%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP037^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:27 AM UTC 2026
% Result : Theorem 0.52s 0.26s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP037^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 19:39:48 UTC 2026
% 0.03/0.11 % CPUTime :
% 0.03/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.03/0.13 Running first-order model finding
% 0.03/0.13 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
% 0.52/0.26 % (583642)Will run a generic schedule for satisfiability detection.
% 0.52/0.26 % (583648)% WARNING: option uhcvi not known.
% 0.52/0.26 % (583648)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=198408126:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.52/0.26 % (583650)dis+10_1_sil=32000:sp=arity:random_seed=1435239968:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.52/0.26 % (583652)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2354851143:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.52/0.26 % (583653)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3276467251:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.52/0.26 % (583649)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3110278551:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.52/0.26 % (583647)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1161131956_2999 on theBenchmark for (2999ds/0Mi)
% 0.52/0.26 % (583648)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.52/0.26 % (583651)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4280907018:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.52/0.26 % (583648)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.52/0.26 % (583650)Instruction limit reached!
% 0.52/0.26 % (583650)------------------------------
% 0.52/0.26 % (583650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.26 % (583650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.26 % (583650)CaDiCaL version: 2.1.3
% 0.52/0.26 % (583650)Termination reason: Instruction limit
% 0.52/0.26 % (583650)Termination phase: Saturation
% 0.52/0.26 % (583650)Time elapsed: 0.025 s
% 0.52/0.26 % (583650)Peak memory usage: 12 MB
% 0.52/0.26 % (583650)Instructions burned: 106 (million)
% 0.52/0.26 % (583651)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.52/0.26 % (583652)Instruction limit reached!
% 0.52/0.26 % (583652)------------------------------
% 0.52/0.26 % (583652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.26 % (583652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.26 % (583652)CaDiCaL version: 2.1.3
% 0.52/0.26 % (583652)Termination reason: Instruction limit
% 0.52/0.26 % (583652)Termination phase: Saturation
% 0.52/0.26 % (583652)Time elapsed: 0.032 s
% 0.52/0.26 % (583652)Peak memory usage: 13 MB
% 0.52/0.26 % (583652)Instructions burned: 134 (million)
% 0.52/0.26 % (583661)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=670016573:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.52/0.26 % (583662)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3552988765:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.52/0.26 % Exception at run slice level
% 0.52/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.52/0.26 % (583653)Instruction limit reached!
% 0.52/0.26 % (583653)------------------------------
% 0.52/0.26 % (583653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.26 % (583653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.26 % (583653)CaDiCaL version: 2.1.3
% 0.52/0.26 % (583653)Termination reason: Instruction limit
% 0.52/0.26 % (583653)Termination phase: Saturation
% 0.52/0.26 % (583653)Time elapsed: 0.053 s
% 0.52/0.26 % (583653)Peak memory usage: 14 MB
% 0.52/0.26 % (583653)Instructions burned: 160 (million)
% 0.52/0.26 % Exception at run slice level
% 0.52/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.52/0.26 % (583666)ott-21_1_sil=16000:fs=off:random_seed=1871201202:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.52/0.26 % (583665)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=294609033:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.52/0.26 % (583651)Instruction limit reached!
% 0.52/0.26 % (583651)------------------------------
% 0.52/0.26 % (583651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.26 % (583651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.26 % (583651)CaDiCaL version: 2.1.3
% 0.52/0.26 % (583651)Termination reason: Instruction limit
% 0.52/0.26 % (583651)Termination phase: Saturation
% 0.52/0.26 % (583651)Time elapsed: 0.060 s
% 0.52/0.26 % (583651)Peak memory usage: 13 MB
% 0.52/0.26 % (583651)Instructions burned: 117 (million)
% 0.52/0.26 % (583667)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1405449938:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.52/0.26 % (583662)Instruction limit reached!
% 0.52/0.26 % (583662)------------------------------
% 0.52/0.26 % (583662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.26 % (583662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.26 % (583662)CaDiCaL version: 2.1.3
% 0.52/0.26 % (583662)Termination reason: Instruction limit
% 0.52/0.26 % (583662)Termination phase: Saturation
% 0.52/0.26 % (583662)Time elapsed: 0.031 s
% 0.52/0.26 % (583662)Peak memory usage: 13 MB
% 0.52/0.26 % (583662)Instructions burned: 132 (million)
% 0.52/0.26 % (583672)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1577940508:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.52/0.26 % (583648) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-583642-583648"...
