%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP328_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 : Tue Sep 29 11:39:22 AM UTC 2026
% Result : Theorem 0.64s 0.52s
% Output : Refutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP328_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 12:54:05 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.33 Running first-order model finding
% 0.03/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.64/0.52 % (2363475)Will run a generic schedule for satisfiability detection.
% 0.64/0.52 % (2363489)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1739745782_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.52 % (2363490)% WARNING: option uhcvi not known.
% 0.64/0.52 % (2363490)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4033674899:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.52 % (2363492)dis+10_1_sil=32000:sp=arity:random_seed=1338696701:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.52 % (2363491)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2980456574:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.52 % (2363493)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=327973925:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.52 % (2363494)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2749888048:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.52 % (2363495)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=599181462:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.52 % (2363489)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.64/0.52 % (2363489)Terminated due to inappropriate strategy.
% 0.64/0.52 % (2363489)------------------------------
% 0.64/0.52 % (2363489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363489)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363489)Termination reason: Inappropriate
% 0.64/0.52 % (2363489)Time elapsed: 0.028 s
% 0.64/0.52 % (2363489)Peak memory usage: 13 MB
% 0.64/0.52 % (2363489)Instructions burned: 114 (million)
% 0.64/0.52 % (2363489)------------------------------
% 0.64/0.52 % (2363489)------------------------------
% 0.64/0.52 % (2363507)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4040128603:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.64/0.52 % (2363492)Instruction limit reached!
% 0.64/0.52 % (2363492)------------------------------
% 0.64/0.52 % (2363492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363492)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363492)Termination reason: Instruction limit
% 0.64/0.52 % (2363492)Termination phase: Property scanning
% 0.64/0.52 % (2363492)Time elapsed: 0.046 s
% 0.64/0.52 % (2363492)Peak memory usage: 12 MB
% 0.64/0.52 % (2363492)Instructions burned: 104 (million)
% 0.64/0.52 % (2363493)Instruction limit reached!
% 0.64/0.52 % (2363493)------------------------------
% 0.64/0.52 % (2363493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363493)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363493)Termination reason: Instruction limit
% 0.64/0.52 % (2363493)Termination phase: Property scanning
% 0.64/0.52 % (2363493)Time elapsed: 0.053 s
% 0.64/0.52 % (2363493)Peak memory usage: 12 MB
% 0.64/0.52 % (2363493)Instructions burned: 117 (million)
% 0.64/0.52 % (2363507)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.64/0.52 % (2363507)Terminated due to inappropriate strategy.
% 0.64/0.52 % (2363507)------------------------------
% 0.64/0.52 % (2363507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363507)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363507)Termination reason: Inappropriate
% 0.64/0.52 % (2363507)Time elapsed: 0.026 s
% 0.64/0.52 % (2363507)Peak memory usage: 13 MB
% 0.64/0.52 % (2363507)Instructions burned: 100 (million)
% 0.64/0.52 % (2363494)Instruction limit reached!
% 0.64/0.52 % (2363494)------------------------------
% 0.64/0.52 % (2363494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363494)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363494)Termination reason: Instruction limit
% 0.64/0.52 % (2363494)Termination phase: Saturation
% 0.64/0.52 % (2363494)Time elapsed: 0.061 s
% 0.64/0.52 % (2363494)Peak memory usage: 14 MB
% 0.64/0.52 % (2363494)Instructions burned: 131 (million)
% 0.64/0.52 % (2363507)------------------------------
% 0.64/0.52 % (2363507)------------------------------
% 0.64/0.52 % (2363511)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=639726074:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.64/0.52 % (2363512)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=517462219:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.64/0.52 % (2363495)Instruction limit reached!
% 0.64/0.52 % (2363495)------------------------------
% 0.64/0.52 % (2363495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363495)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363495)Termination reason: Instruction limit
% 0.64/0.52 % (2363495)Termination phase: Saturation
% 0.64/0.52 % (2363495)Time elapsed: 0.077 s
% 0.64/0.52 % (2363495)Peak memory usage: 14 MB
% 0.64/0.52 % (2363495)Instructions burned: 159 (million)
% 0.64/0.52 % (2363515)ott-21_1_sil=16000:fs=off:random_seed=1374317142:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.64/0.52 % (2363516)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2512828652:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.64/0.52 % (2363520)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=618167558:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.64/0.52 % (2363491) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2363475-2363491"...
