%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP152^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:10:54 AM UTC 2026
% Result : Theorem 2.83s 0.66s
% Output : Refutation 2.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP152^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 20:03:05 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.83/0.66 % (1521744)Will run a generic schedule for satisfiability detection.
% 2.83/0.66 % (1521750)% WARNING: option uhcvi not known.
% 2.83/0.66 % (1521750)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1374305817:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.83/0.66 % (1521749)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=307108552_2999 on theBenchmark for (2999ds/0Mi)
% 2.83/0.66 % (1521751)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4071751227:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.83/0.66 % (1521753)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1749179831:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.83/0.66 % (1521752)dis+10_1_sil=32000:sp=arity:random_seed=3333476009:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.83/0.66 % (1521755)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4222648629:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.83/0.66 % (1521750)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.83/0.66 % (1521754)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=240666805:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.83/0.66 % (1521753)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.83/0.66 % (1521750)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.83/0.66 % (1521752)Instruction limit reached!
% 2.83/0.66 % (1521752)------------------------------
% 2.83/0.66 % (1521752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521752)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521752)Termination reason: Instruction limit
% 2.83/0.66 % (1521752)Termination phase: Property scanning
% 2.83/0.66 % (1521752)Time elapsed: 0.045 s
% 2.83/0.66 % (1521752)Peak memory usage: 11 MB
% 2.83/0.66 % (1521752)Instructions burned: 105 (million)
% 2.83/0.66 % Exception at run slice level
% 2.83/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.83/0.66 % (1521753)Instruction limit reached!
% 2.83/0.66 % (1521753)------------------------------
% 2.83/0.66 % (1521753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521753)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521753)Termination reason: Instruction limit
% 2.83/0.66 % (1521753)Termination phase: Property scanning
% 2.83/0.66 % (1521753)Time elapsed: 0.051 s
% 2.83/0.66 % (1521753)Peak memory usage: 11 MB
% 2.83/0.66 % (1521753)Instructions burned: 118 (million)
% 2.83/0.66 % (1521763)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=765921848:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.83/0.66 % (1521764)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3442333414:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.83/0.66 % (1521765)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=1444806786:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.83/0.66 % (1521755)Instruction limit reached!
% 2.83/0.66 % (1521755)------------------------------
% 2.83/0.66 % (1521755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521755)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521755)Termination reason: Instruction limit
% 2.83/0.66 % (1521755)Termination phase: Saturation
% 2.83/0.66 % (1521755)Time elapsed: 0.069 s
% 2.83/0.66 % (1521755)Peak memory usage: 13 MB
% 2.83/0.66 % (1521755)Instructions burned: 161 (million)
% 2.83/0.66 % (1521754)Instruction limit reached!
% 2.83/0.66 % (1521754)------------------------------
% 2.83/0.66 % (1521754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521754)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521754)Termination reason: Instruction limit
% 2.83/0.66 % (1521754)Termination phase: Saturation
% 2.83/0.66 % (1521754)Time elapsed: 0.073 s
% 2.83/0.66 % (1521754)Peak memory usage: 12 MB
% 2.83/0.66 % (1521754)Instructions burned: 132 (million)
% 2.83/0.66 % (1521765)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.83/0.66 % (1521769)ott-21_1_sil=16000:fs=off:random_seed=1155446644:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.83/0.66 % (1521770)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2920193953:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.83/0.66 % Exception at run slice level
% 2.83/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.83/0.66 % (1521765)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.83/0.66 % (1521764)Instruction limit reached!
% 2.83/0.66 % (1521764)------------------------------
% 2.83/0.66 % (1521764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521764)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521764)Termination reason: Instruction limit
% 2.83/0.66 % (1521764)Termination phase: Saturation
% 2.83/0.66 % (1521764)Time elapsed: 0.057 s
% 2.83/0.66 % (1521764)Peak memory usage: 12 MB
% 2.83/0.66 % (1521764)Instructions burned: 132 (million)
% 2.83/0.66 % (1521773)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3294752350:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.83/0.66 % (1521774)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1512311625:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.83/0.66 % (1521769)Instruction limit reached!
% 2.83/0.66 % (1521769)------------------------------
% 2.83/0.66 % (1521769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521769)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521769)Termination reason: Instruction limit
% 2.83/0.66 % (1521769)Termination phase: Saturation
% 2.83/0.66 % (1521769)Time elapsed: 0.082 s
% 2.83/0.66 % (1521769)Peak memory usage: 13 MB
% 2.83/0.66 % (1521769)Instructions burned: 181 (million)
% 2.83/0.66 % Exception at run slice level
% 2.83/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.83/0.66 % (1521777)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2191110431:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.83/0.66 % (1521778)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2062616588:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.83/0.66 % (1521778)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.83/0.66 % Exception at run slice level
% 2.83/0.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.83/0.66 % (1521781)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=260397262:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.83/0.66 % (1521781)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.83/0.66 % (1521770)Instruction limit reached!