% 0.52/0.26 % (583648)...printing done.
% 0.52/0.26 % (583648)Refutation found. Thanks to Tanya!
% 0.52/0.26 % SZS status Theorem for theBenchmark
% 0.52/0.26 % SZS output start Proof for theBenchmark
% 0.52/0.26 thf(type_def_5, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_6, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_7, type, frechet_strm: ($tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_8, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_9, type, product_unit: $tType).
% 0.52/0.26 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_11, type, formula: ($tType * $tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_12, type, sum_sum: ($tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_13, type, trm: ($tType * $tType) > $tType).
% 0.52/0.26 thf(type_def_14, type, real: $tType).
% 0.52/0.26 thf(type_def_15, type, list: $tType > $tType).
% 0.52/0.26 thf(type_def_16, type, set: $tType > $tType).
% 0.52/0.26 thf(type_def_17, type, sz: $tType).
% 0.52/0.26 thf(type_def_18, type, sf: $tType).
% 0.52/0.26 thf(type_def_19, type, sc: $tType).
% 0.52/0.26 thf(type_def_20, type, c: $tType).
% 0.52/0.26 thf(type_def_21, type, b: $tType).
% 0.52/0.26 thf(type_def_22, type, a: $tType).
% 0.52/0.26 thf(type_def_23, type, sTfun: ($tType * $tType) > $tType).
% 0.52/0.26 thf(func_def_0, type, cARD_1: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_3, type, top: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_4, type, finite_finite: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_6, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_7, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 0.52/0.26 thf(func_def_8, type, denotational_Vagree: !>[X0: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o))).
% 0.52/0.26 thf(func_def_9, type, denota2078997598vative: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > real))).
% 0.52/0.26 thf(func_def_10, type, denota594965758rm_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > real))).
% 0.52/0.26 thf(func_def_11, type, denotational_frechet: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2 > real))).
% 0.52/0.26 thf(func_def_12, type, denota2077489681interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 0.52/0.26 thf(func_def_13, type, freche457001096interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2 > $o))).
% 0.52/0.26 thf(func_def_14, type, frechet_cr_strm: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1 > $o))).
% 0.52/0.26 thf(func_def_15, type, freche227871258interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2))).
% 0.52/0.26 thf(func_def_16, type, freche229654227interp: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 0.52/0.26 thf(func_def_17, type, frechet_raw_term: !>[X0: $tType, X1: $tType]:((frechet_strm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_18, type, frechet_simple_term: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_19, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_20, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o))).
% 0.52/0.26 thf(func_def_21, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.52/0.26 thf(func_def_22, type, top_top: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_23, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.52/0.26 thf(func_def_24, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.52/0.26 thf(func_def_25, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.52/0.26 thf(func_def_26, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.52/0.26 thf(func_def_27, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.52/0.26 thf(func_def_28, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.52/0.26 thf(func_def_29, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.52/0.26 thf(func_def_30, type, domainp: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0 > $o))).
% 0.52/0.26 thf(func_def_31, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.52/0.26 thf(func_def_32, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.52/0.26 thf(func_def_33, type, static_FVDiff: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > set @ sum_sum @ X1 @ X1))).
% 0.52/0.26 thf(func_def_34, type, predicational: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > formula @ X1 @ X0 @ X2))).
% 0.52/0.26 thf(func_def_35, type, dfree: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > $o))).
% 0.52/0.26 thf(func_def_36, type, dsafe: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > $o))).
% 0.52/0.26 thf(func_def_37, type, ffree: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 0.52/0.26 thf(func_def_38, type, prop: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > (X0 > trm @ X1 @ X0) > formula @ X1 @ X2 @ X0))).
% 0.52/0.26 thf(func_def_39, type, set1_formula: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ X0))).
% 0.52/0.26 thf(func_def_40, type, p: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > formula @ X1 @ X0 @ X2))).
% 0.52/0.26 thf(func_def_41, type, empty: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_42, type, f0: !>[X0: $tType, X1: $tType]:((X0 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_43, type, f1: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_44, type, p1: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > formula @ X1 @ X2 @ X0))).
