%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP334_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 : n007.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 11:39:23 AM UTC 2026
% Result : Theorem 0.62s 0.58s
% Output : Refutation 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP334_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n007.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 12:52:55 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 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
% 0.62/0.58 % (1391239)Will run a generic schedule for satisfiability detection.
% 0.62/0.58 % (1391281)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2469247710:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.62/0.58 % (1391276)% WARNING: option uhcvi not known.
% 0.62/0.58 % (1391278)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2920026652:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.62/0.58 % (1391275)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3327637432_2999 on theBenchmark for (2999ds/0Mi)
% 0.62/0.58 % (1391276)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1951435965:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.62/0.58 % (1391279)dis+10_1_sil=32000:sp=arity:random_seed=2601694904:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.62/0.58 % (1391280)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=438197714:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.62/0.58 % (1391282)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1635533308:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.62/0.58 % (1391281)Instruction limit reached!
% 0.62/0.58 % (1391281)------------------------------
% 0.62/0.58 % (1391281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.58 % (1391281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.58 % (1391281)CaDiCaL version: 2.1.3
% 0.62/0.58 % (1391281)Termination reason: Instruction limit
% 0.62/0.58 % (1391281)Termination phase: Saturation
% 0.62/0.58 % (1391281)Time elapsed: 0.044 s
% 0.62/0.58 % (1391281)Peak memory usage: 14 MB
% 0.62/0.58 % (1391281)Instructions burned: 133 (million)
% 0.62/0.58 % (1391275)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.62/0.58 % (1391275)Terminated due to inappropriate strategy.
% 0.62/0.58 % (1391275)------------------------------
% 0.62/0.58 % (1391275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.58 % (1391275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.58 % (1391275)CaDiCaL version: 2.1.3
% 0.62/0.58 % (1391275)Termination reason: Inappropriate
% 0.62/0.58 % (1391275)Time elapsed: 0.039 s
% 0.62/0.58 % (1391275)Peak memory usage: 12 MB
% 0.62/0.58 % (1391275)Instructions burned: 86 (million)
% 0.62/0.58 % (1391275)------------------------------
% 0.62/0.58 % (1391275)------------------------------
% 0.62/0.58 % (1391279)Instruction limit reached!
% 0.62/0.58 % (1391279)------------------------------
% 0.62/0.58 % (1391279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.58 % (1391279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.58 % (1391279)CaDiCaL version: 2.1.3
% 0.62/0.58 % (1391279)Termination reason: Instruction limit
% 0.62/0.58 % (1391279)Termination phase: Saturation
% 0.62/0.58 % (1391279)Time elapsed: 0.049 s
% 0.62/0.58 % (1391279)Peak memory usage: 13 MB
% 0.62/0.58 % (1391279)Instructions burned: 103 (million)
% 0.62/0.58 % (1391305)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=709456678:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.62/0.58 % (1391276) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1391239-1391276"...
% 0.62/0.58 % (1391276)...printing done.
% 0.62/0.58 % (1391280)Instruction limit reached!
% 0.62/0.58 % (1391280)------------------------------
% 0.62/0.58 % (1391280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.58 % (1391280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.58 % (1391280)CaDiCaL version: 2.1.3
% 0.62/0.58 % (1391280)Termination reason: Instruction limit
% 0.62/0.58 % (1391280)Termination phase: Saturation
% 0.62/0.58 % (1391280)Time elapsed: 0.059 s
% 0.62/0.58 % (1391280)Peak memory usage: 13 MB
% 0.62/0.58 % (1391280)Instructions burned: 118 (million)
% 0.62/0.58 % (1391276)Refutation found. Thanks to Tanya!
% 0.62/0.58 % SZS status Theorem for theBenchmark
% 0.62/0.58 % SZS output start Proof for theBenchmark
% 0.62/0.58 tff(type_def_5, type, 'Num1$': $tType).
% 0.62/0.58 tff(type_def_6, type, 'Unit_set$': $tType).
% 0.62/0.58 tff(type_def_7, type, 'Int_bool_fun$': $tType).
% 0.62/0.58 tff(type_def_8, type, 'Nat_set_int_fun$': $tType).
% 0.62/0.58 tff(type_def_9, type, 'Num1_option_option_set$': $tType).
% 0.62/0.58 tff(type_def_10, type, 'Rows_set_int_fun$': $tType).
% 0.62/0.58 tff(type_def_11, type, 'Nat_nat_bool_fun_fun$': $tType).
% 0.62/0.58 tff(type_def_12, type, 'Rows_option_option_set$': $tType).
% 0.62/0.58 tff(type_def_13, type, 'Rows$': $tType).
% 0.62/0.58 tff(type_def_14, type, 'Literal$': $tType).