% 2.83/0.66 % (1521770)------------------------------
% 2.83/0.66 % (1521770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521770)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521770)Termination reason: Instruction limit
% 2.83/0.66 % (1521770)Termination phase: Saturation
% 2.83/0.66 % (1521770)Time elapsed: 0.239 s
% 2.83/0.66 % (1521770)Peak memory usage: 16 MB
% 2.83/0.66 % (1521770)Instructions burned: 478 (million)
% 2.83/0.66 % (1521783)fmb+10_1_sil=64000:random_seed=2518634965:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 2.83/0.66 % (1521750) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1521744-1521750"...
% 2.83/0.66 % (1521750)...printing done.
% 2.83/0.66 % (1521750)Refutation found. Thanks to Tanya!
% 2.83/0.66 % SZS status Theorem for theBenchmark
% 2.83/0.66 % SZS output start Proof for theBenchmark
% 2.83/0.66 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 2.83/0.66 thf(type_def_6, type, multiset: $tType > $tType).
% 2.83/0.66 thf(type_def_7, type, set: $tType > $tType).
% 2.83/0.66 thf(type_def_8, type, a: $tType).
% 2.83/0.66 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 2.83/0.66 thf(func_def_0, type, preorder: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_2, type, plus: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_4, type, minus: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_6, type, top: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_8, type, ab_group_add: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_9, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_10, type, real_V1076094709vector: !>[X0: $tType]:($o)).
% 2.83/0.66 thf(func_def_11, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 2.83/0.66 thf(func_def_12, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.83/0.66 thf(func_def_13, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.83/0.66 thf(func_def_14, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(func_def_15, type, add_mset: !>[X0: $tType]:((X0 > multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_16, type, comm_monoid_sum_mset: !>[X0: $tType]:(((X0 > X0 > X0) > X0 > multiset @ X0 > X0))).
% 2.83/0.66 thf(func_def_17, type, fold_mset: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > X1 > multiset @ X0 > X1))).
% 2.83/0.66 thf(func_def_18, type, is_empty: !>[X0: $tType]:((multiset @ X0 > $o))).
% 2.83/0.66 thf(func_def_19, type, mult: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0))).
% 2.83/0.66 thf(func_def_20, type, mult1: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0))).
% 2.83/0.66 thf(func_def_21, type, multp: !>[X0: $tType]:(((X0 > X0 > $o) > multiset @ X0 > multiset @ X0 > $o))).
% 2.83/0.66 thf(func_def_22, type, set_mset: !>[X0: $tType]:((multiset @ X0 > set @ X0))).
% 2.83/0.66 thf(func_def_23, type, order_preorder_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_24, type, order_215145569der_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_25, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.83/0.66 thf(func_def_26, type, top_top: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(func_def_27, type, prefer310429814s_good: !>[X0: $tType]:((X0 > set @ X0 > set @ product_prod @ X0 @ X0 > set @ X0))).
% 2.83/0.66 thf(func_def_28, type, prefer199794634erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_29, type, prefer1997167224erence: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_30, type, prefer1801827867axioms: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_31, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 2.83/0.66 thf(func_def_32, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 2.83/0.66 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.83/0.66 thf(func_def_34, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 2.83/0.66 thf(func_def_35, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 2.83/0.66 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.83/0.66 thf(func_def_37, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.83/0.66 thf(func_def_38, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.83/0.66 thf(func_def_39, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.83/0.66 thf(func_def_40, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 2.83/0.66 thf(func_def_41, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 2.83/0.66 thf(func_def_42, type, asym: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_43, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 2.83/0.66 thf(func_def_44, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 2.83/0.66 thf(func_def_45, type, irrefl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_46, type, refl_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_47, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_48, type, trans: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 2.83/0.66 thf(func_def_49, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.83/0.66 thf(func_def_50, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 2.83/0.66 thf(func_def_51, type, lex_prod: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 2.83/0.66 thf(func_def_52, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 2.83/0.66 thf(func_def_53, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.83/0.66 thf(func_def_54, type, carrier: set @ a).
% 2.83/0.66 thf(func_def_55, type, relation: set @ product_prod @ a @ a).
% 2.83/0.66 thf(func_def_56, type, x: a).
% 2.83/0.66 thf(func_def_57, type, y: a).
% 2.83/0.66 thf(func_def_61, type, vNOT: ($o > $o)).
% 2.83/0.66 thf(func_def_62, type, vAND: ($o > $o > $o)).
% 2.83/0.66 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.83/0.66 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.83/0.66 thf(func_def_65, type, vIMP: ($o > $o > $o)).
% 2.83/0.66 thf(func_def_66, type, db0: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(func_def_67, type, db1: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(func_def_68, type, db2: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(func_def_69, type, db3: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(func_def_70, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.83/0.66 thf(func_def_71, type, vOR: ($o > $o > $o)).