% 0.52/0.26 thf(func_def_45, type, singleton: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0 > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_46, type, singleton_rel: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > product_prod @ trm @ X0 @ X1 @ X1 > $o))).
% 0.52/0.26 thf(func_def_47, type, const: !>[X0: $tType, X1: $tType]:((real > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_48, type, diffVar: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_49, type, differential: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_50, type, function: !>[X0: $tType, X1: $tType]:((X0 > (X1 > trm @ X0 @ X1) > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_51, type, plus: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_52, type, times: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_53, type, var: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_54, type, set_trm: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > set @ X0))).
% 0.52/0.26 thf(func_def_55, type, left_unique: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > $o))).
% 0.52/0.26 thf(func_def_56, type, right_unique: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > $o))).
% 0.52/0.26 thf(func_def_57, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.52/0.26 thf(func_def_58, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.52/0.26 thf(func_def_59, type, i: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 0.52/0.26 thf(func_def_60, type, nu: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 0.52/0.26 thf(func_def_61, type, nu2: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 0.52/0.26 thf(func_def_62, type, args: (c > trm @ a @ c)).
% 0.52/0.26 thf(func_def_63, type, i2: c).
% 0.52/0.26 thf(func_def_64, type, var2: a).
% 0.52/0.26 thf(func_def_65, type, vid1: sz).
% 0.52/0.26 thf(func_def_66, type, vid2: sz).
% 0.52/0.26 thf(func_def_67, type, vid3: sz).
% 0.52/0.26 thf(func_def_71, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.52/0.26 thf(func_def_72, type, vAND: ($o > $o > $o)).
% 0.52/0.26 thf(func_def_73, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_74, type, db0: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_75, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.52/0.26 thf(func_def_76, type, vOR: ($o > $o > $o)).
% 0.52/0.26 thf(func_def_77, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_78, type, db1: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_79, type, db2: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_80, type, db3: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_81, type, vIMP: ($o > $o > $o)).
% 0.52/0.26 thf(func_def_82, type, sP0: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_83, type, sP1: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_84, type, sP2: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o))).
% 0.52/0.26 thf(func_def_85, type, sP3: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_86, type, sP4: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_87, type, sP5: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o))).
% 0.52/0.26 thf(func_def_88, type, sP6: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o))).
% 0.52/0.26 thf(func_def_89, type, sP7: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_90, type, sP8: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.52/0.26 thf(func_def_91, type, sP9: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > $o))).
% 0.52/0.26 thf(func_def_92, type, sP10: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > $o))).
% 0.52/0.26 thf(func_def_93, type, sP11: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > $o))).
% 0.52/0.26 thf(func_def_94, type, sK12: (product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > denota1663640101rp_ext @ sf @ sc @ sz @ product_unit)).
% 0.52/0.26 thf(func_def_95, type, sK13: (product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz)).
% 0.52/0.26 thf(func_def_96, type, sK14: !>[X0: $tType]:((product_prod @ trm @ X0 @ sz @ sz > trm @ X0 @ sz))).
% 0.52/0.26 thf(func_def_97, type, sK15: !>[X0: $tType]:((product_prod @ trm @ X0 @ sz @ sz > sz))).
% 0.52/0.26 thf(func_def_98, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > X1))).
% 0.52/0.26 thf(func_def_99, type, sK17: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_100, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.52/0.26 thf(func_def_101, type, sK19: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_102, type, sK20: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0))).
% 0.52/0.26 thf(func_def_103, type, sK21: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_104, type, sK22: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_105, type, sK23: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_106, type, sK24: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_107, type, sK25: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1))).
% 0.52/0.26 thf(func_def_108, type, sK26: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_109, type, sK27: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > real))).
% 0.52/0.26 thf(func_def_110, type, sK28: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0))).
% 0.52/0.26 thf(func_def_111, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.52/0.26 thf(func_def_112, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.52/0.26 thf(func_def_113, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.52/0.26 thf(func_def_114, type, sK32: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_115, type, sK33: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_116, type, sK34: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.52/0.26 thf(func_def_117, type, sK35: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.52/0.26 thf(func_def_118, type, sK36: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_119, type, sK37: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_120, type, sK38: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.52/0.26 thf(func_def_121, type, sK39: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.52/0.26 thf(func_def_122, type, sK40: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_123, type, sK41: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_124, type, sK42: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_125, type, sK43: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_126, type, sK44: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_127, type, sK45: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_128, type, sK46: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > real))).
