%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP339_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 : n005.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 11:39:24 AM UTC 2026
% Result : Theorem 0.61s 0.59s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP339_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 12:55:02 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 Running first-order model finding
% 0.16/0.43 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
% 0.61/0.59 % (3964654)Will run a generic schedule for satisfiability detection.
% 0.61/0.59 % (3964666)% WARNING: option uhcvi not known.
% 0.61/0.59 % (3964666)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4079624645:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.61/0.59 % (3964665)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2850007213_2999 on theBenchmark for (2999ds/0Mi)
% 0.61/0.59 % (3964668)dis+10_1_sil=32000:sp=arity:random_seed=703515226:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.61/0.59 % (3964669)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=101728495:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.61/0.59 % (3964667)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3330501076:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.61/0.59 % (3964671)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3580857969:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.61/0.59 % (3964670)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3135690747:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.61/0.59 % (3964665)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.61/0.59 % (3964665)Terminated due to inappropriate strategy.
% 0.61/0.59 % (3964665)------------------------------
% 0.61/0.59 % (3964665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.59 % (3964665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.59 % (3964665)CaDiCaL version: 2.1.3
% 0.61/0.59 % (3964665)Termination reason: Inappropriate
% 0.61/0.59 % (3964665)Time elapsed: 0.044 s
% 0.61/0.59 % (3964665)Peak memory usage: 12 MB
% 0.61/0.59 % (3964665)Instructions burned: 64 (million)
% 0.61/0.59 % (3964665)------------------------------
% 0.61/0.59 % (3964665)------------------------------
% 0.61/0.59 % (3964666) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3964654-3964666"...
% 0.61/0.59 % (3964666)...printing done.
% 0.61/0.59 % (3964666)Refutation found. Thanks to Tanya!
% 0.61/0.59 % SZS status Theorem for theBenchmark
% 0.61/0.59 % SZS output start Proof for theBenchmark
% 0.61/0.59 tff(type_def_5, type, 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_6, type, 'Int_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_7, type, 'A_c_vec_c_vec$': $tType).
% 0.61/0.59 tff(type_def_8, type, 'Nat_nat_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_9, type, 'Int_int_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_10, type, 'A_iarray_iarray_a_iarray_iarray_prod$': $tType).
% 0.61/0.59 tff(type_def_11, type, 'A_iarray_iarray$': $tType).
% 0.61/0.59 tff(type_def_12, type, 'Int_int_prod$': $tType).
% 0.61/0.59 tff(type_def_13, type, 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_14, type, 'A_c_vec_c_vec_a_b_vec_c_vec_prod$': $tType).
% 0.61/0.59 tff(type_def_15, type, 'Nat_list$': $tType).
% 0.61/0.59 tff(type_def_16, type, 'Nat_nat_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_17, type, 'Nat_a_c_vec_c_vec_prod$': $tType).
% 0.61/0.59 tff(type_def_18, type, 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_19, type, 'Int_int_fun$': $tType).
% 0.61/0.59 tff(type_def_20, type, 'Nat_nat_prod$': $tType).
% 0.61/0.59 tff(type_def_21, type, 'A_b_vec_c_vec$': $tType).
% 0.61/0.59 tff(type_def_22, type, 'Nat_a_iarray_iarray_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_23, type, 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_24, type, 'Nat_nat_fun$': $tType).
% 0.61/0.59 tff(type_def_25, type, 'A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_26, type, 'Nat$': $tType).
% 0.61/0.59 tff(type_def_27, type, 'Nat_int_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_28, type, 'A_iarray_iarray_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_29, type, 'Nat_a_b_vec_c_vec_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_30, type, tlbool: $tType).
% 0.61/0.59 tff(type_def_31, type, 'A_b_vec_c_vec_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_32, type, 'Nat_a_iarray_iarray_prod$': $tType).
% 0.61/0.59 tff(type_def_33, type, 'Nat_int_prod$': $tType).
% 0.61/0.59 tff(type_def_34, type, 'Int_nat_prod$': $tType).
% 0.61/0.59 tff(type_def_35, type, 'Nat_a_b_vec_c_vec_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_36, type, 'A$': $tType).