% 0.64/0.52 % (2363491)...printing done.
% 0.64/0.52 % (2363491)Refutation found. Thanks to Tanya!
% 0.64/0.52 % SZS status Theorem for theBenchmark
% 0.64/0.52 % SZS output start Proof for theBenchmark
% 0.64/0.52 tff(type_def_5, type, 'Int_bool_fun$': $tType).
% 0.64/0.52 tff(type_def_6, type, 'Nat_nat_bool_fun_fun$': $tType).
% 0.64/0.52 tff(type_def_7, type, 'Int_set_set_set$': $tType).
% 0.64/0.52 tff(type_def_8, type, 'Int_set$': $tType).
% 0.64/0.52 tff(type_def_9, type, 'Int_int_fun$': $tType).
% 0.64/0.52 tff(type_def_10, type, 'Int_set_set$': $tType).
% 0.64/0.52 tff(type_def_11, type, 'N_set$': $tType).
% 0.64/0.52 tff(type_def_12, type, 'Nat_n_fun$': $tType).
% 0.64/0.52 tff(type_def_13, type, 'Int_set_int_fun$': $tType).
% 0.64/0.52 tff(type_def_14, type, 'N_int_set_fun$': $tType).
% 0.64/0.52 tff(type_def_15, type, 'Nat_nat_fun$': $tType).
% 0.64/0.52 tff(type_def_16, type, 'Nat$': $tType).
% 0.64/0.52 tff(type_def_17, type, 'N_int_fun$': $tType).
% 0.64/0.52 tff(type_def_18, type, 'N$': $tType).
% 0.64/0.52 tff(type_def_19, type, tlbool: $tType).
% 0.64/0.52 tff(type_def_20, type, 'Int_set_int_set_fun$': $tType).
% 0.64/0.52 tff(type_def_21, type, 'Int_n_fun$': $tType).
% 0.64/0.52 tff(type_def_22, type, 'Int_int_set_fun$': $tType).
% 0.64/0.52 tff(type_def_23, type, 'Int_set_n_fun$': $tType).
% 0.64/0.52 tff(type_def_24, type, 'N_n_fun$': $tType).
% 0.64/0.52 tff(type_def_25, type, 'Int_set_bool_fun$': $tType).
% 0.64/0.52 tff(type_def_26, type, 'Int_int_bool_fun_fun$': $tType).
% 0.64/0.52 tff(type_def_27, type, 'Nat_bool_fun$': $tType).
% 0.64/0.52 tff(type_def_28, type, 'N_set_set$': $tType).
% 0.64/0.52 tff(type_def_29, type, 'N_n_bool_fun_fun$': $tType).
% 0.64/0.52 tff(type_def_30, type, 'Nat_int_fun$': $tType).
% 0.64/0.52 tff(type_def_31, type, 'N_bool_fun$': $tType).
% 0.64/0.52 tff(func_def_0, type, 'fun_app$p': ('Int_n_fun$' * $int) > 'N$').
% 0.64/0.52 tff(func_def_1, type, 'plus$e': ('Int_set_set_set$' * 'Int_set_set_set$') > 'Int_set_set_set$').
% 0.64/0.52 tff(func_def_2, type, 'fun_app$r': ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_3, type, 'fun_app$l': ('Int_int_set_fun$' * $int) > 'Int_set$').
% 0.64/0.52 tff(func_def_4, type, 'less$': 'N_n_bool_fun_fun$').
% 0.64/0.52 tff(func_def_5, type, 'uua$': 'Int_set_set$' > 'Int_set_bool_fun$').
% 0.64/0.52 tff(func_def_6, type, 'fun_app$g': ('N_n_bool_fun_fun$' * 'N$') > 'N_bool_fun$').
% 0.64/0.52 tff(func_def_7, type, 'triangle$': 'Nat_nat_fun$').
% 0.64/0.52 tff(func_def_8, type, 'from_nat$': 'Nat_n_fun$').
% 0.64/0.52 tff(func_def_9, type, 'collect$a': 'Int_set_bool_fun$' > 'Int_set_set$').