% 0.52/0.26 thf(func_def_129, type, sK47: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_130, type, sK48: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_131, type, sK49: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_132, type, sK50: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_133, type, sK51: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_134, type, sK52: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_135, type, sK53: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1))).
% 0.52/0.26 thf(func_def_136, type, sK54: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > real))).
% 0.52/0.26 thf(func_def_137, type, sK55: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0))).
% 0.52/0.26 thf(func_def_138, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 0.52/0.26 thf(func_def_139, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.52/0.26 thf(func_def_140, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.52/0.26 thf(func_def_141, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.52/0.26 thf(func_def_142, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.52/0.26 thf(func_def_143, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_144, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_145, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.52/0.26 thf(func_def_146, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.52/0.26 thf(func_def_147, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.52/0.26 thf(func_def_148, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.52/0.26 thf(func_def_149, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_150, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_151, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.52/0.26 thf(func_def_152, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.52/0.26 thf(func_def_153, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.52/0.26 thf(func_def_154, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_155, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_156, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.52/0.26 thf(func_def_157, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.52/0.26 thf(func_def_158, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_159, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_160, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.52/0.26 thf(func_def_161, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_162, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_163, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 0.52/0.26 thf(func_def_164, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 0.52/0.26 thf(func_def_165, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 0.52/0.26 thf(func_def_166, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 0.52/0.26 thf(func_def_167, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 0.52/0.26 thf(func_def_168, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 0.52/0.26 thf(func_def_169, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 0.52/0.26 thf(func_def_170, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 0.52/0.26 thf(func_def_171, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 0.52/0.26 thf(func_def_172, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 0.52/0.26 thf(func_def_173, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 0.52/0.26 thf(func_def_174, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 0.52/0.26 thf(func_def_175, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 0.52/0.26 thf(func_def_176, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 0.52/0.26 thf(func_def_177, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 0.52/0.26 thf(func_def_178, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 0.52/0.26 thf(func_def_179, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 0.52/0.26 thf(func_def_180, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 0.52/0.26 thf(func_def_181, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 0.52/0.26 thf(func_def_182, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 0.52/0.26 thf(func_def_183, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 0.52/0.26 thf(func_def_184, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 0.52/0.26 thf(func_def_185, type, sK103: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_186, type, sK104: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_187, type, sK105: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_188, type, sK106: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_189, type, sK107: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_190, type, sK108: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_191, type, sK109: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_192, type, sK110: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_193, type, sK111: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > real))).
% 0.52/0.26 thf(func_def_194, type, sK112: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_195, type, sK113: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_196, type, sK114: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_197, type, sK115: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_198, type, sK116: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_199, type, sK117: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1))).
% 0.52/0.26 thf(func_def_200, type, sK118: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_201, type, sK119: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_202, type, sK120: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0))).
% 0.52/0.26 thf(func_def_203, type, sK121: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > real))).
% 0.52/0.26 thf(func_def_204, type, sK122: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1))).
% 0.52/0.26 thf(func_def_205, type, sK123: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_206, type, sK124: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_207, type, sK125: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_208, type, sK126: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_209, type, sK127: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_210, type, sK128: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_211, type, sK129: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > X1))).
% 0.52/0.26 thf(func_def_212, type, sK130: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_213, type, sK131: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.52/0.26 thf(func_def_214, type, sK132: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_215, type, sK133: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_216, type, sK134: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_217, type, sK135: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_218, type, sK136: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_219, type, sK137: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_220, type, sK138: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_221, type, sK139: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_222, type, sK140: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > real))).
% 0.52/0.26 thf(func_def_223, type, sK141: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_224, type, sK142: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 0.52/0.26 thf(func_def_225, type, sK143: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 0.52/0.26 thf(func_def_226, type, sK144: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_227, type, sK145: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > X1))).
% 0.52/0.26 thf(func_def_228, type, sK146: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > $o) > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 0.52/0.26 thf(func_def_229, type, sK147: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > $o) > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 0.52/0.26 thf(func_def_230, type, sK148: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_231, type, sK149: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > X1))).
% 0.52/0.26 thf(func_def_232, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit @ X2 > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit))).
