.34/0.68 tff(func_def_276, type, sK157: $int > 'Nat$').
% 1.34/0.68 tff(func_def_277, type, sK159: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_278, type, sK160: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_279, type, sK161: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_280, type, sK162: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_281, type, sK163: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_282, type, sK164: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_283, type, sK165: ('Nat$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_284, type, sK166: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_285, type, sK167: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_286, type, sK168: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_287, type, sK169: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(func_def_288, type, sK170: ('Nat$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_289, type, sK171: ('Nat$' * 'Nat$') > 'Nat$').
% 1.34/0.68 tff(func_def_290, type, sK172: 'Nat$' > 'Nat$').
% 1.34/0.68 tff(func_def_291, type, sK173: 'Nat_bool_fun$' > 'Nat$').
% 1.34/0.68 tff(func_def_292, type, sK174: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 1.34/0.68 tff(pred_def_1, type, 'fun_app$d': ('Nat_set_set_bool_fun$' * 'Nat_set_set$') > $o).
% 1.34/0.69 tff(pred_def_2, type, 'less$e': ('Nat_bool_fun$' * 'Nat_bool_fun$') > $o).
% 1.34/0.69 tff(pred_def_3, type, 'less$f': ('Int_bool_fun$' * 'Int_bool_fun$') > $o).
% 1.34/0.69 tff(pred_def_5, type, 'contracting$': ('Nat_nat_fun$' * 'A_run$' * 'A_run$' * 'Nat_nat_fun$') > $o).
% 1.34/0.69 tff(pred_def_6, type, 'fun_app$': ('Nat_bool_fun$' * 'Nat$') > $o).
% 1.34/0.69 tff(pred_def_7, type, 'fun_app$h': ('Int_set_bool_fun$' * 'Int_set$') > $o).
% 1.34/0.69 tff(pred_def_8, type, 'member$d': ('Nat_bool_fun$' * 'Nat_bool_fun_set$') > $o).
% 1.34/0.69 tff(pred_def_9, type, 'finite$f': 'Nat_bool_fun_set$' > $o).
% 1.34/0.69 tff(pred_def_10, type, 'fun_app$e': ('Int_set_set_bool_fun$' * 'Int_set_set$') > $o).
% 1.34/0.69 tff(pred_def_11, type, 'dense_run$': 'A_run$' > $o).
% 1.34/0.69 tff(pred_def_12, type, 'fun_app$f': ('Nat_set_bool_fun$' * 'Nat_set$') > $o).
% 1.34/0.69 tff(pred_def_13, type, 'dilating$': ('Nat_nat_fun$' * 'A_run$' * 'A_run$') > $o).
% 1.34/0.69 tff(pred_def_14, type, 'less_eq$g': (tlbool * tlbool) > $o).
% 1.34/0.69 tff(pred_def_15, type, 'finite$d': 'Int_set_set_set$' > $o).
% 1.34/0.69 tff(pred_def_16, type, 'less_eq$f': ('Int_bool_fun$' * 'Int_bool_fun$') > $o).
% 1.34/0.69 tff(pred_def_17, type, 'finite$e': 'Nat_set_set_set$' > $o).
% 1.34/0.69 tff(pred_def_18, type, 'less_eq$e': ('Nat_bool_fun$' * 'Nat_bool_fun$') > $o).
% 1.34/0.69 tff(pred_def_19, type, 'fun_app$i': ('Int_bool_fun$' * $int) > $o).
% 1.34/0.69 tff(pred_def_22, type, sP90: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 1.34/0.69 tff(pred_def_23, type, sP91: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 1.34/0.69 tff(pred_def_24, type, sP92: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 1.34/0.69 tff(pred_def_25, type, sP93: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 1.34/0.69 tff(pred_def_27, type, sP95: ($int * $int * $int) > $o).
% 1.34/0.69 tff(pred_def_28, type, sP96: ($int * $int * $int) > $o).
% 1.34/0.69 tff(pred_def_29, type, sP97: ($int * $int * $int) > $o).