% 0.62/0.58 tff(type_def_15, type, 'Rows_set$': $tType).
% 0.62/0.58 tff(type_def_16, type, 'Int_int_fun$': $tType).
% 0.62/0.58 tff(type_def_17, type, 'Num0$': $tType).
% 0.62/0.58 tff(type_def_18, type, 'Rows_option_set$': $tType).
% 0.62/0.58 tff(type_def_19, type, 'Nat_rows_set_fun$': $tType).
% 0.62/0.58 tff(type_def_20, type, 'Nat_nat_fun$': $tType).
% 0.62/0.58 tff(type_def_21, type, 'Nat$': $tType).
% 0.62/0.58 tff(type_def_22, type, 'Nat_num1_set_fun$': $tType).
% 0.62/0.58 tff(type_def_23, type, 'Literal_set$': $tType).
% 0.62/0.58 tff(type_def_24, type, 'Int_num0_set_fun$': $tType).
% 0.62/0.58 tff(type_def_25, type, tlbool: $tType).
% 0.62/0.58 tff(type_def_26, type, 'Num1_option_set$': $tType).
% 0.62/0.58 tff(type_def_27, type, 'Int_rows_set_fun$': $tType).
% 0.62/0.58 tff(type_def_28, type, 'Rows_bool_fun$': $tType).
% 0.62/0.58 tff(type_def_29, type, 'Rows_rows_fun$': $tType).
% 0.62/0.58 tff(type_def_30, type, 'Literal_bool_fun$': $tType).
% 0.62/0.58 tff(type_def_31, type, 'Num0_bool_fun$': $tType).
% 0.62/0.58 tff(type_def_32, type, 'Nat_nat_set_fun$': $tType).
% 0.62/0.58 tff(type_def_33, type, 'Nat_literal_set_fun$': $tType).
% 0.62/0.58 tff(type_def_34, type, 'Nat_num0_set_fun$': $tType).
% 0.62/0.58 tff(type_def_35, type, 'Int_literal_set_fun$': $tType).
% 0.62/0.58 tff(type_def_36, type, 'Literal_set_int_fun$': $tType).
% 0.62/0.58 tff(type_def_37, type, 'Num1_set$': $tType).
% 0.62/0.58 tff(type_def_38, type, 'Literal_option_set$': $tType).
% 0.62/0.58 tff(type_def_39, type, 'Nat_option_set$': $tType).
% 0.62/0.58 tff(type_def_40, type, 'Num0_option_set$': $tType).
% 0.62/0.58 tff(type_def_41, type, 'Num0_set_int_fun$': $tType).
% 0.62/0.58 tff(type_def_42, type, 'Int_int_bool_fun_fun$': $tType).
% 0.62/0.58 tff(type_def_43, type, 'Num1_bool_fun$': $tType).
% 0.62/0.58 tff(type_def_44, type, 'Nat_bool_fun$': $tType).
% 0.62/0.58 tff(type_def_45, type, 'Num1_set_int_fun$': $tType).
% 0.62/0.58 tff(type_def_46, type, 'Num0_set$': $tType).
% 0.62/0.58 tff(type_def_47, type, 'Nat_set$': $tType).
% 0.62/0.58 tff(type_def_48, type, 'Int_num1_set_fun$': $tType).
% 0.62/0.58 tff(type_def_49, type, 'Nat_int_fun$': $tType).
% 0.62/0.58 tff(type_def_50, type, 'Int_nat_set_fun$': $tType).
% 0.62/0.58 tff(func_def_0, type, 'top$o': 'Unit_set$').
% 0.62/0.58 tff(func_def_1, type, 'uua$': 'Rows_set$' > 'Rows_bool_fun$').
% 0.62/0.58 tff(func_def_2, type, 'minus$': 'Rows$' > 'Rows_rows_fun$').
% 0.62/0.58 tff(func_def_3, type, 'fun_app$p': ('Int_rows_set_fun$' * $int) > 'Rows_set$').
% 0.62/0.58 tff(func_def_4, type, 'uue$': 'Num1_set$' > 'Num1_bool_fun$').
% 0.62/0.58 tff(func_def_5, type, 'top$h': 'Num0_set$').
% 0.62/0.58 tff(func_def_6, type, 'top$q': 'Literal_option_set$').
% 0.62/0.58 tff(func_def_7, type, 'fun_app$j': ('Nat_nat_bool_fun_fun$' * 'Nat$') > 'Nat_bool_fun$').
% 0.62/0.58 tff(func_def_8, type, 'card$': 'Rows_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_9, type, 'card$e': 'Num1_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_10, type, 'fun_app$l': ('Nat_nat_set_fun$' * 'Nat$') > 'Nat_set$').