% 0.61/0.59 tff(type_def_37, type, 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$': $tType).
% 0.61/0.59 tff(type_def_38, type, 'Nat_a_b_vec_c_vec_prod$': $tType).
% 0.61/0.59 tff(type_def_39, type, 'Nat_a_iarray_iarray_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_40, type, 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$': $tType).
% 0.61/0.59 tff(type_def_41, type, 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$': $tType).
% 0.61/0.59 tff(type_def_42, type, 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_43, type, 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$': $tType).
% 0.61/0.59 tff(type_def_44, type, 'Nat_a_iarray_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_45, type, 'Int_int_bool_fun_fun$': $tType).
% 0.61/0.59 tff(type_def_46, type, 'A_iarray$': $tType).
% 0.61/0.59 tff(type_def_47, type, 'Int_nat_prod_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_48, type, 'Nat_a_iarray_prod$': $tType).
% 0.61/0.59 tff(type_def_49, type, 'Nat_bool_fun$': $tType).
% 0.61/0.59 tff(type_def_50, type, 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$': $tType).
% 0.61/0.59 tff(type_def_51, type, 'Nat_int_fun$': $tType).
% 0.61/0.59 tff(type_def_52, type, 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$': $tType).
% 0.61/0.59 tff(func_def_0, type, 'snd$g': 'Int_nat_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_1, type, 'foldl$a': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'Nat_list$') > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 0.61/0.59 tff(func_def_2, type, 'b$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 0.61/0.59 tff(func_def_3, type, 'fun_app$l': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$' * 'A_c_vec_c_vec$') > 'Nat_a_b_vec_c_vec_prod_bool_fun$').
% 0.61/0.59 tff(func_def_4, type, 'gauss_Jordan_in_ij_iarrays_PA$': ('A_iarray_iarray_a_iarray_iarray_prod$' * 'Nat$' * 'Nat$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_5, type, 'pair$b': ('Nat$' * 'A_iarray_iarray$') > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_6, type, 'fst$f': 'Nat_int_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_7, type, 'ncols$a': 'A_c_vec_c_vec$' > 'Nat$').
% 0.61/0.59 tff(func_def_8, type, 'fun_app$z': ('Int_int_fun$' * $int) > $int).
% 0.61/0.59 tff(func_def_9, type, 'plus$h': ('Int_nat_prod$' * 'Int_nat_prod$') > 'Int_nat_prod$').
% 0.61/0.59 tff(func_def_10, type, 'pair$d': ('A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$') > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 0.61/0.59 tff(func_def_11, type, 'mat$': 'A$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_12, type, 'gauss_Jordan_column_k_PA$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$').
% 0.61/0.59 tff(func_def_13, type, 'gauss_Jordan_upt_k_PA$': ('A_b_vec_c_vec$' * 'Nat$') > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_14, type, 'fun_app$q': ('Nat_a_b_vec_c_vec_bool_fun_fun$' * 'Nat$') > 'A_b_vec_c_vec_bool_fun$').
% 0.61/0.59 tff(func_def_15, type, 'a$a': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_16, type, 'fst$l': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_17, type, 'pair$e': ('Nat$' * 'Nat$') > 'Nat_nat_prod$').
% 0.61/0.59 tff(func_def_18, type, 'snd$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_19, type, 'pair$h': ($int * $int) > 'Int_int_prod$').
% 0.61/0.59 tff(func_def_20, type, 'fun_app$o': ('A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$') > 'A_iarray_iarray_bool_fun$').
% 0.61/0.59 tff(func_def_21, type, 'pair$a': ('Nat$' * 'A_b_vec_c_vec$') > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_22, type, 'snd$h': 'Int_int_prod$' > $int).
% 0.61/0.59 tff(func_def_23, type, 'fst$e': 'Nat_nat_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_24, type, 'fst$k': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_25, type, 'fun_app$': ('Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' * 'Nat$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_26, type, 'foldl$': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat_list$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_27, type, 'nrows$': 'A_b_vec_c_vec$' > 'Nat$').