% 0.52/0.26 thf(func_def_233, type, sK151: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit @ X2 > X2))).
% 0.52/0.26 thf(func_def_234, type, sK152: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.52/0.26 thf(func_def_235, type, sK153: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 0.52/0.26 thf(func_def_236, type, sK154: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 0.52/0.26 thf(func_def_237, type, sK155: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.52/0.26 thf(func_def_238, type, sK156: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 0.52/0.26 thf(func_def_239, type, sK157: !>[X0: $tType]:((set @ X0 > X0))).
% 0.52/0.26 thf(func_def_240, type, sK158: !>[X0: $tType]:(X0)).
% 0.52/0.26 thf(func_def_241, type, sK159: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > $o) > X1))).
% 0.52/0.26 thf(func_def_242, type, sK160: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > $o) > X1))).
% 0.52/0.26 thf(func_def_243, type, sK161: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_244, type, sK162: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_245, type, sK163: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_246, type, sK164: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_247, type, sK165: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_248, type, sK166: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_249, type, sK167: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_250, type, sK168: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_251, type, sK169: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_252, type, sK170: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_253, type, sK171: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_254, type, sK172: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_255, type, sK173: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > X1))).
% 0.52/0.26 thf(func_def_256, type, sK174: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_257, type, sK175: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_258, type, sK176: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_259, type, sK177: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_260, type, sK178: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_261, type, sK179: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_262, type, sK180: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_263, type, sK181: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > X0 > trm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_264, type, sK182: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.52/0.26 thf(func_def_265, type, sK183: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.52/0.26 thf(func_def_266, type, sK184: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 0.52/0.26 thf(func_def_267, type, sK185: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > trm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_268, type, sK186: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 0.52/0.26 thf(func_def_269, type, sK187: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 0.52/0.26 thf(func_def_270, type, vNOT: ($o > $o)).
% 0.52/0.26 thf(func_def_271, type, sK188: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.52/0.26 thf(func_def_272, type, sK189: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.52/0.26 thf(func_def_273, type, sK190: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_274, type, sK191: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_275, type, sK192: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.52/0.26 thf(func_def_276, type, sK193: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.52/0.26 thf(func_def_277, type, sK194: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.52/0.26 thf(func_def_278, type, sK195: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 0.52/0.26 thf(func_def_279, type, sK196: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0 > $o) > X0))).
% 0.52/0.26 thf(func_def_280, type, sK197: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 0.52/0.26 thf(func_def_281, type, sK198: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 0.52/0.26 thf(func_def_282, type, sK199: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.52/0.26 thf(func_def_283, type, sK200: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_284, type, sK201: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > X1))).
% 0.52/0.26 thf(func_def_285, type, sK202: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_286, type, sK203: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_287, type, sK204: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_288, type, sK205: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_289, type, sK206: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_290, type, sK207: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_291, type, sK208: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_292, type, sK209: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_293, type, sK210: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_294, type, sK211: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_295, type, sK212: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_296, type, sK213: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_297, type, sK214: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_298, type, sK215: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_299, type, sK216: !>[X0: $tType, X1: $tType]:((X0 > (trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_300, type, sK217: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_301, type, sK218: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_302, type, sK219: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_303, type, sK220: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_304, type, sK221: !>[X0: $tType, X1: $tType]:((real > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_305, type, sK222: !>[X0: $tType, X1: $tType]:((real > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_306, type, sK223: !>[X0: $tType, X1: $tType]:((X1 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_307, type, sK224: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_308, type, sK225: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_309, type, sK226: !>[X0: $tType, X1: $tType]:((X0 > (X1 > trm @ X0 @ X1) > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_310, type, sK227: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > X1 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_311, type, sK228: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > X1))).
% 0.52/0.26 thf(func_def_312, type, sK229: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > X0 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_313, type, sK230: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_314, type, sK231: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_315, type, sK232: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_316, type, sK233: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_317, type, sK234: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_318, type, sK235: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0 > frechet_strm @ X1 @ X0))).
% 0.52/0.26 thf(func_def_319, type, sK236: !>[X0: $tType, X1: $tType]:((X1 > frechet_strm @ X0 @ X1))).
% 0.52/0.26 thf(func_def_320, type, sK237: (c > frechet_strm @ a @ c)).
