%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP142^2 : 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 : n015.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 08:10:52 AM UTC 2026
% Result : Theorem 1.22s 0.55s
% Output : Refutation 1.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP142^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 % Computer : n015.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 20:03:03 UTC 2026
% 0.08/0.23 % CPUTime :
% 0.08/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.28 Running first-order model finding
% 0.08/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.22/0.55 % (4042950)Will run a generic schedule for satisfiability detection.
% 1.22/0.55 % (4042955)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3932125_2999 on theBenchmark for (2999ds/0Mi)
% 1.22/0.55 % (4042956)% WARNING: option uhcvi not known.
% 1.22/0.55 % (4042959)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=845619454:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.22/0.55 % (4042958)dis+10_1_sil=32000:sp=arity:random_seed=2189029629:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.22/0.55 % (4042956)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=683992514:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.22/0.55 % (4042960)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3437696720:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.22/0.55 % (4042961)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1067674439:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.22/0.55 % (4042957)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1947761101:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.22/0.55 % (4042959)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.22/0.55 % Exception at run slice level
% 1.22/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.22/0.55 % (4042956)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.22/0.55 % (4042969)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2330819208:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.22/0.55 % (4042958)Instruction limit reached!
% 1.22/0.55 % (4042958)------------------------------
% 1.22/0.55 % (4042958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (4042958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (4042958)CaDiCaL version: 2.1.3
% 1.22/0.55 % (4042958)Termination reason: Instruction limit
% 1.22/0.55 % (4042958)Termination phase: Property scanning
% 1.22/0.55 % (4042958)Time elapsed: 0.081 s
% 1.22/0.55 % (4042958)Peak memory usage: 11 MB
% 1.22/0.55 % (4042958)Instructions burned: 103 (million)
% 1.22/0.55 % (4042959)Instruction limit reached!
% 1.22/0.55 % (4042959)------------------------------
% 1.22/0.55 % (4042959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (4042959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (4042959)CaDiCaL version: 2.1.3
% 1.22/0.55 % (4042959)Termination reason: Instruction limit
% 1.22/0.55 % (4042959)Termination phase: Property scanning
% 1.22/0.55 % (4042959)Time elapsed: 0.091 s
% 1.22/0.55 % (4042959)Peak memory usage: 12 MB
% 1.22/0.55 % (4042959)Instructions burned: 118 (million)
% 1.22/0.55 % (4042960)Instruction limit reached!
% 1.22/0.55 % (4042960)------------------------------
% 1.22/0.55 % (4042960)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (4042960)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (4042960)CaDiCaL version: 2.1.3
% 1.22/0.55 % (4042960)Termination reason: Instruction limit
% 1.22/0.55 % (4042960)Termination phase: Property scanning
% 1.22/0.55 % (4042960)Time elapsed: 0.103 s
% 1.22/0.55 % (4042960)Peak memory usage: 12 MB
% 1.22/0.55 % (4042960)Instructions burned: 131 (million)
% 1.22/0.55 % (4042956)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.22/0.55 % (4042971)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=594484843:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.22/0.55 % (4042972)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=431058781:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.22/0.55 % (4042961)Instruction limit reached!
% 1.22/0.55 % (4042961)------------------------------
% 1.22/0.55 % (4042961)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (4042961)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (4042961)CaDiCaL version: 2.1.3
% 1.22/0.55 % (4042961)Termination reason: Instruction limit
% 1.22/0.55 % (4042961)Termination phase: Saturation
% 1.22/0.55 % (4042961)Time elapsed: 0.125 s
% 1.22/0.55 % (4042961)Peak memory usage: 13 MB
% 1.22/0.55 % (4042961)Instructions burned: 159 (million)
% 1.22/0.55 % Exception at run slice level
% 1.22/0.55 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.22/0.55 % (4042973)ott-21_1_sil=16000:fs=off:random_seed=2817998425:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.22/0.55 % (4042977)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3197089111:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.22/0.55 % (4042976)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3652926691:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 1.22/0.55 % (4042957) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4042950-4042957"...