% 0.61/0.59 tff(func_def_28, type, 'pair$f': ('Nat$' * $int) > 'Nat_int_prod$').
% 0.61/0.59 tff(func_def_29, type, 'snd$e': 'Nat_nat_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_30, type, 'zero$a': 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_31, type, 'fun_app$r': ('Nat_a_iarray_iarray_bool_fun_fun$' * 'Nat$') > 'A_iarray_iarray_bool_fun$').
% 0.61/0.59 tff(func_def_32, type, 'fun_app$m': ('A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray$') > 'Nat_a_iarray_iarray_prod_bool_fun$').
% 0.61/0.59 tff(func_def_33, type, 'pair$l': ('A_c_vec_c_vec$' * 'A_b_vec_c_vec$') > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_34, type, 'fun_app$t': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$').
% 0.61/0.59 tff(func_def_35, type, 'snd$a': 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_36, type, 'pair$j': ('A_c_vec_c_vec$' * 'Nat_a_c_vec_c_vec_prod$') > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_37, type, 'of_nat$': 'Nat_int_fun$').
% 0.61/0.59 tff(func_def_38, type, 'one$': 'A$').
% 0.61/0.59 tff(func_def_39, type, 'upt$': ('Nat$' * 'Nat$') > 'Nat_list$').
% 0.61/0.59 tff(func_def_40, type, 'nrows$a': 'A_c_vec_c_vec$' > 'Nat$').
% 0.61/0.59 tff(func_def_41, type, 'fst$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_42, type, 'fst$a': 'Nat_a_b_vec_c_vec_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_43, type, 'snd$b': 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_44, type, 'fst$g': 'Int_nat_prod$' > $int).
% 0.61/0.59 tff(func_def_45, type, 'zero$b': 'Int_nat_prod$').
% 0.61/0.59 tff(func_def_46, type, 'less$': 'Nat_nat_bool_fun_fun$').
% 0.61/0.59 tff(func_def_47, type, 'nrows_iarray$': 'A_iarray_iarray$' > 'Nat$').
% 0.61/0.59 tff(func_def_48, type, 'pair$i': ('Nat$' * 'A_iarray$') > 'Nat_a_iarray_prod$').
% 0.61/0.59 tff(func_def_49, type, tltrue: tlbool).
% 0.61/0.59 tff(func_def_50, type, 'gauss_Jordan_column_k_PA$a': ('A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$') > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_51, type, 'plus$f': ('Nat_a_iarray_iarray_prod$' * 'Nat_a_iarray_iarray_prod$') > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_52, type, 'plus$': 'Nat$' > 'Nat_nat_fun$').
% 0.61/0.59 tff(func_def_53, type, 'fun_app$a': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$').
% 0.61/0.59 tff(func_def_54, type, 'snd$f': 'Nat_int_prod$' > $int).
% 0.61/0.59 tff(func_def_55, type, 'pair$c': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_56, type, 'plus$k': ('Nat_nat_prod$' * 'Nat_nat_prod$') > 'Nat_nat_prod$').
% 0.61/0.59 tff(func_def_57, type, 'gauss_Jordan_column_k_iarrays_PA$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$').
% 0.61/0.59 tff(func_def_58, type, 'one$a': 'Nat$').
% 0.61/0.59 tff(func_def_59, type, 'fst$i': 'Nat_a_iarray_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_60, type, 'plus$j': ('Nat_int_prod$' * 'Nat_int_prod$') > 'Nat_int_prod$').
% 0.61/0.59 tff(func_def_61, type, 'zero$i': 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_62, type, 'fun_app$v': ('Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$' * 'Nat$') > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 0.61/0.59 tff(func_def_63, type, 'fst$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_64, type, 'fun_app$y': ('Int_int_bool_fun_fun$' * $int) > 'Int_bool_fun$').
% 0.61/0.59 tff(func_def_65, type, 'fst$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_66, type, 'ncols$': 'A_b_vec_c_vec$' > 'Nat$').
% 0.61/0.59 tff(func_def_67, type, 'fst$b': 'Nat_a_iarray_iarray_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_68, type, 'fun_app$u': ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_69, type, 'vector_all_zero_from_index$': 'Nat_a_iarray_prod_bool_fun$').