% 2.83/0.66 thf(func_def_72, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.83/0.66 thf(func_def_73, type, sK0: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.83/0.66 thf(func_def_74, type, sK1: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.83/0.66 thf(func_def_75, type, sK2: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.83/0.66 thf(func_def_76, type, sK3: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_77, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 2.83/0.66 thf(func_def_78, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 2.83/0.66 thf(func_def_79, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 2.83/0.66 thf(func_def_80, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 2.83/0.66 thf(func_def_81, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 2.83/0.66 thf(func_def_82, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 2.83/0.66 thf(func_def_83, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 2.83/0.66 thf(func_def_84, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 2.83/0.66 thf(func_def_85, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 2.83/0.66 thf(func_def_86, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 2.83/0.66 thf(func_def_87, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 2.83/0.66 thf(func_def_88, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 2.83/0.66 thf(func_def_89, type, sK16: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_90, type, sK17: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_91, type, sK18: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_92, type, sK19: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_93, type, sK20: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.83/0.66 thf(func_def_94, type, sK21: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_95, type, sK22: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.83/0.66 thf(func_def_96, type, sK23: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.83/0.66 thf(func_def_97, type, sK24: !>[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))).
% 2.83/0.66 thf(func_def_98, type, sK25: !>[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))).
% 2.83/0.66 thf(func_def_99, type, sK26: !>[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))).
% 2.83/0.66 thf(func_def_100, type, sK27: !>[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))).
% 2.83/0.66 thf(func_def_101, type, sK28: !>[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))).
% 2.83/0.66 thf(func_def_102, type, sK29: !>[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))).
% 2.83/0.66 thf(func_def_103, type, sK30: !>[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))).
% 2.83/0.66 thf(func_def_104, type, sK31: !>[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))).
% 2.83/0.66 thf(func_def_105, type, sK32: !>[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))).
% 2.83/0.66 thf(func_def_106, type, sK33: !>[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))).
% 2.83/0.66 thf(func_def_107, type, sK34: !>[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))).
% 2.83/0.66 thf(func_def_108, type, sK35: !>[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))).
% 2.83/0.66 thf(func_def_109, type, sK36: !>[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))).
% 2.83/0.66 thf(func_def_110, type, sK37: !>[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))).
% 2.83/0.66 thf(func_def_111, type, sK38: !>[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))).
% 2.83/0.66 thf(func_def_112, type, sK39: !>[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))).
% 2.83/0.66 thf(func_def_113, type, sK40: !>[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))).
% 2.83/0.66 thf(func_def_114, type, sK41: !>[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))).
% 2.83/0.66 thf(func_def_115, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 2.83/0.66 thf(func_def_116, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.83/0.66 thf(func_def_117, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.83/0.66 thf(func_def_118, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_119, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.83/0.66 thf(func_def_120, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.83/0.66 thf(func_def_121, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_122, type, sK49: !>[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))).
% 2.83/0.66 thf(func_def_123, type, sK50: !>[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))).
% 2.83/0.66 thf(func_def_124, type, sK51: !>[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))).
% 2.83/0.66 thf(func_def_125, type, sK52: !>[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))).
% 2.83/0.66 thf(func_def_126, type, sK53: !>[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))).
% 2.83/0.66 thf(func_def_127, type, sK54: !>[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))).
% 2.83/0.66 thf(func_def_128, type, sK55: !>[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))).
% 2.83/0.66 thf(func_def_129, type, sK56: !>[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))).
% 2.83/0.66 thf(func_def_130, type, sK57: !>[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))).
% 2.83/0.66 thf(func_def_131, type, sK58: !>[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))).
% 2.83/0.66 thf(func_def_132, type, sK59: !>[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))).
% 2.83/0.66 thf(func_def_133, type, sK60: !>[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))).
% 2.83/0.66 thf(func_def_134, type, sK61: !>[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))).
% 2.83/0.66 thf(func_def_135, type, sK62: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 2.83/0.66 thf(func_def_136, type, sK63: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 2.83/0.66 thf(func_def_137, type, sK64: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_138, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.83/0.66 thf(func_def_139, type, sK66: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_140, type, sK67: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_141, type, sK68: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_142, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 2.83/0.66 thf(func_def_143, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 2.83/0.66 thf(func_def_144, type, sK71: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_145, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 2.83/0.66 thf(func_def_146, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 2.83/0.66 thf(func_def_147, type, sK74: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_148, type, sK75: !>[X0: $tType]:(((X0 > X0 > $o) > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_149, type, sK76: !>[X0: $tType]:(((set @ product_prod @ X0 @ X0 > $o) > set @ product_prod @ X0 @ X0))).
% 2.83/0.66 thf(func_def_150, type, sK77: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_151, type, sK78: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_152, type, sK79: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 2.83/0.66 thf(func_def_153, type, sK80: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.83/0.66 thf(func_def_154, type, sK81: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 2.83/0.66 thf(func_def_155, type, sK82: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.83/0.66 thf(func_def_156, type, sK83: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.83/0.66 thf(func_def_157, type, sK84: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 2.83/0.66 thf(func_def_158, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 2.83/0.66 thf(func_def_159, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 2.83/0.66 thf(func_def_160, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 2.83/0.66 thf(func_def_161, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 2.83/0.66 thf(func_def_162, type, sK89: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 2.83/0.66 thf(func_def_163, type, sK90: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 2.83/0.66 thf(func_def_164, type, sK91: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 2.83/0.66 thf(func_def_165, type, sK92: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 2.83/0.66 thf(func_def_166, type, sK93: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > X0))).