% 1.22/0.55 % (4042972)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.22/0.55 % (4042957)...printing done.
% 1.22/0.55 % (4042957)Refutation found. Thanks to Tanya!
% 1.22/0.55 % SZS status Theorem for theBenchmark
% 1.22/0.55 % SZS output start Proof for theBenchmark
% 1.22/0.55 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 1.22/0.55 thf(type_def_6, type, state: $tType).
% 1.22/0.55 thf(type_def_7, type, com: $tType).
% 1.22/0.55 thf(type_def_8, type, list: $tType > $tType).
% 1.22/0.55 thf(type_def_9, type, set: $tType > $tType).
% 1.22/0.55 thf(type_def_10, type, nat: $tType).
% 1.22/0.55 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 1.22/0.55 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 1.22/0.55 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 1.22/0.55 thf(func_def_2, type, linorder: !>[X0: $tType]:($o)).
% 1.22/0.55 thf(func_def_3, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_4, type, bind: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > list @ X1) > list @ X1))).
% 1.22/0.55 thf(func_def_5, type, butlast: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_6, type, concat: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_7, type, insert: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_8, type, last: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_9, type, lenlex: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 1.22/0.55 thf(func_def_10, type, lex: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 1.22/0.55 thf(func_def_11, type, lexord: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 1.22/0.55 thf(func_def_12, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_13, type, nil: !>[X0: $tType]:(list @ X0)).
% 1.22/0.55 thf(func_def_14, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 1.22/0.55 thf(func_def_15, type, list_update: !>[X0: $tType]:((list @ X0 > nat > X0 > list @ X0))).
% 1.22/0.55 thf(func_def_16, type, listrel: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ list @ X0 @ list @ X1))).
% 1.22/0.55 thf(func_def_17, type, listrel1: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ list @ X0 @ list @ X0))).
% 1.22/0.55 thf(func_def_18, type, maps: !>[X0: $tType, X1: $tType]:(((X0 > list @ X1) > list @ X0 > list @ X1))).
% 1.22/0.55 thf(func_def_19, type, measures: !>[X0: $tType]:((list @ (X0 > nat) > set @ product_prod @ X0 @ X0))).
% 1.22/0.55 thf(func_def_20, type, nth: !>[X0: $tType]:((list @ X0 > nat > X0))).
% 1.22/0.55 thf(func_def_21, type, product_lists: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_22, type, rotate1: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_23, type, subseqs: !>[X0: $tType]:((list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_24, type, take: !>[X0: $tType]:((nat > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_25, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 1.22/0.55 thf(func_def_26, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_27, type, pHoare1053570893_exec1: set @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state).
% 1.22/0.55 thf(func_def_28, type, pHoare1053570959_execs: (state > list @ com > state > $o)).
% 1.22/0.55 thf(func_def_29, type, pHoare1335526537termis: (list @ com > state > $o)).
% 1.22/0.55 thf(func_def_30, type, cond: ((state > $o) > com > com > com)).
% 1.22/0.55 thf(func_def_31, type, do: ((state > set @ state) > com)).
% 1.22/0.55 thf(func_def_32, type, semi: (com > com > com)).
% 1.22/0.55 thf(func_def_33, type, while: ((state > $o) > com > com)).
% 1.22/0.55 thf(func_def_34, type, exec: (state > com > state > $o)).
% 1.22/0.55 thf(func_def_35, type, termi: (com > state > $o)).
% 1.22/0.55 thf(func_def_36, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 1.22/0.55 thf(func_def_37, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.22/0.55 thf(func_def_38, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.22/0.55 thf(func_def_39, type, irrefl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 1.22/0.55 thf(func_def_40, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.22/0.55 thf(func_def_41, type, transitive_rtrancl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0))).
% 1.22/0.55 thf(func_def_42, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.22/0.55 thf(func_def_43, type, c: com).
% 1.22/0.55 thf(func_def_44, type, c2: com).
% 1.22/0.55 thf(func_def_45, type, cs: list @ com).
% 1.22/0.55 thf(func_def_46, type, s: state).
% 1.22/0.55 thf(func_def_47, type, s2: state).