% 0.52/0.26 thf(func_def_322, type, sK239: !>[X0: $tType]:((X0 > X0))).
% 0.52/0.26 thf(f1,axiom,(
% 0.52/0.26 ! [X8 : c] : (dfree @ a @ c @ (args @ X8))),
% 0.52/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_free)).
% 0.52/0.26 thf(f5,axiom,(
% 0.52/0.26 ! [X0 : $tType,X1 : $tType] : (((domainp @ trm @ X1 @ X0 @ frechet_strm @ X1 @ X0 @ frechet_cr_strm @ X1 @ X0)) = dfree @ X1 @ X0)),
% 0.52/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_strm_Odomain)).
% 0.52/0.26 thf(f175,axiom,(
% 0.52/0.26 ! [X0 : $tType,X1 : $tType] : (domainp @ X1 @ X0 = (^[X2 : (X1 > X0 > $o), X3 : X1] : (? [X4 : X0] : (X2 @ X3 @ X4))))),
% 0.52/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Domainp__iff)).
% 0.52/0.26 thf(f288,conjecture,(
% 0.52/0.26 (dfree @ a @ c @ (args @ i2))),
% 0.52/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.52/0.26 thf(f289,negated_conjecture,(
% 0.52/0.26 ~(dfree @ a @ c @ (args @ i2))),
% 0.52/0.26 inference(negated_conjecture,[status(cth)],[f288])).
% 0.52/0.26 thf(f290,plain,(
% 0.52/0.26 ! [X0 : c] : (dfree @ a @ c @ (args @ X0))),
% 0.52/0.26 inference(rectify,[],[f1])).
% 0.52/0.26 thf(f291,plain,(
% 0.52/0.26 ! [X0 : c] : (((dfree @ a @ c @ (args @ X0))) = $true)),
% 0.52/0.26 inference(fool_elimination,[],[f290])).
% 0.52/0.26 thf(f513,plain,(
% 0.52/0.26 ! [X0 : $tType,X1 : $tType] : (domainp @ X1 @ X0 = (^[X2 : (X1 > X0 > $o), X3 : X1] : (? [X4 : X0] : (X2 @ X3 @ X4))))),
% 0.52/0.26 inference(rectify,[],[f175])).
% 0.52/0.26 thf(f514,plain,(
% 0.52/0.26 ! [X0 : $tType,X1 : $tType] : (domainp @ X1 @ X0 = (^[Y0 : X1 > X0 > $o]: ((^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: (Y0 @ Y1 @ Y2)))))))),
% 0.52/0.26 inference(fool_elimination,[],[f513])).
% 0.52/0.26 thf(f674,plain,(
% 0.52/0.26 ~(dfree @ a @ c @ (args @ i2))),
% 0.52/0.26 inference(rectify,[],[f289])).
% 0.52/0.26 thf(f675,plain,(
% 0.52/0.26 ~ (((dfree @ a @ c @ (args @ i2))) = $true)),
% 0.52/0.26 inference(fool_elimination,[],[f674])).
% 0.52/0.26 thf(f687,plain,(
% 0.52/0.26 (((dfree @ a @ c @ (args @ i2))) != $true)),
% 0.52/0.26 inference(flattening,[],[f675])).
% 0.52/0.26 thf(f1028,plain,(
% 0.52/0.26 ( ! [X0 : c] : ((((dfree @ a @ c @ (args @ X0))) = $true)) )),
% 0.52/0.26 inference(cnf_transformation,[],[f291])).
% 0.52/0.26 thf(f1032,plain,(
% 0.52/0.26 ( ! [X1 : $tType,X0 : $tType] : ((((domainp @ trm @ X1 @ X0 @ frechet_strm @ X1 @ X0 @ frechet_cr_strm @ X1 @ X0)) = dfree @ X1 @ X0)) )),
% 0.52/0.26 inference(cnf_transformation,[],[f5])).
% 0.52/0.26 thf(f1261,plain,(
% 0.52/0.26 ( ! [X1 : $tType,X0 : $tType] : ((domainp @ X1 @ X0 = (^[Y0 : X1 > X0 > $o]: ((^[Y1 : X1]: (?? @ X0 @ (^[Y2 : X0]: (Y0 @ Y1 @ Y2)))))))) )),
% 0.52/0.26 inference(cnf_transformation,[],[f514])).