% 0.64/0.52 tff(func_def_10, type, 'fun_app$o': ('N_int_fun$' * 'N$') > $int).
% 0.64/0.52 tff(func_def_11, type, 'fun_app$m': ('Int_set_n_fun$' * 'Int_set$') > 'N$').
% 0.64/0.52 tff(func_def_12, type, 'uuc$': 'Int_int_bool_fun_fun$').
% 0.64/0.52 tff(func_def_13, type, 'plus$c': ('N_set$' * 'N_set$') > 'N_set$').
% 0.64/0.52 tff(func_def_14, type, 'fun_app$e': ('Nat_int_fun$' * 'Nat$') > $int).
% 0.64/0.52 tff(func_def_15, type, 'fun_app$b': ('Int_int_fun$' * $int) > $int).
% 0.64/0.52 tff(func_def_16, type, 'ja$': 'Nat$').
% 0.64/0.52 tff(func_def_17, type, 'uud$': $int > 'Int_int_fun$').
% 0.64/0.52 tff(func_def_18, type, 'a$': 'Nat$').
% 0.64/0.52 tff(func_def_19, type, 'i$': 'N$').
% 0.64/0.52 tff(func_def_20, type, 'zero$': 'Int_set$').
% 0.64/0.52 tff(func_def_21, type, 'of_nat$': 'Nat_int_fun$').
% 0.64/0.52 tff(func_def_22, type, 'fun_app$a': ('Int_int_bool_fun_fun$' * $int) > 'Int_bool_fun$').
% 0.64/0.52 tff(func_def_23, type, 'plus$a': ('Int_set_set$' * 'Int_set_set$') > 'Int_set_set$').
% 0.64/0.52 tff(func_def_24, type, 'member$a': $int > 'Int_set_bool_fun$').
% 0.64/0.52 tff(func_def_25, type, tltrue: tlbool).
% 0.64/0.52 tff(func_def_26, type, 'plus$': 'N$' > 'N_n_fun$').
% 0.64/0.52 tff(func_def_27, type, 'less_eq$': 'N_n_bool_fun_fun$').
% 0.64/0.52 tff(func_def_28, type, 'minus$': 'N$' > 'N_n_fun$').
% 0.64/0.52 tff(func_def_29, type, 'fun_app$f': ('N_n_fun$' * 'N$') > 'N$').
% 0.64/0.52 tff(func_def_30, type, 'fun_app$n': ('Int_set_int_fun$' * 'Int_set$') > $int).
% 0.64/0.52 tff(func_def_31, type, 'fun_app$i': ('Nat_n_fun$' * 'Nat$') > 'N$').
% 0.64/0.52 tff(func_def_32, type, 'iterate_add$': 'Nat$' > 'Int_int_fun$').
% 0.64/0.52 tff(func_def_33, type, 'collect$b': 'Int_bool_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_34, type, 'plus$d': ('N_set_set$' * 'N_set_set$') > 'N_set_set$').
% 0.64/0.52 tff(func_def_35, type, 'uu$': 'N_set$' > 'N_bool_fun$').
% 0.64/0.52 tff(func_def_36, type, 'collect$': 'N_bool_fun$' > 'N_set$').
% 0.64/0.52 tff(func_def_37, type, tlfalse: tlbool).
% 0.64/0.52 tff(func_def_38, type, 'nat$': $int > 'Nat$').
% 0.64/0.52 tff(func_def_39, type, 'zero$a': 'N$').
% 0.64/0.52 tff(func_def_40, type, 'plus$b': 'Int_set$' > 'Int_set_int_set_fun$').
% 0.64/0.52 tff(func_def_41, type, 'minus$a': 'Int_set$' > 'Int_set_int_set_fun$').
% 0.64/0.52 tff(func_def_42, type, 'fun_app$h': ('Int_set_int_set_fun$' * 'Int_set$') > 'Int_set$').
% 0.64/0.52 tff(func_def_43, type, 'less$a': 'Int_set$' > 'Int_set_bool_fun$').
% 0.64/0.52 tff(func_def_44, type, 'less_eq$a': 'Int_set$' > 'Int_set_bool_fun$').