% 1.22/0.55 thf(func_def_51, type, vAND: ($o > $o > $o)).
% 1.22/0.55 thf(func_def_52, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.22/0.55 thf(func_def_53, type, vIMP: ($o > $o > $o)).
% 1.22/0.55 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.22/0.55 thf(func_def_56, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_57, type, vNOT: ($o > $o)).
% 1.22/0.55 thf(func_def_58, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.22/0.55 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_60, type, vOR: ($o > $o > $o)).
% 1.22/0.55 thf(func_def_61, type, db3: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_63, type, db7: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_64, type, db6: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_65, type, db5: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_66, type, db4: !>[X0: $tType]:(X0)).
% 1.22/0.55 thf(func_def_67, type, sP0: (com > list @ com > list @ com > state > (state > $o) > state > $o)).
% 1.22/0.55 thf(func_def_68, type, sP1: (list @ com > list @ com > state > (state > $o) > state > $o)).
% 1.22/0.55 thf(func_def_69, type, sK2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 1.22/0.55 thf(func_def_70, type, sK3: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 1.22/0.55 thf(func_def_71, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 1.22/0.55 thf(func_def_72, type, sK5: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 1.22/0.55 thf(func_def_73, type, sK6: !>[X0: $tType, X1: $tType]:((set @ product_prod @ product_prod @ X1 @ X0 @ product_prod @ X1 @ X0 > X0 > X1 > X0 > X1 > X1))).
% 1.22/0.55 thf(func_def_74, type, sK7: !>[X0: $tType, X1: $tType]:((set @ product_prod @ product_prod @ X1 @ X0 @ product_prod @ X1 @ X0 > X0 > X1 > X0 > X1 > X0))).
% 1.22/0.55 thf(func_def_75, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 1.22/0.55 thf(func_def_76, type, sK9: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 1.22/0.55 thf(func_def_77, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X0))).
% 1.22/0.55 thf(func_def_78, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1 > X1 > X0 > X1))).
% 1.22/0.55 thf(func_def_79, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 1.22/0.55 thf(func_def_80, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 1.22/0.55 thf(func_def_81, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 1.22/0.55 thf(func_def_82, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 1.22/0.55 thf(func_def_83, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 1.22/0.55 thf(func_def_84, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 1.22/0.55 thf(func_def_85, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 1.22/0.55 thf(func_def_86, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 1.22/0.55 thf(func_def_87, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 1.22/0.55 thf(func_def_88, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 1.22/0.55 thf(func_def_89, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 1.22/0.55 thf(func_def_90, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 1.22/0.55 thf(func_def_91, type, sK24: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1))).
% 1.22/0.55 thf(func_def_92, type, sK25: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0))).
% 1.22/0.55 thf(func_def_93, type, sK26: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0))).
% 1.22/0.55 thf(func_def_94, type, sK27: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_95, type, sK28: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1))).
% 1.22/0.55 thf(func_def_96, type, sK29: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_97, type, sK30: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1 > X0))).
% 1.22/0.55 thf(func_def_98, type, sK31: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1 > X0))).
% 1.22/0.55 thf(func_def_99, type, sK32: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1))).
% 1.22/0.55 thf(func_def_100, type, sK33: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1))).
% 1.22/0.55 thf(func_def_101, type, sK34: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_102, type, sK35: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1 > X0))).
% 1.22/0.55 thf(func_def_103, type, sK36: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1))).
% 1.22/0.55 thf(func_def_104, type, sK37: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_105, type, sK38: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_106, type, sK39: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_107, type, sK40: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_108, type, sK41: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_109, type, sK42: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_110, type, sK43: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_111, type, sK44: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_112, type, sK45: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_113, type, sK46: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_114, type, sK47: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_115, type, sK48: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_116, type, sK49: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_117, type, sK50: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_118, type, sK51: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_119, type, sK52: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_120, type, sK53: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_121, type, sK54: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_122, type, sK55: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_123, type, sK56: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_124, type, sK57: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_125, type, sK58: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.22/0.55 thf(func_def_126, type, sK59: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_127, type, sK60: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.22/0.55 thf(func_def_128, type, sK61: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.22/0.55 thf(func_def_129, type, sK62: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.22/0.55 thf(func_def_130, type, sK63: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_131, type, sK64: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.22/0.55 thf(func_def_132, type, sK65: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.22/0.55 thf(func_def_133, type, sK66: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_134, type, sK67: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_135, type, sK68: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_136, type, sK69: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_137, type, sK70: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1))).