% 0.62/0.58 tff(func_def_11, type, 'collect$a': 'Nat_bool_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_12, type, 'fun_app$t': ('Int_num1_set_fun$' * $int) > 'Num1_set$').
% 0.62/0.58 tff(func_def_13, type, 'one$': 'Rows$').
% 0.62/0.58 tff(func_def_14, type, 'fun_app$n': ('Nat_num0_set_fun$' * 'Nat$') > 'Num0_set$').
% 0.62/0.58 tff(func_def_15, type, 'collect$c': 'Num0_bool_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_16, type, 'top$c': 'Num1_option_option_set$').
% 0.62/0.58 tff(func_def_17, type, 'top$': 'Rows_set$').
% 0.62/0.58 tff(func_def_18, type, 'fun_app$b': ('Int_int_fun$' * $int) > $int).
% 0.62/0.58 tff(func_def_19, type, 'uu$': $int > 'Int_int_fun$').
% 0.62/0.58 tff(func_def_20, type, 'fun_app$s': ('Int_num0_set_fun$' * $int) > 'Num0_set$').
% 0.62/0.58 tff(func_def_21, type, 'card$l': 'Nat_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_22, type, 'fun_app$y': ('Num1_set_int_fun$' * 'Num1_set$') > $int).
% 0.62/0.58 tff(func_def_23, type, 'top$e': 'Num1_set$').
% 0.62/0.58 tff(func_def_24, type, 'zero$': 'Rows$').
% 0.62/0.58 tff(func_def_25, type, 'collect$b': 'Literal_bool_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_26, type, 'of_nat$': 'Nat_int_fun$').
% 0.62/0.58 tff(func_def_27, type, 'fun_app$a': ('Int_int_bool_fun_fun$' * $int) > 'Int_bool_fun$').
% 0.62/0.58 tff(func_def_28, type, 'uuf$': 'Int_int_bool_fun_fun$').
% 0.62/0.58 tff(func_def_29, type, 'fun_app$v': ('Nat_set_int_fun$' * 'Nat_set$') > $int).
% 0.62/0.58 tff(func_def_30, type, 'top$r': 'Nat_option_set$').
% 0.62/0.58 tff(func_def_31, type, 'top$f': 'Nat_set$').
% 0.62/0.58 tff(func_def_32, type, 'fun_app$z': ('Nat_nat_fun$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_33, type, 'fun_app$k': ('Nat_rows_set_fun$' * 'Nat$') > 'Rows_set$').
% 0.62/0.58 tff(func_def_34, type, 'card$h': 'Num0_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_35, type, tltrue: tlbool).
% 0.62/0.58 tff(func_def_36, type, 'uub$': 'Nat_set$' > 'Nat_bool_fun$').
% 0.62/0.58 tff(func_def_37, type, 'fun_app$w': ('Literal_set_int_fun$' * 'Literal_set$') > $int).
% 0.62/0.58 tff(func_def_38, type, 'card$g': 'Literal_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_39, type, 'card$i': 'Unit_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_40, type, 'card$f': 'Nat_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_41, type, 'top$k': 'Num0_bool_fun$').
% 0.62/0.58 tff(func_def_42, type, 'top$g': 'Literal_set$').
% 0.62/0.58 tff(func_def_43, type, 'card$j': 'Num0_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_44, type, 'top$a': 'Rows_option_option_set$').
% 0.62/0.58 tff(func_def_45, type, 'fun_app$q': ('Int_nat_set_fun$' * $int) > 'Nat_set$').
% 0.62/0.58 tff(func_def_46, type, 'fun_app$m': ('Nat_literal_set_fun$' * 'Nat$') > 'Literal_set$').
% 0.62/0.58 tff(func_def_47, type, 'card$a': 'Rows_option_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_48, type, 'top$p': 'Num0_option_set$').
% 0.62/0.58 tff(func_def_49, type, 'card$k': 'Literal_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_50, type, 'uuc$': 'Literal_set$' > 'Literal_bool_fun$').
% 0.62/0.58 tff(func_def_51, type, 'uud$': 'Num0_set$' > 'Num0_bool_fun$').
% 0.62/0.58 tff(func_def_52, type, 'fun_app$h': ('Nat_int_fun$' * 'Nat$') > $int).
% 0.62/0.58 tff(func_def_53, type, 'top$b': 'Rows_option_set$').
% 0.62/0.58 tff(func_def_54, type, 'collect$d': 'Num1_bool_fun$' > 'Num1_set$').
% 0.62/0.58 tff(func_def_55, type, 'fun_app$r': ('Int_literal_set_fun$' * $int) > 'Literal_set$').
% 0.62/0.58 tff(func_def_56, type, 'top$i': 'Num1_bool_fun$').