% 0.61/0.59 tff(func_def_70, type, 'plus$l': ('A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_71, type, 'plus$c': ('Nat_a_b_vec_c_vec_prod$' * 'Nat_a_b_vec_c_vec_prod$') > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_72, type, 'matrix_to_iarray$a': 'A_b_vec_c_vec$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_73, type, 'plus$d': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$').
% 0.61/0.59 tff(func_def_74, type, 'zero$h': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_75, type, 'pair$k': ('Nat$' * 'A_c_vec_c_vec$') > 'Nat_a_c_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_76, type, 'column_iarray$': ('Nat$' * 'A_iarray_iarray$') > 'A_iarray$').
% 0.61/0.59 tff(func_def_77, type, 'fun_app$w': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$').
% 0.61/0.59 tff(func_def_78, type, 'zero$j': 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_79, type, 'divides_aux$': 'Int_int_prod_bool_fun$').
% 0.61/0.59 tff(func_def_80, type, 'less_eq$': 'Nat_nat_bool_fun_fun$').
% 0.61/0.59 tff(func_def_81, type, 'snd$i': 'Nat_a_iarray_prod$' > 'A_iarray$').
% 0.61/0.59 tff(func_def_82, type, 'plus$e': ('A_iarray_iarray$' * 'A_iarray_iarray$') > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_83, type, 'zero$c': 'Nat_a_c_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_84, type, 'zero$': 'A$').
% 0.61/0.59 tff(func_def_85, type, 'matrix_to_iarray$': 'A_c_vec_c_vec$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_86, type, 'plus$i': ('A_b_vec_c_vec$' * 'A_b_vec_c_vec$') > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_87, type, 'plus$g': ('Int_int_prod$' * 'Int_int_prod$') > 'Int_int_prod$').
% 0.61/0.59 tff(func_def_88, type, tlfalse: tlbool).
% 0.61/0.59 tff(func_def_89, type, 'zero$g': 'Int_int_prod$').
% 0.61/0.59 tff(func_def_90, type, 'nat$': $int > 'Nat$').
% 0.61/0.59 tff(func_def_91, type, 'fst$h': 'Int_int_prod$' > $int).
% 0.61/0.59 tff(func_def_92, type, 'zero$e': 'Nat_nat_prod$').
% 0.61/0.59 tff(func_def_93, type, 'zero$f': 'Nat_int_prod$').
% 0.61/0.59 tff(func_def_94, type, 'snd$l': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_95, type, 'pair$': ('A_c_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_96, type, 'gauss_Jordan_upt_k_iarrays_PA$': ('A_iarray_iarray$' * 'Nat$') > 'A_iarray_iarray_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_97, type, 'suc$': 'Nat_nat_fun$').
% 0.61/0.59 tff(func_def_98, type, 'plus$a': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$').
% 0.61/0.59 tff(func_def_99, type, 'pair$g': ($int * 'Nat$') > 'Int_nat_prod$').
% 0.61/0.59 tff(func_def_100, type, 'fun_app$b': ('Nat_int_fun$' * 'Nat$') > $int).
% 0.61/0.59 tff(func_def_101, type, 'fst$j': 'Nat_a_c_vec_c_vec_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_102, type, 'zero$d': 'Nat$').
% 0.61/0.59 tff(func_def_103, type, 'a$': 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_104, type, 'ka$': 'Nat$').
% 0.61/0.59 tff(func_def_105, type, 'snd$j': 'Nat_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_106, type, 'plus$b': ('A_c_vec_c_vec$' * 'A_c_vec_c_vec$') > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_107, type, 'mat_iarray$': ('A$' * 'Nat$') > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_108, type, 'k$': 'Nat$').
% 0.61/0.59 tff(func_def_109, type, 'snd$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_110, type, 'snd$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_111, type, 'snd$k': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'Nat_a_c_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_116, type, sK0: 'Nat_a_iarray_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_117, type, sK1: 'Nat_a_iarray_prod_bool_fun$' > 'A_iarray$').