% 1.22/0.55 thf(func_def_138, type, sK71: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0))).
% 1.22/0.55 thf(func_def_139, type, sK72: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_140, type, sK73: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_141, type, sK74: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1))).
% 1.22/0.55 thf(func_def_142, type, sK75: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_143, type, sK76: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_144, type, sK77: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_145, type, sK78: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_146, type, sK79: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_147, type, sK80: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_148, type, sK81: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_149, type, sK82: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_150, type, sK83: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_151, type, sK84: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_152, type, sK85: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_153, type, sK86: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 1.22/0.55 thf(func_def_154, type, sK87: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 1.22/0.55 thf(func_def_155, type, sK88: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 1.22/0.55 thf(func_def_156, type, sK89: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 1.22/0.55 thf(func_def_157, type, sK90: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_158, type, sK91: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 1.22/0.55 thf(func_def_159, type, sK92: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 1.22/0.55 thf(func_def_160, type, sK93: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_161, type, sK94: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_162, type, sK95: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_163, type, sK96: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_164, type, sK97: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_165, type, sK98: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_166, type, sK99: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_167, type, sK100: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 1.22/0.55 thf(func_def_168, type, sK101: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_169, type, sK102: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_170, type, sK103: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_171, type, sK104: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_172, type, sK105: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 1.22/0.55 thf(func_def_173, type, sK106: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_174, type, sK107: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_175, type, sK108: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_176, type, sK109: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_177, type, sK110: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_178, type, sK111: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_179, type, sK112: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_180, type, sK113: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_181, type, sK114: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_182, type, sK115: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_183, type, sK116: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_184, type, sK117: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_185, type, sK118: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_186, type, sK119: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_187, type, sK120: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_188, type, sK121: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_189, type, sK122: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_190, type, sK123: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_191, type, sK124: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_192, type, sK125: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_193, type, sK126: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_194, type, sK127: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_195, type, sK128: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 1.22/0.55 thf(func_def_196, type, sK129: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_197, type, sK130: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 1.22/0.55 thf(func_def_198, type, sK131: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_199, type, sK132: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 1.22/0.55 thf(func_def_200, type, sK133: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_201, type, sK134: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 1.22/0.55 thf(func_def_202, type, sK135: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_203, type, sK136: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_204, type, sK137: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_205, type, sK138: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_206, type, sK139: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_207, type, sK140: ((state > list @ com > state > $o) > state)).
% 1.22/0.55 thf(func_def_208, type, sK141: ((state > list @ com > state > $o) > com)).
% 1.22/0.55 thf(func_def_209, type, sK142: ((state > list @ com > state > $o) > state)).
% 1.22/0.55 thf(func_def_210, type, sK143: ((state > list @ com > state > $o) > list @ com)).
% 1.22/0.55 thf(func_def_211, type, sK144: ((state > list @ com > state > $o) > state)).
% 1.22/0.55 thf(func_def_212, type, sK145: ((state > list @ com > state > $o) > state)).
% 1.22/0.55 thf(func_def_213, type, sK146: (state > list @ com > state > com)).
% 1.22/0.55 thf(func_def_214, type, sK147: (state > list @ com > state > state)).
% 1.22/0.55 thf(func_def_215, type, sK148: (state > list @ com > state > list @ com)).
% 1.22/0.55 thf(func_def_216, type, sK149: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_217, type, sK150: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_218, type, sK151: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_219, type, sK152: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_220, type, sK153: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_221, type, sK154: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_222, type, sK155: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_223, type, sK156: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_224, type, sK157: !>[X0: $tType]:(((X0 > $o) > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_225, type, sK158: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_226, type, sK159: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_227, type, sK160: !>[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))).