% 2.83/0.66 thf(func_def_167, type, sK94: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_168, type, sK95: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_169, type, sK96: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > X0))).
% 2.83/0.66 thf(func_def_170, type, sK97: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_171, type, sK98: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_172, type, sK99: !>[X0: $tType]:((multiset @ X0 > X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_173, type, sK100: !>[X0: $tType]:((multiset @ X0 > X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_174, type, sK101: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_175, type, sK102: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_176, type, sK103: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_177, type, sK104: !>[X0: $tType]:((X0 > multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_178, type, sK105: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > multiset @ X0 > X0))).
% 2.83/0.66 thf(func_def_179, type, sK106: !>[X0: $tType]:((multiset @ X0 > X0))).
% 2.83/0.66 thf(func_def_180, type, sK107: !>[X0: $tType]:((multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_181, type, sK108: !>[X0: $tType]:((multiset @ X0 > X0))).
% 2.83/0.66 thf(func_def_182, type, sK109: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > X1))).
% 2.83/0.66 thf(func_def_183, type, sK110: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X0))).
% 2.83/0.66 thf(func_def_184, type, sK111: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X1))).
% 2.83/0.66 thf(func_def_185, type, sK112: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > X0))).
% 2.83/0.66 thf(func_def_186, type, sK113: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X0))).
% 2.83/0.66 thf(func_def_187, type, sK114: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X1))).
% 2.83/0.66 thf(func_def_188, type, sK115: !>[X0: $tType]:(((multiset @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_189, type, sK116: !>[X0: $tType]:(((multiset @ X0 > $o) > multiset @ X0))).
% 2.83/0.66 thf(func_def_190, type, sK117: !>[X0: $tType]:((multiset @ X0 > X0))).
% 2.83/0.66 thf(func_def_191, type, sK118: !>[X0: $tType]:((multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_192, type, sK119: !>[X0: $tType]:(((multiset @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_193, type, sK120: !>[X0: $tType]:(((multiset @ X0 > $o) > multiset @ X0))).
% 2.83/0.66 thf(func_def_194, type, sK121: !>[X0: $tType]:(((multiset @ X0 > $o) > X0))).
% 2.83/0.66 thf(func_def_195, type, sK122: !>[X0: $tType]:(((multiset @ X0 > $o) > multiset @ X0))).
% 2.83/0.66 thf(func_def_196, type, sK123: !>[X0: $tType]:((multiset @ multiset @ X0 > X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_197, type, sK124: !>[X0: $tType]:((multiset @ multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_198, type, sK125: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_199, type, sK126: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_200, type, sK127: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_201, type, sK128: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_202, type, sK129: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_203, type, sK130: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_204, type, sK131: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_205, type, sK132: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_206, type, sK133: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_207, type, sK134: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_208, type, sK135: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_209, type, sK136: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_210, type, sK137: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_211, type, sK138: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_212, type, sK139: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_213, type, sK140: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (set @ X0 > $o) > set @ X0))).
% 2.83/0.66 thf(func_def_214, type, sK141: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 2.83/0.66 thf(func_def_215, type, sK142: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 2.83/0.66 thf(func_def_216, type, sK143: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 2.83/0.66 thf(func_def_217, type, sK144: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 2.83/0.66 thf(func_def_218, type, sK145: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 2.83/0.66 thf(func_def_219, type, sK146: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X1 > set @ product_prod @ X0 @ X0 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 2.83/0.66 thf(func_def_220, type, sK147: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_221, type, sK148: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_222, type, sK149: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_223, type, sK150: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_224, type, sK151: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_225, type, sK152: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_226, type, sK153: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_227, type, sK154: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_228, type, sK155: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_229, type, sK156: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_230, type, sK157: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_231, type, sK158: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_232, type, sK159: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_233, type, sK160: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_234, type, sK161: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_235, type, sK162: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_236, type, sK163: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_237, type, sK164: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_238, type, sK165: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_239, type, sK166: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 2.83/0.66 thf(func_def_240, type, sK167: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 2.83/0.66 thf(func_def_241, type, sK168: !>[X0: $tType]:((X0 > multiset @ X0 > X0 > multiset @ X0 > multiset @ X0))).
% 2.83/0.66 thf(func_def_242, type, sK169: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 2.83/0.66 thf(func_def_243, type, sK170: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_244, type, sK171: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_245, type, sK172: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_246, type, sK173: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_247, type, sK174: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_248, type, sK175: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_249, type, sK176: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_250, type, sK177: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_251, type, sK178: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_252, type, sK179: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_253, type, sK180: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_254, type, sK181: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_255, type, sK182: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_256, type, sK183: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_257, type, sK184: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_258, type, sK185: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_259, type, sK186: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_260, type, sK187: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_261, type, sK188: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_262, type, sK189: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_263, type, sK190: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0))).
% 2.83/0.66 thf(func_def_264, type, sK191: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X0 @ X0))).