% 0.52/0.26 thf(f1403,plain,(
% 0.52/0.26 (((dfree @ a @ c @ (args @ i2))) != $true)),
% 0.52/0.26 inference(cnf_transformation,[],[f687])).
% 0.52/0.26 thf(f1406,plain,(
% 0.52/0.26 ( ! [X1 : $tType,X0 : $tType] : ((dfree @ X1 @ X0 = (((^[Y0 : trm @ X1 @ X0 > frechet_strm @ X1 @ X0 > $o]: ((^[Y1 : trm @ X1 @ X0]: (?? @ frechet_strm @ X1 @ X0 @ (^[Y2 : frechet_strm @ X1 @ X0]: (Y0 @ Y1 @ Y2)))))) @ frechet_cr_strm @ X1 @ X0)))) )),
% 0.52/0.26 inference(definition_unfolding,[],[f1032,f1261])).
% 0.52/0.26 thf(f1407,plain,(
% 0.52/0.26 ( ! [X0 : c] : (($true = (((^[Y0 : trm @ a @ c > frechet_strm @ a @ c > $o]: ((^[Y1 : trm @ a @ c]: (?? @ frechet_strm @ a @ c @ (^[Y2 : frechet_strm @ a @ c]: (Y0 @ Y1 @ Y2)))))) @ frechet_cr_strm @ a @ c @ (args @ X0))))) )),
% 0.52/0.26 inference(definition_unfolding,[],[f1028,f1406])).
% 0.52/0.26 thf(f1484,plain,(
% 0.52/0.26 ($true != (((^[Y0 : trm @ a @ c > frechet_strm @ a @ c > $o]: ((^[Y1 : trm @ a @ c]: (?? @ frechet_strm @ a @ c @ (^[Y2 : frechet_strm @ a @ c]: (Y0 @ Y1 @ Y2)))))) @ frechet_cr_strm @ a @ c @ (args @ i2))))),
% 0.52/0.26 inference(definition_unfolding,[],[f1403,f1406])).
% 0.52/0.26 thf(f1511,plain,(
% 0.52/0.26 ($true != ((?? @ frechet_strm @ a @ c @ (frechet_cr_strm @ a @ c @ (args @ i2)))))),
% 0.52/0.26 inference(beta-eta_normalization,[],[f1484])).
% 0.52/0.26 thf(f1512,plain,(
% 0.52/0.26 ( ! [X1 : frechet_strm @ a @ c] : (($false = ((frechet_cr_strm @ a @ c @ (args @ i2) @ X1)))) )),
% 0.52/0.26 inference(pi_proxy_clausification,[],[f1511])).
% 0.52/0.26 thf(f2033,plain,(
% 0.52/0.26 ( ! [X0 : c] : (($true = ((?? @ frechet_strm @ a @ c @ (frechet_cr_strm @ a @ c @ (args @ X0)))))) )),
% 0.52/0.26 inference(beta-eta_normalization,[],[f1407])).
% 0.52/0.26 thf(f2034,plain,(
% 0.52/0.26 ( ! [X0 : c] : (($true = ((frechet_cr_strm @ a @ c @ (args @ X0) @ (sK237 @ X0))))) )),
% 0.52/0.26 inference(sigma_proxy_clausification,[],[f2033])).
% 0.52/0.26 thf(f4665,plain,(
% 0.52/0.26 ($true = $false)),
% 0.52/0.26 inference(constrained_superposition,[],[f1512,f2034])).
% 0.52/0.26 thf(f4668,plain,(
% 0.52/0.26 $false),
% 0.52/0.26 inference(trivial_inequality_removal,[],[f4665])).
% 0.52/0.26 % SZS output end Proof for theBenchmark
% 0.52/0.26 % (583648)------------------------------
% 0.52/0.26 % (583648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.26 % (583648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.26 % (583648)CaDiCaL version: 2.1.3
% 0.52/0.26 % (583648)Termination reason: Refutation
% 0.52/0.26 % (583648)Time elapsed: 0.089 s
% 0.52/0.26 % (583648)Peak memory usage: 14 MB
% 0.52/0.26 % (583648)Instructions burned: 260 (million)
% 0.52/0.26 % (583642)Success in time 0.123 s
% 0.52/0.26 % Vampire exiting
%------------------------------------------------------------------------------