% 1.22/0.55 thf(func_def_228, type, sK161: !>[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))).
% 1.22/0.55 thf(func_def_229, type, sK162: !>[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))).
% 1.22/0.55 thf(func_def_230, type, sK163: !>[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))).
% 1.22/0.55 thf(func_def_231, type, sK164: !>[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))).
% 1.22/0.55 thf(func_def_232, type, sK165: !>[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))).
% 1.22/0.55 thf(func_def_233, type, sK166: !>[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))).
% 1.22/0.55 thf(func_def_234, type, sK167: !>[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))).
% 1.22/0.55 thf(func_def_235, type, sK168: !>[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))).
% 1.22/0.55 thf(func_def_236, type, sK169: !>[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))).
% 1.22/0.55 thf(func_def_237, type, sK170: !>[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))).
% 1.22/0.55 thf(func_def_238, type, sK171: !>[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))).
% 1.22/0.55 thf(func_def_239, type, sK172: !>[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))).
% 1.22/0.55 thf(func_def_240, type, sK173: !>[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))).
% 1.22/0.55 thf(func_def_241, type, sK174: !>[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))).
% 1.22/0.55 thf(func_def_242, type, sK175: !>[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))).
% 1.22/0.55 thf(func_def_243, type, sK176: !>[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))).
% 1.22/0.55 thf(func_def_244, type, sK177: !>[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))).
% 1.22/0.55 thf(func_def_245, type, sK178: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.22/0.55 thf(func_def_246, type, sK179: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.22/0.55 thf(func_def_247, type, sK180: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.22/0.55 thf(func_def_248, type, sK181: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_249, type, sK182: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.22/0.55 thf(func_def_250, type, sK183: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.22/0.55 thf(func_def_251, type, sK184: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_252, type, sK185: !>[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))).
% 1.22/0.55 thf(func_def_253, type, sK186: !>[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))).
% 1.22/0.55 thf(func_def_254, type, sK187: !>[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))).
% 1.22/0.55 thf(func_def_255, type, sK188: !>[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))).
% 1.22/0.55 thf(func_def_256, type, sK189: !>[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))).
% 1.22/0.55 thf(func_def_257, type, sK190: !>[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))).
% 1.22/0.55 thf(func_def_258, type, sK191: !>[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))).
% 1.22/0.55 thf(func_def_259, type, sK192: !>[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))).
% 1.22/0.55 thf(func_def_260, type, sK193: !>[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))).
% 1.22/0.55 thf(func_def_261, type, sK194: !>[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))).
% 1.22/0.55 thf(func_def_262, type, sK195: !>[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))).
% 1.22/0.55 thf(func_def_263, type, sK196: !>[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))).
% 1.22/0.55 thf(func_def_264, type, sK197: !>[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))).
% 1.22/0.55 thf(func_def_265, type, sK198: (com > state > com > state)).
% 1.22/0.55 thf(func_def_266, type, sK199: (com > state > (state > $o) > state)).
% 1.22/0.55 thf(func_def_267, type, sK200: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > X0))).
% 1.22/0.55 thf(func_def_268, type, sK201: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > X1))).
% 1.22/0.55 thf(func_def_269, type, sK202: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > list @ X0))).
% 1.22/0.55 thf(func_def_270, type, sK203: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > set @ product_prod @ X0 @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_271, type, sK204: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_272, type, sK205: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_273, type, sK206: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_274, type, sK207: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_275, type, sK208: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_276, type, sK209: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_277, type, sK210: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 1.22/0.55 thf(func_def_278, type, sK211: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X1 > X0))).
% 1.22/0.55 thf(func_def_279, type, sK212: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X1 > list @ X0))).
% 1.22/0.55 thf(func_def_280, type, sK213: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > X0 > list @ X1 > X1))).
% 1.22/0.55 thf(func_def_281, type, sK214: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > X0 > list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_282, type, sK215: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X1))).
% 1.22/0.55 thf(func_def_283, type, sK216: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > X0))).