% 2.83/0.66 thf(func_def_265, type, sK192: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_266, type, sK193: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_267, type, sK194: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_268, type, sK195: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_269, type, sK196: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1))).
% 2.83/0.66 thf(func_def_270, type, sK197: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_271, type, sK198: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_272, type, sK199: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_273, type, sK200: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_274, type, sK201: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_275, type, sK202: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_276, type, sK203: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_277, type, sK204: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_278, type, sK205: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_279, type, sK206: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_280, type, sK207: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_281, type, sK208: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_282, type, sK209: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_283, type, sK210: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_284, type, sK211: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_285, type, sK212: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_286, type, sK213: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_287, type, sK214: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_288, type, sK215: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_289, type, sK216: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_290, type, sK217: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_291, type, sK218: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_292, type, sK219: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_293, type, sK220: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_294, type, sK221: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_295, type, sK222: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_296, type, sK223: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_297, type, sK224: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_298, type, sK225: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_299, type, sK226: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_300, type, sK227: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_301, type, sK228: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_302, type, sK229: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_303, type, sK230: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_304, type, sK231: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_305, type, sK232: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_306, type, sK233: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_307, type, sK234: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_308, type, sK235: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_309, type, sK236: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_310, type, sK237: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_311, type, sK238: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_312, type, sK239: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_313, type, sK240: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_314, type, sK241: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_315, type, sK242: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_316, type, sK243: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_317, type, sK244: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_318, type, sK245: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_319, type, sK246: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_320, type, sK247: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_321, type, sK248: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_322, type, sK249: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_323, type, sK250: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_324, type, sK251: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_325, type, sK252: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_326, type, sK253: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_327, type, sK254: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_328, type, sK255: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_329, type, sK256: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_330, type, sK257: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_331, type, sK258: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_332, type, sK259: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_333, type, sK260: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_334, type, sK261: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_335, type, sK262: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_336, type, sK263: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_337, type, sK264: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_338, type, sK265: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_339, type, sK266: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_340, type, sK267: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_341, type, sK268: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_342, type, sK269: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_343, type, sK270: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_344, type, sK271: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_345, type, sK272: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_346, type, sK273: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_347, type, sK274: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_348, type, sK275: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_349, type, sK276: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_350, type, sK277: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_351, type, sK278: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_352, type, sK279: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_353, type, sK280: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_354, type, sK281: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_355, type, sK282: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_356, type, sK283: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_357, type, sK284: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_358, type, sK285: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_359, type, sK286: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_360, type, sK287: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_361, type, sK288: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_362, type, sK289: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_363, type, sK290: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_364, type, sK291: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_365, type, sK292: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_366, type, sK293: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_367, type, sK294: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_368, type, sK295: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_369, type, sK296: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_370, type, sK297: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_371, type, sK298: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_372, type, sK299: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_373, type, sK300: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_374, type, sK301: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_375, type, sK302: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_376, type, sK303: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_377, type, sK304: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_378, type, sK305: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_379, type, sK306: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_380, type, sK307: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_381, type, sK308: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_382, type, sK309: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_383, type, sK310: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_384, type, sK311: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_385, type, sK312: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_386, type, sK313: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_387, type, sK314: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_388, type, sK315: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_389, type, sK316: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_390, type, sK317: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_391, type, sK318: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_392, type, sK319: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_393, type, sK320: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_394, type, sK321: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_395, type, sK322: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_396, type, sK323: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_397, type, sK324: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_398, type, sK325: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_399, type, sK326: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_400, type, sK327: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_401, type, sK328: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_402, type, sK329: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_403, type, sK330: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_404, type, sK331: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_405, type, sK332: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_406, type, sK333: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_407, type, sK334: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_408, type, sK335: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_409, type, sK336: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_410, type, sK337: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_411, type, sK338: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_412, type, sK339: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_413, type, sK340: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_414, type, sK341: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_415, type, sK342: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_416, type, sK343: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_417, type, sK344: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_418, type, sK345: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_419, type, sK346: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_420, type, sK347: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_421, type, sK348: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_422, type, sK349: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_423, type, sK350: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_424, type, sK351: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_425, type, sK352: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_426, type, sK353: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_427, type, sK354: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_428, type, sK355: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_429, type, sK356: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_430, type, sK357: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_431, type, sK358: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_432, type, sK359: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_433, type, sK360: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_434, type, sK361: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_435, type, sK362: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_436, type, sK363: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_437, type, sK364: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_438, type, sK365: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_439, type, sK366: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_440, type, sK367: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_441, type, sK368: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_442, type, sK369: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_443, type, sK370: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_444, type, sK371: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_445, type, sK372: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_446, type, sK373: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_447, type, sK374: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_448, type, sK375: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_449, type, sK376: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_450, type, sK377: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_451, type, sK378: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_452, type, sK379: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_453, type, sK380: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_454, type, sK381: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_455, type, sK382: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_456, type, sK383: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_457, type, sK384: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_458, type, sK385: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_459, type, sK386: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_460, type, sK387: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_461, type, sK388: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_462, type, sK389: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_463, type, sK390: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_464, type, sK391: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_465, type, sK392: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_466, type, sK393: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_467, type, sK394: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_468, type, sK395: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_469, type, sK396: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_470, type, sK397: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_471, type, sK398: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_472, type, sK399: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_473, type, sK400: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_474, type, sK401: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_475, type, sK402: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_476, type, sK403: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_477, type, sK404: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_478, type, sK405: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_479, type, sK406: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_480, type, sK407: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_481, type, sK408: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_482, type, sK409: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_483, type, sK410: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_484, type, sK411: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_485, type, sK412: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_486, type, sK413: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_487, type, sK414: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_488, type, sK415: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_489, type, sK416: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_490, type, sK417: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_491, type, sK418: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_492, type, sK419: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_493, type, sK420: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_494, type, sK421: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_495, type, sK422: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_496, type, sK423: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_497, type, sK424: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_498, type, sK425: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_499, type, sK426: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_500, type, sK427: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_501, type, sK428: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_502, type, sK429: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_503, type, sK430: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_504, type, sK431: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_505, type, sK432: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_506, type, sK433: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_507, type, sK434: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_508, type, sK435: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_509, type, sK436: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_510, type, sK437: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_511, type, sK438: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_512, type, sK439: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.83/0.66 thf(func_def_514, type, db4: !>[X0: $tType]:(X0)).