% 0.64/0.52 tff(func_def_45, type, 'fun_app$k': ('N_int_set_fun$' * 'N$') > 'Int_set$').
% 0.64/0.52 tff(func_def_46, type, 'fun_app$q': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$').
% 0.64/0.52 tff(func_def_47, type, 'uub$': 'Int_set$' > 'Int_bool_fun$').
% 0.64/0.52 tff(func_def_48, type, 'x$': 'N$').
% 0.64/0.52 tff(func_def_49, type, 'to_nat$': 'N$' > 'Nat$').
% 0.64/0.52 tff(func_def_55, type, sK28: ('Int_bool_fun$' * 'Int_bool_fun$') > $int).
% 0.64/0.52 tff(func_def_56, type, sK29: 'Nat_bool_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_57, type, sK30: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_58, type, sK31: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_59, type, sK32: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_60, type, sK33: 'N_int_set_fun$' > 'N$').
% 0.64/0.52 tff(func_def_61, type, sK34: 'N_int_set_fun$' > 'N$').
% 0.64/0.52 tff(func_def_62, type, sK35: 'Int_int_set_fun$' > $int).
% 0.64/0.52 tff(func_def_63, type, sK36: 'Int_int_set_fun$' > $int).
% 0.64/0.52 tff(func_def_64, type, sK37: 'Int_set_n_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_65, type, sK38: 'Int_set_n_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_66, type, sK39: 'Int_set_int_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_67, type, sK40: 'Int_set_int_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_68, type, sK41: 'Int_set_int_set_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_69, type, sK42: 'Int_set_int_set_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_70, type, sK43: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_71, type, sK44: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_72, type, sK45: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_73, type, sK46: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_74, type, sK47: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_75, type, sK48: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_76, type, sK49: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_77, type, sK50: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_78, type, sK51: 'N_int_set_fun$' > 'N$').
% 0.64/0.52 tff(func_def_79, type, sK52: 'N_int_set_fun$' > 'N$').
% 0.64/0.52 tff(func_def_80, type, sK53: 'Int_int_set_fun$' > $int).
% 0.64/0.52 tff(func_def_81, type, sK54: 'Int_int_set_fun$' > $int).
% 0.64/0.52 tff(func_def_82, type, sK55: 'Int_set_n_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_83, type, sK56: 'Int_set_n_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_84, type, sK57: 'Int_set_int_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_85, type, sK58: 'Int_set_int_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_86, type, sK59: 'Int_set_int_set_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_87, type, sK60: 'Int_set_int_set_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_88, type, sK61: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_89, type, sK62: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_90, type, sK63: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_91, type, sK64: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_92, type, sK65: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_93, type, sK66: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_94, type, sK67: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_95, type, sK68: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_96, type, sK69: 'Int_set_n_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_97, type, sK70: 'Int_set_n_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_98, type, sK71: 'Int_set_int_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_99, type, sK72: 'Int_set_int_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_100, type, sK73: 'Int_set_int_set_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_101, type, sK74: 'Int_set_int_set_fun$' > 'Int_set$').
% 0.64/0.52 tff(func_def_102, type, sK75: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_103, type, sK76: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_104, type, sK77: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_105, type, sK78: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_106, type, sK79: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_107, type, sK80: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_108, type, sK81: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_109, type, sK82: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_110, type, sK83: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_111, type, sK84: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_112, type, sK85: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_113, type, sK86: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_114, type, sK87: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_115, type, sK88: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_116, type, sK89: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_117, type, sK90: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_118, type, sK91: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_119, type, sK92: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_120, type, sK93: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_121, type, sK94: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_122, type, sK95: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_123, type, sK96: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_124, type, sK97: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_125, type, sK98: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_126, type, sK99: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_127, type, sK100: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_128, type, sK101: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_129, type, sK102: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_130, type, sK103: ('Int_set$' * 'Int_set_set$' * 'Int_set_set$') > 'Int_set$').
% 0.64/0.52 tff(func_def_131, type, sK104: ('Int_set$' * 'Int_set_set$' * 'Int_set_set$') > 'Int_set$').
% 0.64/0.52 tff(func_def_132, type, sK105: ('N$' * 'N_set$' * 'N_set$') > 'N$').