% 1.22/0.55 thf(func_def_284, type, sK217: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_285, type, sK218: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > list @ X0 > list @ X1 > list @ X0))).
% 1.22/0.55 thf(func_def_286, type, sK219: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_287, type, sK220: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > X0 > list @ X0 > X0))).
% 1.22/0.55 thf(func_def_288, type, sK221: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0 > list @ X0))).
% 1.22/0.55 thf(func_def_289, type, sK222: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_290, type, sK223: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_291, type, sK224: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_292, type, sK225: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_293, type, sK226: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_294, type, sK227: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0))).
% 1.22/0.55 thf(func_def_295, type, sK228: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > X0))).
% 1.22/0.55 thf(func_def_296, type, sK229: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_297, type, sK230: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_298, type, sK231: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_299, type, sK232: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_300, type, sK233: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_301, type, sK234: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_302, type, sK235: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_303, type, sK236: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_304, type, sK237: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_305, type, sK238: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_306, type, sK239: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_307, type, sK240: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_308, type, sK241: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_309, type, sK242: !>[X0: $tType]:((nat > list @ X0))).
% 1.22/0.55 thf(func_def_310, type, sK243: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > X1))).
% 1.22/0.55 thf(func_def_311, type, sK244: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_312, type, sK245: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > X0))).
% 1.22/0.55 thf(func_def_313, type, sK246: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_314, type, sK247: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > X2))).
% 1.22/0.55 thf(func_def_315, type, sK248: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X2))).
% 1.22/0.55 thf(func_def_316, type, sK249: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 1.22/0.55 thf(func_def_317, type, sK250: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_318, type, sK251: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 1.22/0.55 thf(func_def_319, type, sK252: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 1.22/0.55 thf(func_def_320, type, sK253: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_321, type, sK254: !>[X0: $tType]:((list @ X0 > list @ X0 > X0))).
% 1.22/0.55 thf(func_def_322, type, sK255: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_323, type, sK256: !>[X0: $tType]:((list @ X0 > list @ X0 > X0))).
% 1.22/0.55 thf(func_def_324, type, sK257: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_325, type, sK258: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_326, type, sK259: !>[X0: $tType]:((list @ X0 > list @ X0 > nat))).
% 1.22/0.55 thf(func_def_327, type, sK260: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > nat))).
% 1.22/0.55 thf(func_def_328, type, sK261: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > list @ X0 > list @ X0 > nat))).
% 1.22/0.55 thf(func_def_329, type, sK262: !>[X0: $tType]:((list @ X0 > list @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_330, type, sK263: !>[X0: $tType]:((nat > (nat > X0 > $o) > nat))).
% 1.22/0.55 thf(func_def_331, type, sK264: !>[X0: $tType]:((nat > (nat > X0 > $o) > list @ X0))).
% 1.22/0.55 thf(func_def_332, type, sK265: !>[X0: $tType]:((nat > list @ X0 > (nat > X0 > $o) > nat))).
% 1.22/0.55 thf(func_def_333, type, sK266: !>[X0: $tType]:(((nat > X0 > $o) > nat > X0))).
% 1.22/0.55 thf(func_def_334, type, sK267: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > set @ product_prod @ X0 @ X1 > nat))).
% 1.22/0.55 thf(func_def_335, type, sK268: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_336, type, sK269: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_337, type, sK270: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_338, type, sK271: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_339, type, sK272: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_340, type, sK273: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_341, type, sK274: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 1.22/0.55 thf(func_def_342, type, sK275: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_343, type, sK276: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_344, type, sK277: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_345, type, sK278: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_346, type, sK279: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_347, type, sK280: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ list @ X0))).
% 1.22/0.55 thf(func_def_348, type, sK281: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > list @ X0))).
% 1.22/0.55 thf(func_def_349, type, sK282: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_350, type, sK283: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X0))).
% 1.22/0.55 thf(func_def_351, type, sK284: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X1))).
% 1.22/0.55 thf(func_def_352, type, sK285: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > list @ X1))).
% 1.22/0.55 thf(func_def_353, type, sK286: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X0))).