% 0.61/0.59 tff(func_def_118, type, sK2: 'Nat_nat_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_119, type, sK3: 'Nat_nat_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_120, type, sK4: 'Nat_int_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_121, type, sK5: 'Nat_int_prod_bool_fun$' > $int).
% 0.61/0.59 tff(func_def_122, type, sK6: 'Int_nat_prod_bool_fun$' > $int).
% 0.61/0.59 tff(func_def_123, type, sK7: 'Int_nat_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_124, type, sK8: 'Int_int_prod_bool_fun$' > $int).
% 0.61/0.59 tff(func_def_125, type, sK9: 'Int_int_prod_bool_fun$' > $int).
% 0.61/0.59 tff(func_def_126, type, sK10: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_127, type, sK11: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_128, type, sK12: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_129, type, sK13: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_130, type, sK14: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_131, type, sK15: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_132, type, sK16: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_133, type, sK17: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_134, type, sK18: 'Int_int_prod$' > $int).
% 0.61/0.59 tff(func_def_135, type, sK19: 'Int_int_prod$' > $int).
% 0.61/0.59 tff(func_def_136, type, sK20: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_137, type, sK21: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_138, type, sK22: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_139, type, sK23: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_140, type, sK24: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_141, type, sK25: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_142, type, sK26: 'Nat_a_iarray_iarray_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_143, type, sK27: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_144, type, sK28: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_145, type, sK29: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_146, type, sK30: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_147, type, sK31: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_148, type, sK32: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_149, type, sK33: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_150, type, sK34: 'Nat_a_iarray_iarray_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_151, type, sK35: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_152, type, sK36: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_153, type, sK37: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_154, type, sK38: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_155, type, sK39: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_156, type, sK40: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_157, type, sK41: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_158, type, sK42: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_159, type, sK43: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_160, type, sK44: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_161, type, sK45: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_162, type, sK46: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat$').
% 0.61/0.59 tff(func_def_163, type, sK47: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_164, type, sK48: 'Nat_int_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_165, type, sK49: 'Nat_int_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_166, type, sK50: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_167, type, sK51: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_168, type, sK52: 'Nat_int_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_169, type, sK53: 'Nat_int_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_170, type, sK54: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_171, type, sK55: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_172, type, sK56: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_173, type, sK57: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_174, type, sK58: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_175, type, sK59: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_176, type, sK60: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_177, type, sK61: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_178, type, sK62: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_179, type, sK63: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_180, type, sK64: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_181, type, sK65: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_182, type, sK66: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_183, type, sK67: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_184, type, sK68: 'Nat_nat_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_185, type, sK69: 'Nat_nat_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_186, type, sK70: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_187, type, sK71: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_188, type, sK72: 'Nat$' > 'Nat$').
% 0.61/0.59 tff(func_def_189, type, sK73: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_190, type, sK74: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_191, type, sK75: 'Nat$' > 'Nat$').
% 0.61/0.59 tff(func_def_192, type, sK76: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_193, type, sK77: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_194, type, sK78: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_195, type, sK79: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_196, type, sK80: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_197, type, sK81: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_198, type, sK82: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_199, type, sK83: 'Nat$' > 'Nat$').
% 0.61/0.59 tff(func_def_200, type, sK84: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_201, type, sK85: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_202, type, sK86: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_203, type, sK87: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_204, type, sK88: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_205, type, sK89: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_206, type, sK90: 'Nat$' > 'Nat$').
% 0.61/0.59 tff(func_def_207, type, sK91: 'Nat$' > 'Nat$').
% 0.61/0.59 tff(func_def_208, type, sK92: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_209, type, sK93: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.61/0.59 tff(func_def_210, type, sK94: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_211, type, sK95: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_212, type, sK96: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_213, type, sK97: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_214, type, sK98: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_215, type, sK99: 'Nat_bool_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_216, type, sK105: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_217, type, sK106: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_218, type, sK107: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_219, type, sK108: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_220, type, sK109: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_221, type, sK110: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_222, type, sK111: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_223, type, sK112: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_224, type, sK113: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_225, type, sK114: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_226, type, sK115: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_227, type, sK116: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_228, type, sK117: $int > $int).