% 0.62/0.58 tff(func_def_57, type, 'fun_app$u': ('Rows_set_int_fun$' * 'Rows_set$') > $int).
% 0.62/0.58 tff(func_def_58, type, 'top$n': 'Rows_bool_fun$').
% 0.62/0.58 tff(func_def_59, type, 'collect$': 'Rows_bool_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_60, type, 'top$l': 'Literal_bool_fun$').
% 0.62/0.58 tff(func_def_61, type, tlfalse: tlbool).
% 0.62/0.58 tff(func_def_62, type, 'nat$': $int > 'Nat$').
% 0.62/0.58 tff(func_def_63, type, 'top$d': 'Num1_option_set$').
% 0.62/0.58 tff(func_def_64, type, 'abs$': $int > 'Rows$').
% 0.62/0.58 tff(func_def_65, type, 'fun_app$x': ('Num0_set_int_fun$' * 'Num0_set$') > $int).
% 0.62/0.58 tff(func_def_66, type, 'card$c': 'Num1_option_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_67, type, 'card$d': 'Num1_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_68, type, 'fun_app$o': ('Nat_num1_set_fun$' * 'Nat$') > 'Num1_set$').
% 0.62/0.58 tff(func_def_69, type, 'top$m': 'Nat_bool_fun$').
% 0.62/0.58 tff(func_def_70, type, 'card$b': 'Rows_option_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_71, type, 'fun_app$i': ('Rows_rows_fun$' * 'Rows$') > 'Rows$').
% 0.62/0.58 tff(func_def_77, type, sK0: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_78, type, sK1: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_79, type, sK2: ('Rows_bool_fun$' * 'Rows_bool_fun$') > 'Rows$').
% 0.62/0.58 tff(func_def_80, type, sK3: ('Nat_bool_fun$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_81, type, sK4: ('Literal_bool_fun$' * 'Literal_bool_fun$') > 'Literal$').
% 0.62/0.58 tff(func_def_82, type, sK5: ('Num0_bool_fun$' * 'Num0_bool_fun$') > 'Num0$').
% 0.62/0.58 tff(func_def_83, type, sK6: ('Num1_bool_fun$' * 'Num1_bool_fun$') > 'Num1$').
% 0.62/0.58 tff(func_def_84, type, sK7: 'Nat$' > 'Nat$').
% 0.62/0.58 tff(func_def_85, type, sK8: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_86, type, sK9: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_87, type, sK10: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_88, type, sK11: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_89, type, sK12: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_90, type, sK13: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_91, type, sK14: 'Nat$' > 'Nat$').
% 0.62/0.58 tff(func_def_92, type, sK15: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_93, type, sK16: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_94, type, sK17: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_95, type, sK18: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_96, type, sK19: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_97, type, sK20: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_98, type, sK21: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_99, type, sK22: ('Nat$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_100, type, sK23: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_101, type, sK24: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_102, type, sK25: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_103, type, sK26: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_104, type, sK27: ('Nat$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_105, type, sK28: ('Nat$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_106, type, sK29: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_107, type, sK30: 'Nat_rows_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_108, type, sK31: 'Nat_nat_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_109, type, sK32: 'Nat_literal_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_110, type, sK33: 'Nat_num0_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_111, type, sK34: 'Nat_num1_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_112, type, sK35: 'Nat_int_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_113, type, sK36: 'Nat_rows_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_114, type, sK37: 'Nat_nat_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_115, type, sK38: 'Nat_literal_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_116, type, sK39: 'Nat_num0_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_117, type, sK40: 'Nat_num1_set_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_118, type, sK41: 'Nat_int_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_119, type, sK42: ('Nat$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_120, type, sK43: 'Nat$' > 'Nat$').
% 0.62/0.58 tff(func_def_121, type, sK44: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_122, type, sK45: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_123, type, sK46: 'Nat$' > 'Nat$').
% 0.62/0.58 tff(func_def_124, type, sK47: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_125, type, sK48: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_126, type, sK49: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_127, type, sK50: 'Nat$' > 'Nat$').
% 0.62/0.58 tff(func_def_128, type, sK51: $int > $int).
% 0.62/0.58 tff(func_def_129, type, sK52: $int > $int).
% 0.62/0.58 tff(func_def_130, type, sK53: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_131, type, sK54: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_132, type, sK55: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_133, type, sK56: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_134, type, sK57: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_135, type, sK58: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_136, type, sK59: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_137, type, sK60: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_138, type, sK61: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_139, type, sK62: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_140, type, sK63: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_141, type, sK64: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_142, type, sK65: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_143, type, sK66: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_144, type, sK67: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_145, type, sK68: 'Int_num1_set_fun$' > $int).