% 1.22/0.55 thf(func_def_354, type, sK287: !>[X0: $tType, X1: $tType]:((list @ X0 > set @ product_prod @ X1 @ X0 > list @ X1 > X1))).
% 1.22/0.55 thf(func_def_355, type, sK288: !>[X0: $tType]:((list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_356, type, sK289: !>[X0: $tType]:((X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_357, type, sK290: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_358, type, sK291: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_359, type, sK292: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_360, type, sK293: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_361, type, sK294: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_362, type, sK295: !>[X0: $tType]:((X0 > set @ product_prod @ X0 @ X0 > X0 > X0))).
% 1.22/0.55 thf(func_def_363, type, sK296: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 1.22/0.55 thf(func_def_364, type, sK297: !>[X0: $tType]:((list @ X0 > X0))).
% 1.22/0.55 thf(func_def_365, type, sK298: (list @ com > state > com > state)).
% 1.22/0.55 thf(f262,axiom,(
% 1.22/0.55 (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ s2)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 1.22/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.22/0.55 thf(f263,axiom,(
% 1.22/0.55 (termi @ c @ s)),
% 1.22/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 1.22/0.55 thf(f264,axiom,(
% 1.22/0.55 ! [X0 : state,X1 : state] : ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ X0) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ X1)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) => ((termi @ c @ X0) => (! [X2 : state] : ((exec @ X1 @ c2 @ X2) => (pHoare1335526537termis @ cs @ X2)) & (termi @ c2 @ X1))))),
% 1.22/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
% 1.22/0.55 thf(f265,conjecture,(
% 1.22/0.55 (termi @ c2 @ s2)),
% 1.22/0.55 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)).
% 1.22/0.55 thf(f266,negated_conjecture,(
% 1.22/0.55 ~(termi @ c2 @ s2)),
% 1.22/0.55 inference(negated_conjecture,[status(cth)],[f265])).
% 1.22/0.55 thf(f608,plain,(
% 1.22/0.55 (member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ s2)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))),
% 1.22/0.55 inference(rectify,[],[f262])).
% 1.22/0.55 thf(f609,plain,(
% 1.22/0.55 (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ s2)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))) = $true)),
% 1.22/0.55 inference(fool_elimination,[],[f608])).
% 1.22/0.55 thf(f610,plain,(
% 1.22/0.55 (termi @ c @ s)),
% 1.22/0.55 inference(rectify,[],[f263])).
% 1.22/0.55 thf(f611,plain,(
% 1.22/0.55 (((termi @ c @ s)) = $true)),
% 1.22/0.55 inference(fool_elimination,[],[f610])).
% 1.22/0.55 thf(f612,plain,(
% 1.22/0.55 ! [X0 : state,X1 : state] : ((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ X0) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ X1)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1)) => ((termi @ c @ X0) => (! [X2 : state] : ((exec @ X1 @ c2 @ X2) => (pHoare1335526537termis @ cs @ X2)) & (termi @ c2 @ X1))))),
% 1.22/0.55 inference(rectify,[],[f264])).
% 1.22/0.55 thf(f613,plain,(
% 1.22/0.55 ! [X0 : state,X1 : state] : ((((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ X0) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ X1)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))) = $true) => ((((termi @ c @ X0)) = $true) => (! [X2 : state] : ((((exec @ X1 @ c2 @ X2)) = $true) => (((pHoare1335526537termis @ cs @ X2)) = $true)) & (((termi @ c2 @ X1)) = $true))))),
% 1.22/0.55 inference(fool_elimination,[],[f612])).
% 1.22/0.55 thf(f614,plain,(
% 1.22/0.55 ~(termi @ c2 @ s2)),
% 1.22/0.55 inference(rectify,[],[f266])).
% 1.22/0.55 thf(f615,plain,(
% 1.22/0.55 ~ (((termi @ c2 @ s2)) = $true)),
% 1.22/0.55 inference(fool_elimination,[],[f614])).
% 1.22/0.55 thf(f659,plain,(
% 1.22/0.55 (((termi @ c2 @ s2)) != $true)),
% 1.22/0.55 inference(flattening,[],[f615])).