% 2.83/0.66 thf(f9,axiom,(
% 2.83/0.66 (total_on @ a @ carrier @ relation)),
% 2.83/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_total)).
% 2.83/0.66 thf(f43,axiom,(
% 2.83/0.66 ! [X0 : $tType] : (total_on @ X0 = (^[X1 : set @ X0, X2 : set @ product_prod @ X0 @ X0] : (! [X3 : X0] : ((member @ X0 @ X3 @ X1) => ! [X4 : X0] : ((member @ X0 @ X4 @ X1) => ((X3 != X4) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X4 @ X3) @ X2) | (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X3 @ X4) @ X2))))))))),
% 2.83/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_total__on__def)).
% 2.83/0.66 thf(f288,axiom,(
% 2.83/0.66 (member @ a @ x @ carrier)),
% 2.83/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 2.83/0.66 thf(f289,axiom,(
% 2.83/0.66 (member @ a @ y @ carrier)),
% 2.83/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 2.83/0.66 thf(f290,axiom,(
% 2.83/0.66 (x != y)),
% 2.83/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 2.83/0.66 thf(f291,conjecture,(
% 2.83/0.66 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)),
% 2.83/0.66 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 2.83/0.66 thf(f292,negated_conjecture,(
% 2.83/0.66 ~((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation))),
% 2.83/0.66 inference(negated_conjecture,[status(cth)],[f291])).
% 2.83/0.66 thf(f309,plain,(
% 2.83/0.66 (total_on @ a @ carrier @ relation)),
% 2.83/0.66 inference(rectify,[],[f9])).
% 2.83/0.66 thf(f310,plain,(
% 2.83/0.66 (((total_on @ a @ carrier @ relation)) = $true)),
% 2.83/0.66 inference(fool_elimination,[],[f309])).
% 2.83/0.66 thf(f357,plain,(
% 2.83/0.66 ! [X0 : $tType] : (total_on @ X0 = (^[X1 : set @ X0, X2 : set @ product_prod @ X0 @ X0] : (! [X3 : X0] : ((member @ X0 @ X3 @ X1) => ! [X4 : X0] : ((member @ X0 @ X4 @ X1) => ((X3 != X4) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X4 @ X3) @ X2) | (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ X3 @ X4) @ X2))))))))),
% 2.83/0.66 inference(rectify,[],[f43])).
% 2.83/0.66 thf(f358,plain,(
% 2.83/0.66 ! [X0 : $tType] : (total_on @ X0 = (^[Y0 : set @ X0]: ((^[Y1 : set @ product_prod @ X0 @ X0]: (!! @ X0 @ (^[Y2 : X0]: ((member @ X0 @ Y2 @ Y0) => (!! @ X0 @ (^[Y3 : X0]: ((member @ X0 @ Y3 @ Y0) => ((~ (Y2 = Y3)) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y2 @ Y3) @ Y1) | (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y3 @ Y2) @ Y1)))))))))))))),
% 2.83/0.66 inference(fool_elimination,[],[f357])).
% 2.83/0.66 thf(f686,plain,(
% 2.83/0.66 (member @ a @ x @ carrier)),
% 2.83/0.66 inference(rectify,[],[f288])).
% 2.83/0.66 thf(f687,plain,(
% 2.83/0.66 (((member @ a @ x @ carrier)) = $true)),
% 2.83/0.66 inference(fool_elimination,[],[f686])).
% 2.83/0.66 thf(f688,plain,(
% 2.83/0.66 (member @ a @ y @ carrier)),
% 2.83/0.66 inference(rectify,[],[f289])).
% 2.83/0.66 thf(f689,plain,(
% 2.83/0.66 (((member @ a @ y @ carrier)) = $true)),
% 2.83/0.66 inference(fool_elimination,[],[f688])).