% 0.62/0.58 tff(func_def_146, type, sK69: 'Int_num1_set_fun$' > $int).
% 0.62/0.58 tff(func_def_147, type, sK70: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_148, type, sK71: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_149, type, sK72: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_150, type, sK73: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_151, type, sK74: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_152, type, sK75: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_153, type, sK76: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_154, type, sK77: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_155, type, sK78: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_156, type, sK79: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_157, type, sK80: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_158, type, sK81: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_159, type, sK82: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_160, type, sK83: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_161, type, sK84: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_162, type, sK85: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_163, type, sK86: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_164, type, sK87: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_165, type, sK88: 'Int_num1_set_fun$' > $int).
% 0.62/0.58 tff(func_def_166, type, sK89: 'Int_num1_set_fun$' > $int).
% 0.62/0.58 tff(func_def_167, type, sK90: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_168, type, sK91: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_169, type, sK92: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_170, type, sK93: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_171, type, sK94: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_172, type, sK95: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_173, type, sK96: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_174, type, sK97: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_175, type, sK98: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_176, type, sK99: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_177, type, sK100: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_178, type, sK101: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_179, type, sK102: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_180, type, sK103: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_181, type, sK104: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_182, type, sK105: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_183, type, sK106: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_184, type, sK107: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_185, type, sK108: 'Num1_set_int_fun$' > 'Num1_set$').
% 0.62/0.58 tff(func_def_186, type, sK109: 'Num1_set_int_fun$' > 'Num1_set$').
% 0.62/0.58 tff(func_def_187, type, sK110: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_188, type, sK111: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_189, type, sK112: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_190, type, sK113: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_191, type, sK114: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_192, type, sK115: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_193, type, sK116: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_194, type, sK117: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_195, type, sK118: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_196, type, sK119: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_197, type, sK120: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_198, type, sK121: 'Int_rows_set_fun$' > $int).
% 0.62/0.58 tff(func_def_199, type, sK122: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_200, type, sK123: 'Int_nat_set_fun$' > $int).
% 0.62/0.58 tff(func_def_201, type, sK124: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_202, type, sK125: 'Int_literal_set_fun$' > $int).
% 0.62/0.58 tff(func_def_203, type, sK126: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_204, type, sK127: 'Int_num0_set_fun$' > $int).
% 0.62/0.58 tff(func_def_205, type, sK128: 'Int_num1_set_fun$' > $int).
% 0.62/0.58 tff(func_def_206, type, sK129: 'Int_num1_set_fun$' > $int).
% 0.62/0.58 tff(func_def_207, type, sK130: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_208, type, sK131: 'Rows_set_int_fun$' > 'Rows_set$').
% 0.62/0.58 tff(func_def_209, type, sK132: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_210, type, sK133: 'Nat_set_int_fun$' > 'Nat_set$').
% 0.62/0.58 tff(func_def_211, type, sK134: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_212, type, sK135: 'Literal_set_int_fun$' > 'Literal_set$').
% 0.62/0.58 tff(func_def_213, type, sK136: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_214, type, sK137: 'Num0_set_int_fun$' > 'Num0_set$').
% 0.62/0.58 tff(func_def_215, type, sK138: 'Num1_set$' > 'Num1$').
% 0.62/0.58 tff(func_def_216, type, sK139: 'Num0_set$' > 'Num0$').
% 0.62/0.58 tff(func_def_217, type, sK140: 'Literal_set$' > 'Literal$').
% 0.62/0.58 tff(func_def_218, type, sK141: 'Nat_set$' > 'Nat$').
% 0.62/0.58 tff(func_def_219, type, sK142: 'Rows_set$' > 'Rows$').
% 0.62/0.58 tff(func_def_220, type, sK143: 'Num1$').
% 0.62/0.58 tff(func_def_221, type, sK144: 'Num0$').
% 0.62/0.58 tff(func_def_222, type, sK145: 'Literal$').
% 0.62/0.58 tff(func_def_223, type, sK146: 'Nat$').
% 0.62/0.58 tff(func_def_224, type, sK147: 'Rows$').
% 0.62/0.58 tff(func_def_225, type, sK148: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_226, type, sK149: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_227, type, sK150: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_228, type, sK151: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_229, type, sK152: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_230, type, sK153: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_231, type, sK154: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_232, type, sK155: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_233, type, sK156: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_234, type, sK157: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_235, type, sK158: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_236, type, sK159: 'Int_int_bool_fun_fun$' > $int).