% 0.64/0.52 tff(func_def_133, type, sK106: ('N$' * 'N_set$' * 'N_set$') > 'N$').
% 0.64/0.52 tff(func_def_134, type, sK107: ($int * 'Int_set$' * 'Int_set$') > $int).
% 0.64/0.52 tff(func_def_135, type, sK108: ($int * 'Int_set$' * 'Int_set$') > $int).
% 0.64/0.52 tff(func_def_136, type, sK109: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_137, type, sK110: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_138, type, sK111: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_139, type, sK112: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_140, type, sK113: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_141, type, sK114: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_142, type, sK115: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_143, type, sK116: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_144, type, sK117: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_145, type, sK118: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_146, type, sK119: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_147, type, sK120: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_148, type, sK121: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_149, type, sK122: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_150, type, sK123: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_151, type, sK124: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_152, type, sK125: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_153, type, sK126: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_154, type, sK127: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_155, type, sK128: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_156, type, sK129: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_157, type, sK130: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_158, type, sK131: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_159, type, sK132: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_160, type, sK133: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_161, type, sK134: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_162, type, sK135: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_163, type, sK136: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_164, type, sK137: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_165, type, sK138: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_166, type, sK139: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_167, type, sK140: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_168, type, sK141: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_169, type, sK142: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_170, type, sK143: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_171, type, sK144: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_172, type, sK145: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_173, type, sK146: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_174, type, sK147: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_175, type, sK148: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_176, type, sK149: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_177, type, sK150: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_178, type, sK151: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_179, type, sK152: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_180, type, sK153: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_181, type, sK154: 'Int_int_bool_fun_fun$' > $int).
% 0.64/0.52 tff(func_def_182, type, sK155: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_183, type, sK156: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_184, type, sK157: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_185, type, sK158: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_186, type, sK159: 'N_n_bool_fun_fun$' > 'N$').
% 0.64/0.52 tff(func_def_187, type, sK160: 'N_bool_fun$' > 'N$').
% 0.64/0.52 tff(func_def_188, type, sK161: ('N_bool_fun$' * 'N$') > 'N$').
% 0.64/0.52 tff(func_def_189, type, sK162: 'N_bool_fun$' > 'N$').
% 0.64/0.52 tff(func_def_190, type, sK163: 'N_bool_fun$' > 'N$').
% 0.64/0.52 tff(func_def_191, type, sK164: ('N_bool_fun$' * 'N$') > 'N$').
% 0.64/0.52 tff(func_def_192, type, sK165: 'N_bool_fun$' > 'N$').
% 0.64/0.52 tff(func_def_193, type, sK166: 'N_bool_fun$' > 'N$').
% 0.64/0.52 tff(func_def_194, type, sK167: 'N_bool_fun$' > 'N$').
% 0.64/0.52 tff(func_def_195, type, sK168: $int > $int).
% 0.64/0.52 tff(func_def_196, type, sK169: $int > $int).
% 0.64/0.52 tff(func_def_197, type, sK170: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_198, type, sK171: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_199, type, sK172: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_200, type, sK173: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_201, type, sK174: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_202, type, sK175: 'Nat_bool_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_203, type, sK176: 'Nat_bool_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_204, type, sK177: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_205, type, sK178: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_206, type, sK179: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_207, type, sK180: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_208, type, sK181: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_209, type, sK182: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_210, type, sK183: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_211, type, sK184: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_212, type, sK185: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_213, type, sK186: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_214, type, sK187: ('Nat$' * 'Nat$') > 'Nat$').
% 0.64/0.52 tff(func_def_215, type, sK188: 'Nat_int_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_216, type, sK189: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_217, type, sK190: 'Nat_int_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_218, type, sK191: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_219, type, sK192: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_220, type, sK193: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_221, type, sK194: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_222, type, sK195: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_223, type, sK196: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_224, type, sK197: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_225, type, sK198: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_226, type, sK199: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_227, type, sK200: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_228, type, sK201: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_229, type, sK202: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_230, type, sK203: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_231, type, sK204: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_232, type, sK205: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_233, type, sK206: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_234, type, sK207: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_235, type, sK208: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_236, type, sK209: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_237, type, sK210: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_238, type, sK211: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_239, type, sK212: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_240, type, sK213: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_241, type, sK214: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_242, type, sK215: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_243, type, sK216: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_244, type, sK217: 'Int_n_fun$' > $int).