% 1.34/0.69 tff(pred_def_30, type, sP98: ($int * $int * $int) > $o).
% 1.34/0.69 tff(f47,conjecture,(
% 1.34/0.69 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$'))),
% 1.34/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture46)).
% 1.34/0.69 tff(f48,negated_conjecture,(
% 1.34/0.69 ~ 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$'))),
% 1.34/0.69 inference(negated_conjecture,[status(cth)],[f47])).
% 1.34/0.69 tff(f50,axiom,(
% 1.34/0.69 ! [X0 : 'Nat$'] : ~$less('fun_app$b'('of_nat$','fun_app$c'('g$',X0)),'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0)))),
% 1.34/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48)).
% 1.34/0.69 tff(f51,axiom,(
% 1.34/0.69 ! [X0 : 'Nat$'] : ~$less('fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0)),'fun_app$b'('of_nat$','fun_app$c'('g$',X0)))),
% 1.34/0.69 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49)).
% 1.34/0.69 tff(f817,definition,(
% 1.34/0.69 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 1.34/0.69 introduced(theory,[tha_order_totality])).
% 1.34/0.69 tff(f822,plain,(
% 1.34/0.69 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) != 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$'))),
% 1.34/0.69 inference(flattening,[],[f48])).
% 1.34/0.69 tff(f1463,plain,(
% 1.34/0.69 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) != 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$'))),
% 1.34/0.69 inference(cnf_transformation,[],[f822])).
% 1.34/0.69 tff(f1464,plain,(
% 1.34/0.69 ( ! [X0 : 'Nat$'] : (~$less('fun_app$b'('of_nat$','fun_app$c'('g$',X0)),'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0)))) )),
% 1.34/0.69 inference(cnf_transformation,[],[f50])).
% 1.34/0.69 tff(f1465,plain,(
% 1.34/0.69 ( ! [X0 : 'Nat$'] : (~$less('fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0)),'fun_app$b'('of_nat$','fun_app$c'('g$',X0)))) )),
% 1.34/0.69 inference(cnf_transformation,[],[f51])).
% 1.34/0.69 tff(f2751,plain,(
% 1.34/0.69 ( ! [X0 : 'Nat$'] : ($less('fun_app$b'('of_nat$','fun_app$c'('g$',X0)),'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0))) | 'fun_app$b'('of_nat$','fun_app$c'('g$',X0)) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0))) )),
% 1.34/0.69 inference(resolution,[],[f1465,f817])).
% 1.34/0.69 tff(f2752,plain,(
% 1.34/0.69 ( ! [X0 : 'Nat$'] : ('fun_app$b'('of_nat$','fun_app$c'('g$',X0)) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0))) )),
% 1.34/0.69 inference(forward_subsumption_resolution,[],[f2751,f1464])).
% 1.34/0.69 tff(f2754,plain,(
% 1.34/0.69 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) != 'fun_app$b'('of_nat$','fun_app$c'('g$','n$'))),
% 1.34/0.69 inference(superposition,[],[f1463,f2752])).
% 1.34/0.69 tff(f2757,plain,(
% 1.34/0.69 $false),
% 1.34/0.69 inference(trivial_inequality_removal,[],[f2754])).
% 1.34/0.69 % SZS output end Proof for theBenchmark
% 1.34/0.69 % (3511510)------------------------------
% 1.34/0.69 % (3511510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.34/0.69 % (3511510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.34/0.69 % (3511510)CaDiCaL version: 2.1.3
% 1.34/0.69 % (3511510)Termination reason: Refutation
% 1.34/0.69 % (3511510)Time elapsed: 0.084 s
% 1.34/0.69 % (3511510)Peak memory usage: 14 MB
% 1.34/0.69 % (3511510)Instructions burned: 76 (million)
% 1.34/0.69 % (3511483)Success in time 0.266 s
% 1.34/0.69 % Vampire exiting
%------------------------------------------------------------------------------