% 0.62/0.58 tff(func_def_237, type, sK165: 'Nat_int_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_238, type, sK166: 'Nat_int_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_239, type, sK167: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_240, type, sK168: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_241, type, sK169: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_242, type, sK170: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_243, type, sK171: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_244, type, sK172: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_245, type, sK173: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_246, type, sK174: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_247, type, sK175: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_248, type, sK176: 'Int_int_fun$' > $int).
% 0.62/0.58 tff(func_def_249, type, sK177: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_250, type, sK178: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_251, type, sK179: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_252, type, sK180: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_253, type, sK181: 'Nat_nat_bool_fun_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_254, type, sK182: ('Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_255, type, sK183: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_256, type, sK184: 'Nat$' > 'Nat$').
% 0.62/0.58 tff(func_def_257, type, sK185: 'Nat_nat_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_258, type, sK186: 'Nat_nat_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_259, type, sK187: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_260, type, sK188: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_261, type, sK189: ('Nat$' * 'Nat$' * 'Nat_bool_fun$') > 'Nat$').
% 0.62/0.58 tff(func_def_262, type, sK190: ('Nat_bool_fun$' * 'Nat$') > 'Nat$').
% 0.62/0.58 tff(func_def_263, type, sK191: 'Nat_bool_fun$' > 'Nat$').
% 0.62/0.58 tff(func_def_264, type, sK192: $int > 'Nat$').
% 0.62/0.58 tff(func_def_265, type, sK193: ($int * 'Int_bool_fun$') > $int).
% 0.62/0.58 tff(func_def_266, type, sK194: ($int * 'Int_bool_fun$') > $int).
% 0.62/0.58 tff(func_def_267, type, sK195: $int > 'Nat$').
% 0.62/0.58 tff(func_def_268, type, sK196: $int > 'Nat$').
% 0.62/0.58 tff(func_def_269, type, sK197: $int > 'Nat$').
% 0.62/0.58 tff(func_def_270, type, sK198: $int > 'Nat$').
% 0.62/0.58 tff(func_def_271, type, sK199: $int > 'Nat$').
% 0.62/0.58 tff(func_def_272, type, sK200: ('Nat$' * 'Num1_set$') > 'Num1_set$').
% 0.62/0.58 tff(func_def_273, type, sK201: ('Nat$' * 'Num0_set$') > 'Num0_set$').
% 0.62/0.58 tff(func_def_274, type, sK202: ('Nat$' * 'Literal_set$') > 'Literal_set$').
% 0.62/0.58 tff(func_def_275, type, sK203: ('Nat$' * 'Nat_set$') > 'Nat_set$').
% 0.62/0.58 tff(func_def_276, type, sK204: ('Nat$' * 'Rows_set$') > 'Rows_set$').
% 0.62/0.58 tff(pred_def_1, type, 'less$e': ('Num1_bool_fun$' * 'Num1_bool_fun$') > $o).
% 0.62/0.58 tff(pred_def_2, type, 'less$c': ('Num0_set$' * 'Num0_set$') > $o).
% 0.62/0.58 tff(pred_def_3, type, 'less$': ('Rows_set$' * 'Rows_set$') > $o).
% 0.62/0.58 tff(pred_def_4, type, 'member$d': ('Rows$' * 'Rows_set$') > $o).
% 0.62/0.58 tff(pred_def_5, type, 'less_eq$d': ('Num1_set$' * 'Num1_set$') > $o).
% 0.62/0.58 tff(pred_def_6, type, 'fun_app$d': ('Num0_bool_fun$' * 'Num0$') > $o).
% 0.62/0.58 tff(pred_def_7, type, 'less$b': ('Literal_set$' * 'Literal_set$') > $o).
% 0.62/0.58 tff(pred_def_8, type, 'less$f': ('Num0_bool_fun$' * 'Num0_bool_fun$') > $o).
% 0.62/0.58 tff(pred_def_9, type, 'fun_app$c': ('Num1_bool_fun$' * 'Num1$') > $o).
% 0.62/0.58 tff(pred_def_10, type, 'less_eq$': ('Rows_set$' * 'Rows_set$') > $o).
% 0.62/0.58 tff(pred_def_11, type, 'less_eq$b': ('Literal_set$' * 'Literal_set$') > $o).
% 0.62/0.58 tff(pred_def_12, type, 'member$b': ('Literal$' * 'Literal_set$') > $o).
% 0.62/0.58 tff(pred_def_13, type, 'less$g': ('Literal_bool_fun$' * 'Literal_bool_fun$') > $o).
% 0.62/0.58 tff(pred_def_14, type, 'fun_app$': ('Int_bool_fun$' * $int) > $o).
% 0.62/0.58 tff(pred_def_15, type, 'member$c': ('Nat$' * 'Nat_set$') > $o).
% 0.62/0.58 tff(pred_def_16, type, 'less$h': ('Nat_bool_fun$' * 'Nat_bool_fun$') > $o).