% 0.61/0.59 tff(func_def_229, type, sK118: $int > $int).
% 0.61/0.59 tff(func_def_230, type, sK119: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_231, type, sK120: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_232, type, sK121: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_233, type, sK122: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_234, type, sK123: 'Int_int_bool_fun_fun$' > $int).
% 0.61/0.59 tff(func_def_235, type, sK124: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_236, type, sK125: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_237, type, sK126: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_238, type, sK127: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_239, type, sK128: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_240, type, sK129: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_241, type, sK130: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_242, type, sK131: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_243, type, sK132: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_244, type, sK133: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_245, type, sK134: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_246, type, sK135: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_247, type, sK136: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_248, type, sK137: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_249, type, sK138: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_250, type, sK139: 'Int_int_fun$' > $int).
% 0.61/0.59 tff(func_def_251, type, sK140: ('A_c_vec_c_vec$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'Nat_a_b_vec_c_vec_prod$').
% 0.61/0.59 tff(func_def_252, type, sK141: ('A_iarray_iarray$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'Nat_a_iarray_iarray_prod$').
% 0.61/0.59 tff(func_def_253, type, sK142: ('A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_254, type, sK143: ('Nat$' * 'Nat_a_b_vec_c_vec_prod$') > 'A_b_vec_c_vec$').
% 0.61/0.59 tff(func_def_255, type, sK144: ('Nat$' * 'Nat_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_256, type, sK145: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_257, type, sK146: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_258, type, sK147: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_259, type, sK148: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_260, type, sK149: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_261, type, sK150: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_262, type, sK151: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_263, type, sK152: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_264, type, sK153: ('Nat$' * 'Nat$') > 'Nat$').
% 0.61/0.59 tff(func_def_265, type, sK154: 'Nat_nat_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_266, type, sK155: 'Nat_nat_fun$' > 'Nat$').
% 0.61/0.59 tff(func_def_267, type, sK156: ('Nat_a_b_vec_c_vec_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > 'A_c_vec_c_vec$').
% 0.61/0.59 tff(func_def_268, type, sK157: ('Nat_a_iarray_iarray_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_269, type, sK158: ('A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$') > 'A_iarray_iarray$').
% 0.61/0.59 tff(func_def_270, type, sK159: ('A_b_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$') > 'Nat$').
% 0.61/0.59 tff(func_def_271, type, sK160: ('A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$') > 'Nat$').
% 0.61/0.59 tff(pred_def_1, type, 'fun_app$n': ('A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$') > $o).
% 0.61/0.59 tff(pred_def_2, type, 'fun_app$f': ('Int_nat_prod_bool_fun$' * 'Int_nat_prod$') > $o).
% 0.61/0.59 tff(pred_def_3, type, 'fun_app$p': ('A_b_vec_c_vec_bool_fun$' * 'A_b_vec_c_vec$') > $o).
% 0.61/0.59 tff(pred_def_4, type, 'fun_app$g': ('Int_int_prod_bool_fun$' * 'Int_int_prod$') > $o).
% 0.61/0.59 tff(pred_def_5, type, 'fun_app$j': ('A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$') > $o).
% 0.61/0.59 tff(pred_def_6, type, 'fun_app$d': ('Nat_nat_prod_bool_fun$' * 'Nat_nat_prod$') > $o).
% 0.61/0.59 tff(pred_def_7, type, 'fun_app$e': ('Nat_int_prod_bool_fun$' * 'Nat_int_prod$') > $o).
% 0.61/0.59 tff(pred_def_8, type, 'fun_app$i': ('Nat_a_b_vec_c_vec_prod_bool_fun$' * 'Nat_a_b_vec_c_vec_prod$') > $o).
% 0.61/0.59 tff(pred_def_9, type, 'fun_app$k': ('Nat_a_iarray_iarray_prod_bool_fun$' * 'Nat_a_iarray_iarray_prod$') > $o).
% 0.61/0.59 tff(pred_def_10, type, 'fun_app$x': ('Int_bool_fun$' * $int) > $o).