% 2.83/0.66 thf(f690,plain,(
% 2.83/0.66 ~((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation))),
% 2.83/0.66 inference(rectify,[],[f292])).
% 2.83/0.66 thf(f691,plain,(
% 2.83/0.66 ~((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true))),
% 2.83/0.66 inference(fool_elimination,[],[f690])).
% 2.83/0.66 thf(f932,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) != $true) & (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) != $true)),
% 2.83/0.66 inference(ennf_transformation,[],[f691])).
% 2.83/0.66 thf(f997,plain,(
% 2.83/0.66 (((total_on @ a @ carrier @ relation)) = $true)),
% 2.83/0.66 inference(cnf_transformation,[],[f310])).
% 2.83/0.66 thf(f1037,plain,(
% 2.83/0.66 ( ! [X0 : $tType] : ((total_on @ X0 = (^[Y0 : set @ X0]: ((^[Y1 : set @ product_prod @ X0 @ X0]: (!! @ X0 @ (^[Y2 : X0]: ((member @ X0 @ Y2 @ Y0) => (!! @ X0 @ (^[Y3 : X0]: ((member @ X0 @ Y3 @ Y0) => ((~ (Y2 = Y3)) => ((member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y2 @ Y3) @ Y1) | (member @ product_prod @ X0 @ X0 @ (product_Pair @ X0 @ X0 @ Y3 @ Y2) @ Y1)))))))))))))) )),
% 2.83/0.66 inference(cnf_transformation,[],[f358])).
% 2.83/0.66 thf(f1325,plain,(
% 2.83/0.66 (((member @ a @ x @ carrier)) = $true)),
% 2.83/0.66 inference(cnf_transformation,[],[f687])).
% 2.83/0.66 thf(f1326,plain,(
% 2.83/0.66 (((member @ a @ y @ carrier)) = $true)),
% 2.83/0.66 inference(cnf_transformation,[],[f689])).
% 2.83/0.66 thf(f1327,plain,(
% 2.83/0.66 (x != y)),
% 2.83/0.66 inference(cnf_transformation,[],[f290])).
% 2.83/0.66 thf(f1328,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) != $true)),
% 2.83/0.66 inference(cnf_transformation,[],[f932])).
% 2.83/0.66 thf(f1329,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) != $true)),
% 2.83/0.66 inference(cnf_transformation,[],[f932])).
% 2.83/0.66 thf(f1331,definition,(
% 2.83/0.66 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.83/0.66 introduced(theory,[fool_exhaustiveness_axiom])).
% 2.83/0.66 thf(f1341,plain,(
% 2.83/0.66 ($true = (((^[Y0 : set @ a]: ((^[Y1 : set @ product_prod @ a @ a]: (!! @ a @ (^[Y2 : a]: ((member @ a @ Y2 @ Y0) => (!! @ a @ (^[Y3 : a]: ((member @ a @ Y3 @ Y0) => ((~ (Y2 = Y3)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y2 @ Y3) @ Y1) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y3 @ Y2) @ Y1)))))))))))) @ carrier @ relation)))),
% 2.83/0.66 inference(definition_unfolding,[],[f997,f1037])).
% 2.83/0.66 thf(f3888,plain,(
% 2.83/0.66 ($true = ((!! @ a @ (^[Y0 : a]: ((member @ a @ Y0 @ carrier) => (!! @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ carrier) => ((~ (Y0 = Y1)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ Y1) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y1 @ Y0) @ relation)))))))))))),
% 2.83/0.66 inference(beta-eta_normalization,[],[f1341])).
% 2.83/0.66 thf(f3889,plain,(
% 2.83/0.66 ( ! [X1 : a] : (($true = (((^[Y0 : a]: ((member @ a @ Y0 @ carrier) => (!! @ a @ (^[Y1 : a]: ((member @ a @ Y1 @ carrier) => ((~ (Y0 = Y1)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ Y1) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y1 @ Y0) @ relation)))))))) @ X1)))) )),
% 2.83/0.66 inference(pi_proxy_clausification,[],[f3888])).
% 2.83/0.66 thf(f3890,plain,(
% 2.83/0.66 ( ! [X1 : a] : (($true = (((member @ a @ X1 @ carrier) => (!! @ a @ (^[Y0 : a]: ((member @ a @ Y0 @ carrier) => ((~ (X1 = Y0)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ Y0) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ X1) @ relation)))))))))) )),
% 2.83/0.66 inference(beta-eta_normalization,[],[f3889])).
% 2.83/0.66 thf(f3891,plain,(
% 2.83/0.66 ( ! [X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($true = ((!! @ a @ (^[Y0 : a]: ((member @ a @ Y0 @ carrier) => ((~ (X1 = Y0)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ Y0) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ X1) @ relation))))))))) )),
% 2.83/0.66 inference(imp_proxy_clausification,[],[f3890])).
% 2.83/0.66 thf(f3892,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($true = (((^[Y0 : a]: ((member @ a @ Y0 @ carrier) => ((~ (X1 = Y0)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ Y0) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ Y0 @ X1) @ relation))))) @ X2)))) )),
% 2.83/0.66 inference(pi_proxy_clausification,[],[f3891])).