% 1.22/0.55 thf(f888,plain,(
% 1.22/0.55 ! [X0 : state,X1 : state] : (((! [X2 : state] : ((((pHoare1335526537termis @ cs @ X2)) = $true) | (((exec @ X1 @ c2 @ X2)) != $true)) & (((termi @ c2 @ X1)) = $true)) | (((termi @ c @ X0)) != $true)) | (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ X0) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ X1)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))) != $true))),
% 1.22/0.55 inference(ennf_transformation,[],[f613])).
% 1.22/0.55 thf(f889,plain,(
% 1.22/0.55 ! [X0 : state,X1 : state] : ((! [X2 : state] : ((((pHoare1335526537termis @ cs @ X2)) = $true) | (((exec @ X1 @ c2 @ X2)) != $true)) & (((termi @ c2 @ X1)) = $true)) | (((termi @ c @ X0)) != $true) | (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ X0) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ X1)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))) != $true))),
% 1.22/0.55 inference(flattening,[],[f888])).
% 1.22/0.55 thf(f1368,plain,(
% 1.22/0.55 (((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ s) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ s2)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))) = $true)),
% 1.22/0.55 inference(cnf_transformation,[],[f609])).
% 1.22/0.55 thf(f1369,plain,(
% 1.22/0.55 (((termi @ c @ s)) = $true)),
% 1.22/0.55 inference(cnf_transformation,[],[f611])).
% 1.22/0.55 thf(f1370,plain,(
% 1.22/0.55 ( ! [X0 : state,X1 : state] : ((((member @ product_prod @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ product_prod @ list @ com @ state @ product_prod @ list @ com @ state @ (product_Pair @ list @ com @ state @ (cons @ com @ c @ nil @ com) @ X0) @ (product_Pair @ list @ com @ state @ (cons @ com @ c2 @ cs) @ X1)) @ (transitive_rtrancl @ product_prod @ list @ com @ state @ pHoare1053570893_exec1))) != $true) | (((termi @ c @ X0)) != $true) | (((termi @ c2 @ X1)) = $true)) )),
% 1.22/0.55 inference(cnf_transformation,[],[f889])).
% 1.22/0.55 thf(f1372,plain,(
% 1.22/0.55 (((termi @ c2 @ s2)) != $true)),
% 1.22/0.55 inference(cnf_transformation,[],[f659])).
% 1.22/0.55 thf(f2210,plain,(
% 1.22/0.55 ($true != $true) | (((termi @ c @ s)) != $true) | (((termi @ c2 @ s2)) = $true)),
% 1.22/0.55 inference(constrained_superposition,[],[f1370,f1368])).
% 1.22/0.55 thf(f2211,plain,(
% 1.22/0.55 (((termi @ c @ s)) != $true) | (((termi @ c2 @ s2)) = $true)),
% 1.22/0.55 inference(trivial_inequality_removal,[],[f2210])).
% 1.22/0.55 thf(f2213,plain,(
% 1.22/0.55 (((termi @ c2 @ s2)) = $true)),
% 1.22/0.55 inference(forward_subsumption_resolution,[],[f2211,f1369])).
% 1.22/0.55 thf(f2214,plain,(
% 1.22/0.55 $false),
% 1.22/0.55 inference(forward_subsumption_resolution,[],[f2213,f1372])).
% 1.22/0.55 % SZS output end Proof for theBenchmark
% 1.22/0.55 % (4042957)------------------------------
% 1.22/0.55 % (4042957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (4042957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (4042957)CaDiCaL version: 2.1.3
% 1.22/0.55 % (4042957)Termination reason: Refutation
% 1.22/0.55 % (4042957)Time elapsed: 0.177 s
% 1.22/0.55 % (4042957)Peak memory usage: 14 MB
% 1.22/0.55 % (4042957)Instructions burned: 216 (million)
% 1.22/0.55 % (4042950)Success in time 0.262 s
% 1.22/0.55 % Vampire exiting
%------------------------------------------------------------------------------