% 0.64/0.52 tff(func_def_245, type, sK218: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_246, type, sK219: 'N_n_fun$' > 'N$').
% 0.64/0.52 tff(func_def_247, type, sK220: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_248, type, sK221: 'Int_int_fun$' > $int).
% 0.64/0.52 tff(func_def_249, type, sK222: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_250, type, sK223: 'N_int_fun$' > 'N$').
% 0.64/0.52 tff(func_def_251, type, sK224: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_252, type, sK225: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_253, type, sK226: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_254, type, sK227: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_255, type, sK228: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_256, type, sK229: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_257, type, sK230: 'Nat_bool_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_258, type, sK231: 'Nat$' > 'Nat$').
% 0.64/0.52 tff(func_def_259, type, sK232: 'Nat_bool_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_260, type, sK233: 'Nat_nat_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_261, type, sK234: 'Nat_nat_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_262, type, sK235: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_263, type, sK236: 'Nat_int_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_264, type, sK237: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_265, type, sK238: 'Nat_int_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_266, type, sK239: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_267, type, sK240: 'Nat_n_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_268, type, sK241: 'Nat_nat_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_269, type, sK242: 'Nat_nat_fun$' > 'Nat$').
% 0.64/0.52 tff(func_def_270, type, sK243: ('Int_set$' * 'Int_set$') > $int).
% 0.64/0.52 tff(func_def_271, type, sK244: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_272, type, sK245: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.64/0.52 tff(func_def_273, type, sK246: ('Int_set$' * 'Int_set$') > $int).
% 0.64/0.52 tff(func_def_274, type, sK247: ('Int_set$' * 'Int_set$') > $int).
% 0.64/0.52 tff(func_def_275, type, sK248: ('Int_set$' * 'Int_set$') > $int).
% 0.64/0.52 tff(pred_def_1, type, 'member$c': ('N_set$' * 'N_set_set$') > $o).
% 0.64/0.52 tff(pred_def_2, type, 'member$b': ('N$' * 'N_set$') > $o).
% 0.64/0.52 tff(pred_def_3, type, 'member$': ('Int_set$' * 'Int_set_set$') > $o).
% 0.64/0.52 tff(pred_def_4, type, 'less_eq$c': ('Int_set_set$' * 'Int_set_set$') > $o).
% 0.64/0.52 tff(pred_def_5, type, 'fun_app$c': ('Int_set_bool_fun$' * 'Int_set$') > $o).
% 0.64/0.52 tff(pred_def_6, type, 'less_eq$b': ('N_set$' * 'N_set$') > $o).
% 0.64/0.52 tff(pred_def_7, type, 'fun_app$': ('Int_bool_fun$' * $int) > $o).
% 0.64/0.52 tff(pred_def_8, type, 'member$d': ('Int_set_set$' * 'Int_set_set_set$') > $o).
% 0.64/0.52 tff(pred_def_9, type, 'fun_app$d': ('N_bool_fun$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_10, type, 'fun_app$j': ('Nat_bool_fun$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_13, type, sP0: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_14, type, sP1: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_15, type, sP2: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_16, type, sP3: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_17, type, sP4: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_18, type, sP5: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_19, type, sP6: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_20, type, sP7: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_21, type, sP8: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_22, type, sP9: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_23, type, sP10: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_24, type, sP11: ('N$' * 'N$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_25, type, sP12: ('N$' * 'N$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_26, type, sP13: ('N$' * 'N$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_27, type, sP14: ('N$' * 'N$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_28, type, sP15: ('N$' * 'N$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_29, type, sP16: ('N$' * 'N$' * 'N$') > $o).
% 0.64/0.52 tff(pred_def_30, type, sP17: ($int * $int * $int) > $o).
% 0.64/0.52 tff(pred_def_31, type, sP18: ($int * $int * $int) > $o).
% 0.64/0.52 tff(pred_def_32, type, sP19: ($int * $int * $int) > $o).