% 0.62/0.58 tff(pred_def_17, type, 'less_eq$c': ('Num0_set$' * 'Num0_set$') > $o).
% 0.62/0.58 tff(pred_def_18, type, 'less$d': ('Num1_set$' * 'Num1_set$') > $o).
% 0.62/0.58 tff(pred_def_19, type, 'member$': ('Num1$' * 'Num1_set$') > $o).
% 0.62/0.58 tff(pred_def_21, type, 'less$i': ('Rows_bool_fun$' * 'Rows_bool_fun$') > $o).
% 0.62/0.58 tff(pred_def_22, type, 'less$a': ('Nat_set$' * 'Nat_set$') > $o).
% 0.62/0.58 tff(pred_def_23, type, 'fun_app$g': ('Rows_bool_fun$' * 'Rows$') > $o).
% 0.62/0.58 tff(pred_def_24, type, 'less_eq$a': ('Nat_set$' * 'Nat_set$') > $o).
% 0.62/0.58 tff(pred_def_25, type, 'member$a': ('Num0$' * 'Num0_set$') > $o).
% 0.62/0.58 tff(pred_def_26, type, 'fun_app$e': ('Literal_bool_fun$' * 'Literal$') > $o).
% 0.62/0.58 tff(pred_def_27, type, 'fun_app$f': ('Nat_bool_fun$' * 'Nat$') > $o).
% 0.62/0.58 tff(pred_def_30, type, sP160: ($int * $int * $int) > $o).
% 0.62/0.58 tff(pred_def_31, type, sP161: ($int * $int * $int) > $o).
% 0.62/0.58 tff(pred_def_32, type, sP162: ($int * $int * $int) > $o).
% 0.62/0.58 tff(pred_def_33, type, sP163: ($int * $int * $int) > $o).
% 0.62/0.58 tff(f8,conjecture,(
% 0.62/0.58 ($less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)) => $less(0,'fun_app$h'('of_nat$','card$'('top$')))) & (~$less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)) => $less($difference('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)),'fun_app$h'('of_nat$','card$'('top$'))))),
% 0.62/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture7)).
% 0.62/0.58 tff(f9,negated_conjecture,(
% 0.62/0.58 ~(($less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)) => $less(0,'fun_app$h'('of_nat$','card$'('top$')))) & (~$less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)) => $less($difference('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)),'fun_app$h'('of_nat$','card$'('top$')))))),
% 0.62/0.58 inference(negated_conjecture,[status(cth)],[f8])).
% 0.62/0.58 tff(f141,axiom,(
% 0.62/0.58 $less(0,'fun_app$h'('of_nat$','card$'('top$')))),
% 0.62/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139)).
% 0.62/0.58 tff(f566,axiom,(
% 0.62/0.58 ! [X0 : $int,X1 : $int] : ($lesseq(X0,$difference(X1,1)) <=> $less(X0,X1))),
% 0.62/0.58 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564)).
% 0.62/0.58 tff(f625,plain,(
% 0.62/0.58 ~(($less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)) => $less(0,'fun_app$h'('of_nat$','card$'('top$')))) & (~$less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)) => $less($sum('fun_app$h'('of_nat$','card$'('top$')),$uminus($sum(0,1))),'fun_app$h'('of_nat$','card$'('top$')))))),
% 0.62/0.58 inference(theory_normalization,[],[f9])).
% 0.62/0.58 tff(f796,plain,(
% 0.62/0.58 ! [X0 : $int,X1 : $int] : (~$less($sum(X1,$uminus(1)),X0) <=> $less(X0,X1))),
% 0.62/0.58 inference(theory_normalization,[],[f566])).
% 0.62/0.58 tff(f825,definition,(
% 0.62/0.58 ( ! [X0 : $int] : (~$less(X0,X0)) )),
% 0.62/0.58 introduced(theory,[tha_non-reflexivity])).
% 0.62/0.58 tff(f844,plain,(
% 0.62/0.58 (~$less(0,'fun_app$h'('of_nat$','card$'('top$'))) & $less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1))) | (~$less($sum('fun_app$h'('of_nat$','card$'('top$')),$uminus($sum(0,1))),'fun_app$h'('of_nat$','card$'('top$'))) & ~$less('fun_app$h'('of_nat$','card$'('top$')),$sum(0,1)))),
% 0.62/0.58 inference(ennf_transformation,[],[f625])).
% 0.62/0.58 tff(f1391,plain,(
% 0.62/0.58 ~$less($sum('fun_app$h'('of_nat$','card$'('top$')),$uminus($sum(0,1))),'fun_app$h'('of_nat$','card$'('top$'))) | ~$less(0,'fun_app$h'('of_nat$','card$'('top$')))),
% 0.62/0.58 inference(cnf_transformation,[],[f844])).