% 2.83/0.66 thf(f3893,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($true = (((member @ a @ X2 @ carrier) => ((~ (X1 = X2)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ relation))))))) )),
% 2.83/0.66 inference(beta-eta_normalization,[],[f3892])).
% 2.83/0.66 thf(f3894,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($false = ((member @ a @ X2 @ carrier))) | ($true = (((~ (X1 = X2)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ relation)))))) )),
% 2.83/0.66 inference(imp_proxy_clausification,[],[f3893])).
% 2.83/0.66 thf(f3895,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($false = ((member @ a @ X2 @ carrier))) | ($false = ((~ (X1 = X2)))) | ($true = (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ relation))))) )),
% 2.83/0.66 inference(imp_proxy_clausification,[],[f3894])).
% 2.83/0.66 thf(f3896,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($false = ((member @ a @ X2 @ carrier))) | ($true = ((X1 = X2))) | ($true = (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ relation))))) )),
% 2.83/0.66 inference(not_proxy_clausification,[],[f3895])).
% 2.83/0.66 thf(f3897,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ a @ X1 @ carrier)) = $false) | ($false = ((member @ a @ X2 @ carrier))) | (X1 = X2) | ($true = (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ relation) | (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ relation))))) )),
% 2.83/0.66 inference(equality_proxy_clausification,[],[f3896])).
% 2.83/0.66 thf(f3898,plain,(
% 2.83/0.66 ( ! [X2 : a,X1 : a] : ((((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X2 @ X1) @ relation)) = $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ X1 @ X2) @ relation)) = $true) | (X1 = X2) | ($false = ((member @ a @ X2 @ carrier))) | (((member @ a @ X1 @ carrier)) = $false)) )),
% 2.83/0.66 inference(or_proxy_clausification,[],[f3897])).
% 2.83/0.66 thf(f3973,plain,(
% 2.83/0.66 ($true != $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $false)),
% 2.83/0.66 inference(constrained_superposition,[],[f1328,f1331])).
% 2.83/0.66 thf(f3974,plain,(
% 2.83/0.66 ($true != $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) = $false)),
% 2.83/0.66 inference(constrained_superposition,[],[f1329,f1331])).
% 2.83/0.66 thf(f3976,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ y @ x) @ relation)) = $false)),
% 2.83/0.66 inference(trivial_inequality_removal,[],[f3974])).
% 2.83/0.66 thf(f3977,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $false)),
% 2.83/0.66 inference(trivial_inequality_removal,[],[f3973])).
% 2.83/0.66 thf(f10759,plain,(
% 2.83/0.66 ($true = $false) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true) | (x = y) | (((member @ a @ x @ carrier)) = $false) | (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(constrained_superposition,[],[f3976,f3898])).
% 2.83/0.66 thf(f10768,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true) | (x = y) | (((member @ a @ x @ carrier)) = $false) | (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(trivial_inequality_removal,[],[f10759])).
% 2.83/0.66 thf(f10830,plain,(
% 2.83/0.66 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true) | (((member @ a @ x @ carrier)) = $false) | (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(forward_subsumption_resolution,[],[f10768,f1327])).
% 2.83/0.66 thf(f10838,plain,(
% 2.83/0.66 ($true = $false) | (((member @ a @ x @ carrier)) = $false) | (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(forward_demodulation,[],[f10830,f3977])).
% 2.83/0.66 thf(f10839,plain,(
% 2.83/0.66 (((member @ a @ x @ carrier)) = $false) | (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(trivial_inequality_removal,[],[f10838])).
% 2.83/0.66 thf(f10846,plain,(
% 2.83/0.66 ($true = $false) | (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(forward_demodulation,[],[f10839,f1325])).
% 2.83/0.66 thf(f10847,plain,(
% 2.83/0.66 (((member @ a @ y @ carrier)) = $false)),
% 2.83/0.66 inference(trivial_inequality_removal,[],[f10846])).
% 2.83/0.66 thf(f11519,plain,(
% 2.83/0.66 ($true = $false)),
% 2.83/0.66 inference(constrained_superposition,[],[f1326,f10847])).
% 2.83/0.66 thf(f11523,plain,(
% 2.83/0.66 $false),
% 2.83/0.66 inference(trivial_inequality_removal,[],[f11519])).
% 2.83/0.66 % SZS output end Proof for theBenchmark
% 2.83/0.66 % (1521750)------------------------------
% 2.83/0.66 % (1521750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.83/0.66 % (1521750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/0.66 % (1521750)CaDiCaL version: 2.1.3
% 2.83/0.66 % (1521750)Termination reason: Refutation
% 2.83/0.66 % (1521750)Time elapsed: 0.398 s
% 2.83/0.66 % (1521750)Peak memory usage: 24 MB
% 2.83/0.66 % (1521750)Instructions burned: 1501 (million)
% 2.83/0.66 % (1521744)Success in time 0.447 s
% 2.83/0.66 % Vampire exiting
%------------------------------------------------------------------------------