% 0.64/0.52 tff(pred_def_33, type, sP20: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_34, type, sP21: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_35, type, sP22: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_36, type, sP23: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_37, type, sP24: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_38, type, sP25: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_39, type, sP26: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(pred_def_40, type, sP27: ('Nat$' * 'Nat$' * 'Nat$') > $o).
% 0.64/0.52 tff(f6,conjecture,(
% 0.64/0.52 ($less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) => $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) = 'fun_app$e'('of_nat$','to_nat$'('x$'))) & (~$less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) => $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$difference('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) = 'fun_app$e'('of_nat$','to_nat$'('x$')))),
% 0.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture5)).
% 0.64/0.52 tff(f7,negated_conjecture,(
% 0.64/0.52 ~(($less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) => $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) = 'fun_app$e'('of_nat$','to_nat$'('x$'))) & (~$less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) => $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$difference('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) = 'fun_app$e'('of_nat$','to_nat$'('x$'))))),
% 0.64/0.52 inference(negated_conjecture,[status(cth)],[f6])).
% 0.64/0.52 tff(f13,axiom,(
% 0.64/0.52 ! [X0 : $int,X1 : $int] : $sum($difference(X0,X1),X1) = X0),
% 0.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11)).
% 0.64/0.52 tff(f18,axiom,(
% 0.64/0.52 'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$')),
% 0.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16)).
% 0.64/0.52 tff(f26,axiom,(
% 0.64/0.52 ! [X0 : 'N$',X1 : 'N$'] : ('fun_app$d'('fun_app$g'('less_eq$',X0),X1) => $lesseq('fun_app$e'('of_nat$','to_nat$'(X0)),'fun_app$e'('of_nat$','to_nat$'(X1))))),
% 0.64/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24)).
% 0.64/0.52 tff(f623,plain,(
% 0.64/0.52 ~(($less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) => $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) = 'fun_app$e'('of_nat$','to_nat$'('x$'))) & (~$less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) => 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$')))))))),
% 0.64/0.52 inference(theory_normalization,[],[f7])).
% 0.64/0.52 tff(f627,plain,(
% 0.64/0.52 ! [X0 : $int,X1 : $int] : $sum($sum(X0,$uminus(X1)),X1) = X0),
% 0.64/0.52 inference(theory_normalization,[],[f13])).
% 0.64/0.52 tff(f634,plain,(
% 0.64/0.52 ! [X0 : 'N$',X1 : 'N$'] : ('fun_app$d'('fun_app$g'('less_eq$',X0),X1) => ~$less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0))))),
% 0.64/0.52 inference(theory_normalization,[],[f26])).
% 0.64/0.52 tff(f864,definition,(
% 0.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.64/0.52 introduced(theory,[tha_commutativity])).
% 0.64/0.52 tff(f967,plain,(
% 0.64/0.52 ('fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) & $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) | ('fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) & ~$less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))))),
% 0.64/0.52 inference(ennf_transformation,[],[f623])).
% 0.64/0.52 tff(f971,plain,(
% 0.64/0.52 ! [X0 : 'N$',X1 : 'N$'] : (~$less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0))) | ~'fun_app$d'('fun_app$g'('less_eq$',X0),X1))),
% 0.64/0.52 inference(ennf_transformation,[],[f634])).
% 0.64/0.52 tff(f2018,plain,(
% 0.64/0.52 $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) | 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$')))))),
% 0.64/0.52 inference(cnf_transformation,[],[f967])).
% 0.64/0.52 tff(f2042,plain,(
% 0.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum($sum(X0,$uminus(X1)),X1) = X0) )),
% 0.64/0.52 inference(cnf_transformation,[],[f627])).
% 0.64/0.52 tff(f2047,plain,(
% 0.64/0.52 'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$')),
% 0.64/0.52 inference(cnf_transformation,[],[f18])).
% 0.64/0.52 tff(f2062,plain,(
% 0.64/0.52 ( ! [X0 : 'N$',X1 : 'N$'] : (~$less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0))) | ~'fun_app$d'('fun_app$g'('less_eq$',X0),X1)) )),
% 0.64/0.52 inference(cnf_transformation,[],[f971])).
% 0.64/0.52 tff(f3712,definition,(
% 0.64/0.52 spl249_1 <=> $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))),
% 0.64/0.52 introduced(definition,[new_symbols(definition,[spl249_1])],[avatar_definition])).