% 0.61/0.59 tff(pred_def_11, type, 'fun_app$h': ('A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$') > $o).
% 0.61/0.59 tff(pred_def_12, type, 'fun_app$c': ('Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$') > $o).
% 0.61/0.59 tff(pred_def_13, type, 'fun_app$s': ('Nat_bool_fun$' * 'Nat$') > $o).
% 0.61/0.59 tff(pred_def_16, type, sP100: ($int * $int * $int) > $o).
% 0.61/0.59 tff(pred_def_17, type, sP101: ($int * $int * $int) > $o).
% 0.61/0.59 tff(pred_def_18, type, sP102: ($int * $int * $int) > $o).
% 0.61/0.59 tff(pred_def_19, type, sP103: ($int * $int * $int) > $o).
% 0.61/0.59 tff(f1,conjecture,(
% 0.61/0.59 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 0.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture0)).
% 0.61/0.59 tff(f2,negated_conjecture,(
% 0.61/0.59 ~ 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 0.61/0.59 inference(negated_conjecture,[status(cth)],[f1])).
% 0.61/0.59 tff(f8,axiom,(
% 0.61/0.59 ! [X0 : 'Nat_a_b_vec_c_vec_prod$'] : 'pair$a'('fst$a'(X0),'snd$a'(X0)) = X0),
% 0.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6)).
% 0.61/0.59 tff(f10,axiom,(
% 0.61/0.59 ! [X0 : 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'] : 'pair$'('fst$'(X0),'snd$'(X0)) = X0),
% 0.61/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8)).
% 0.61/0.59 tff(f799,definition,(
% 0.61/0.59 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.61/0.59 introduced(theory,[tha_commutativity])).
% 0.61/0.59 tff(f811,plain,(
% 0.61/0.59 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 0.61/0.59 inference(flattening,[],[f2])).
% 0.61/0.59 tff(f1314,plain,(
% 0.61/0.59 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),
% 0.61/0.59 inference(cnf_transformation,[],[f811])).
% 0.61/0.59 tff(f1320,plain,(
% 0.61/0.59 ( ! [X0 : 'Nat_a_b_vec_c_vec_prod$'] : ('pair$a'('fst$a'(X0),'snd$a'(X0)) = X0) )),
% 0.61/0.59 inference(cnf_transformation,[],[f8])).
% 0.61/0.59 tff(f1322,plain,(
% 0.61/0.59 ( ! [X0 : 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'] : ('pair$'('fst$'(X0),'snd$'(X0)) = X0) )),
% 0.61/0.59 inference(cnf_transformation,[],[f10])).
% 0.61/0.59 tff(f4749,plain,(
% 0.61/0.59 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$'))))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$'))))))),
% 0.61/0.59 inference(forward_demodulation,[],[f1314,f799])).
% 0.61/0.59 tff(f4750,plain,(
% 0.61/0.59 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$'))))))),
% 0.61/0.59 inference(forward_demodulation,[],[f4749,f1320])).
% 0.61/0.59 tff(f4751,plain,(
% 0.61/0.59 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$')))))),'nat$'($sum(1,'fun_app$b'('of_nat$','ka$'))))))),
% 0.61/0.59 inference(forward_demodulation,[],[f4750,f1322])).
% 0.61/0.59 tff(f4752,plain,(
% 0.61/0.59 $false),
% 0.61/0.59 inference(trivial_inequality_removal,[],[f4751])).
% 0.61/0.59 % SZS output end Proof for theBenchmark
% 0.61/0.59 % (3964666)------------------------------
% 0.61/0.59 % (3964666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.59 % (3964666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.59 % (3964666)CaDiCaL version: 2.1.3
% 0.61/0.59 % (3964666)Termination reason: Refutation
% 0.61/0.59 % (3964666)Time elapsed: 0.067 s
% 0.61/0.59 % (3964666)Peak memory usage: 14 MB
% 0.61/0.59 % (3964666)Instructions burned: 149 (million)
% 0.61/0.59 % (3964654)Success in time 0.144 s
% 0.61/0.59 % Vampire exiting
%------------------------------------------------------------------------------