% 0.62/0.58 tff(f1678,plain,(
% 0.62/0.58 $less(0,'fun_app$h'('of_nat$','card$'('top$')))),
% 0.62/0.58 inference(cnf_transformation,[],[f141])).
% 0.62/0.58 tff(f2322,plain,(
% 0.62/0.58 ( ! [X0 : $int,X1 : $int] : ($less(X0,X1) | $less($sum(X1,$uminus(1)),X0)) )),
% 0.62/0.58 inference(cnf_transformation,[],[f796])).
% 0.62/0.58 tff(f2801,plain,(
% 0.62/0.58 ( ! [X0 : $int,X1 : $int] : ($less($sum(X1,-1),X0) | $less(X0,X1)) )),
% 0.62/0.58 inference(evaluation,[],[f2322])).
% 0.62/0.58 tff(f2867,plain,(
% 0.62/0.58 ~$less($sum('fun_app$h'('of_nat$','card$'('top$')),-1),'fun_app$h'('of_nat$','card$'('top$'))) | ~$less(0,'fun_app$h'('of_nat$','card$'('top$')))),
% 0.62/0.58 inference(evaluation,[],[f1391])).
% 0.62/0.58 tff(f3070,definition,(
% 0.62/0.58 spl205_46 <=> $less($sum('fun_app$h'('of_nat$','card$'('top$')),-1),'fun_app$h'('of_nat$','card$'('top$')))),
% 0.62/0.58 introduced(definition,[new_symbols(definition,[spl205_46])],[avatar_definition])).
% 0.62/0.58 tff(f3072,plain,(
% 0.62/0.58 ~$less($sum('fun_app$h'('of_nat$','card$'('top$')),-1),'fun_app$h'('of_nat$','card$'('top$'))) | spl205_46),
% 0.62/0.58 inference(avatar_component_clause,[],[f3070])).
% 0.62/0.58 tff(f3075,definition,(
% 0.62/0.58 spl205_47 <=> $less(0,'fun_app$h'('of_nat$','card$'('top$')))),
% 0.62/0.58 introduced(definition,[new_symbols(definition,[spl205_47])],[avatar_definition])).
% 0.62/0.58 tff(f3078,plain,(
% 0.62/0.58 ~spl205_47 | ~spl205_46),
% 0.62/0.58 inference(avatar_split_clause,[],[f2867,f3070,f3075])).
% 0.62/0.58 tff(f3089,plain,(
% 0.62/0.58 spl205_47),
% 0.62/0.58 inference(avatar_split_clause,[],[f1678,f3075])).
% 0.62/0.58 tff(f3337,plain,(
% 0.62/0.58 $less('fun_app$h'('of_nat$','card$'('top$')),'fun_app$h'('of_nat$','card$'('top$'))) | spl205_46),
% 0.62/0.58 inference(resolution,[],[f2801,f3072])).
% 0.62/0.58 tff(f3346,plain,(
% 0.62/0.58 $false | spl205_46),
% 0.62/0.58 inference(forward_subsumption_resolution,[],[f3337,f825])).
% 0.62/0.58 tff(f3347,plain,(
% 0.62/0.58 spl205_46),
% 0.62/0.58 inference(avatar_contradiction_clause,[],[f3346])).
% 0.62/0.58 cnf(s73, plain, ~spl205_46 | ~spl205_47, inference(sat_conversion,[],[f3078])).
% 0.62/0.58 cnf(s82, plain, spl205_47, inference(sat_conversion,[],[f3089])).
% 0.62/0.58 cnf(s106, plain, spl205_46, inference(sat_conversion,[],[f3347])).
% 0.62/0.58 cnf(s108, plain, $false, inference(rat,[],[s73,s82,s106])).
% 0.62/0.58 tff(f3348,plain,(
% 0.62/0.58 $false),
% 0.62/0.58 inference(avatar_sat_refutation,[],[s108])).
% 0.62/0.58 % SZS output end Proof for theBenchmark
% 0.62/0.58 % (1391276)------------------------------
% 0.62/0.58 % (1391276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.62/0.58 % (1391276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.58 % (1391276)CaDiCaL version: 2.1.3
% 0.62/0.58 % (1391276)Termination reason: Refutation
% 0.62/0.58 % (1391276)Time elapsed: 0.057 s
% 0.62/0.58 % (1391276)Peak memory usage: 15 MB
% 0.62/0.58 % (1391276)Instructions burned: 109 (million)
% 0.62/0.58 % (1391239)Success in time 0.14 s
% 0.62/0.58 % Vampire exiting
%------------------------------------------------------------------------------