% 0.64/0.52 tff(f3713,plain,(
% 0.64/0.52 $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) | ~spl249_1),
% 0.64/0.52 inference(avatar_component_clause,[],[f3712])).
% 0.64/0.52 tff(f3714,plain,(
% 0.64/0.52 ~$less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) | spl249_1),
% 0.64/0.52 inference(avatar_component_clause,[],[f3712])).
% 0.64/0.52 tff(f3721,definition,(
% 0.64/0.52 spl249_3 <=> 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$')))))),
% 0.64/0.52 introduced(definition,[new_symbols(definition,[spl249_3])],[avatar_definition])).
% 0.64/0.52 tff(f3723,plain,(
% 0.64/0.52 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) | spl249_3),
% 0.64/0.52 inference(avatar_component_clause,[],[f3721])).
% 0.64/0.52 tff(f3725,plain,(
% 0.64/0.52 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) | spl249_1),
% 0.64/0.52 inference(forward_subsumption_resolution,[],[f2018,f3714])).
% 0.64/0.52 tff(f3726,plain,(
% 0.64/0.52 ~spl249_3 | spl249_1),
% 0.64/0.52 inference(avatar_split_clause,[],[f3725,f3712,f3721])).
% 0.64/0.52 tff(f4446,plain,(
% 0.64/0.52 ( ! [X0 : $int,X1 : $int] : ($sum(X1,$sum(X0,$uminus(X1))) = X0) )),
% 0.64/0.52 inference(forward_demodulation,[],[f2042,f864])).
% 0.64/0.52 tff(f4934,plain,(
% 0.64/0.52 'fun_app$e'('of_nat$','to_nat$'('x$')) != 'fun_app$e'('of_nat$','to_nat$'('x$')) | spl249_3),
% 0.64/0.52 inference(superposition,[],[f3723,f4446])).
% 0.64/0.52 tff(f4953,plain,(
% 0.64/0.52 $false | spl249_3),
% 0.64/0.52 inference(trivial_inequality_removal,[],[f4934])).
% 0.64/0.52 tff(f4954,plain,(
% 0.64/0.52 spl249_3),
% 0.64/0.52 inference(avatar_contradiction_clause,[],[f4953])).
% 0.64/0.52 tff(f5407,plain,(
% 0.64/0.52 ~'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$') | ~spl249_1),
% 0.64/0.52 inference(resolution,[],[f3713,f2062])).
% 0.64/0.52 tff(f5410,plain,(
% 0.64/0.52 $false | ~spl249_1),
% 0.64/0.52 inference(forward_subsumption_resolution,[],[f5407,f2047])).
% 0.64/0.52 tff(f5411,plain,(
% 0.64/0.52 ~spl249_1),
% 0.64/0.52 inference(avatar_contradiction_clause,[],[f5410])).
% 0.64/0.52 cnf(s1196, plain, spl249_1 | ~spl249_3, inference(sat_conversion,[],[f3726])).
% 0.64/0.52 cnf(s1996, plain, spl249_3, inference(sat_conversion,[],[f4954])).
% 0.64/0.52 cnf(s2220, plain, ~spl249_1, inference(sat_conversion,[],[f5411])).
% 0.64/0.52 cnf(s2238, plain, $false, inference(rat,[],[s1196,s1996,s2220])).
% 0.64/0.52 tff(f5412,plain,(
% 0.64/0.52 $false),
% 0.64/0.52 inference(avatar_sat_refutation,[],[s2238])).
% 0.64/0.52 % SZS output end Proof for theBenchmark
% 0.64/0.52 % (2363491)------------------------------
% 0.64/0.52 % (2363491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.52 % (2363491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.52 % (2363491)CaDiCaL version: 2.1.3
% 0.64/0.52 % (2363491)Termination reason: Refutation
% 0.64/0.52 % (2363491)Time elapsed: 0.120 s
% 0.64/0.52 % (2363491)Peak memory usage: 17 MB
% 0.64/0.52 % (2363491)Instructions burned: 239 (million)
% 0.64/0.52 % (2363475)Success in time 0.182 s
% 0.64/0.52 % Vampire exiting
%------------------------------------------------------------------------------