%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP135^2 : 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 : n002.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 08:10:50 AM UTC 2026
% Result : Theorem 2.38s 0.59s
% Output : Refutation 2.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP135^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n002.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 20:01:38 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 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
% 2.38/0.59 % (1776424)Will run a generic schedule for satisfiability detection.
% 2.38/0.59 % (1776433)% WARNING: option uhcvi not known.
% 2.38/0.59 % (1776433)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2213606742:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.38/0.59 % (1776432)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2043562861_2999 on theBenchmark for (2999ds/0Mi)
% 2.38/0.59 % (1776433)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.59 % (1776435)dis+10_1_sil=32000:sp=arity:random_seed=2758809360:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.38/0.59 % (1776434)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3543197702:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.38/0.59 % (1776436)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2938545527:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.38/0.59 % (1776438)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=627751835:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.38/0.59 % (1776437)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2531750743:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.38/0.59 % (1776433)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.38/0.59 % (1776436)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.59 % Exception at run slice level
% 2.38/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.59 % (1776435)Instruction limit reached!
% 2.38/0.59 % (1776435)------------------------------
% 2.38/0.59 % (1776435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776435)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776435)Termination reason: Instruction limit
% 2.38/0.59 % (1776435)Termination phase: Saturation
% 2.38/0.59 % (1776435)Time elapsed: 0.047 s
% 2.38/0.59 % (1776435)Peak memory usage: 12 MB
% 2.38/0.59 % (1776435)Instructions burned: 105 (million)
% 2.38/0.59 % (1776436)Instruction limit reached!
% 2.38/0.59 % (1776436)------------------------------
% 2.38/0.59 % (1776436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776436)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776436)Termination reason: Instruction limit
% 2.38/0.59 % (1776436)Termination phase: Saturation
% 2.38/0.59 % (1776436)Time elapsed: 0.052 s
% 2.38/0.59 % (1776436)Peak memory usage: 13 MB
% 2.38/0.59 % (1776436)Instructions burned: 116 (million)
% 2.38/0.59 % (1776437)Instruction limit reached!
% 2.38/0.59 % (1776437)------------------------------
% 2.38/0.59 % (1776437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776437)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776437)Termination reason: Instruction limit
% 2.38/0.59 % (1776437)Termination phase: Saturation
% 2.38/0.59 % (1776437)Time elapsed: 0.059 s
% 2.38/0.59 % (1776437)Peak memory usage: 13 MB
% 2.38/0.59 % (1776437)Instructions burned: 132 (million)
% 2.38/0.59 % (1776457)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=973897804:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.38/0.59 % (1776458)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=11770469:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.38/0.59 % (1776459)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=813817769:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.38/0.59 % (1776438)Instruction limit reached!
% 2.38/0.59 % (1776438)------------------------------
% 2.38/0.59 % (1776438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776438)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776438)Termination reason: Instruction limit
% 2.38/0.59 % (1776438)Termination phase: Saturation
% 2.38/0.59 % (1776438)Time elapsed: 0.072 s
% 2.38/0.59 % (1776438)Peak memory usage: 14 MB
% 2.38/0.59 % (1776438)Instructions burned: 160 (million)
% 2.38/0.59 % (1776461)ott-21_1_sil=16000:fs=off:random_seed=2421869232:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.38/0.59 % (1776459)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.59 % (1776464)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2404106173:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.38/0.59 % Exception at run slice level
% 2.38/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.59 % (1776459)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.38/0.59 % (1776467)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=363988080:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.38/0.59 % (1776458)Instruction limit reached!
% 2.38/0.59 % (1776458)------------------------------
% 2.38/0.59 % (1776458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776458)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776458)Termination reason: Instruction limit
% 2.38/0.59 % (1776458)Termination phase: Saturation
% 2.38/0.59 % (1776458)Time elapsed: 0.058 s
% 2.38/0.59 % (1776458)Peak memory usage: 13 MB
% 2.38/0.59 % (1776458)Instructions burned: 132 (million)
% 2.38/0.59 % (1776470)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4093594610:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.38/0.59 % (1776461)Instruction limit reached!
% 2.38/0.59 % (1776461)------------------------------
% 2.38/0.59 % (1776461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776461)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776461)Termination reason: Instruction limit
% 2.38/0.59 % (1776461)Termination phase: Saturation
% 2.38/0.59 % (1776461)Time elapsed: 0.080 s
% 2.38/0.59 % (1776461)Peak memory usage: 13 MB
% 2.38/0.59 % (1776461)Instructions burned: 180 (million)
% 2.38/0.59 % Exception at run slice level
% 2.38/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.59 % (1776479)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=295689375:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.38/0.59 % (1776481)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=3688252123: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)
% 2.38/0.59 % (1776481)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.59 % Exception at run slice level
% 2.38/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.38/0.59 % (1776518)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3661076489:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.38/0.59 % (1776518)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.38/0.59 % (1776464)Instruction limit reached!
% 2.38/0.59 % (1776464)------------------------------
% 2.38/0.59 % (1776464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.59 % (1776464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.59 % (1776464)CaDiCaL version: 2.1.3
% 2.38/0.59 % (1776464)Termination reason: Instruction limit
% 2.38/0.59 % (1776464)Termination phase: Saturation
% 2.38/0.59 % (1776464)Time elapsed: 0.193 s
% 2.38/0.59 % (1776464)Peak memory usage: 15 MB
% 2.38/0.59 % (1776464)Instructions burned: 479 (million)
% 2.38/0.59 % (1776524)fmb+10_1_sil=64000:random_seed=215156124:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.38/0.59 % (1776433) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1776424-1776433"...
% 2.38/0.59 % (1776433)...printing done.
% 2.38/0.59 % (1776433)Refutation found. Thanks to Tanya!
% 2.38/0.59 % SZS status Theorem for theBenchmark
% 2.38/0.59 % SZS output start Proof for theBenchmark
% 2.38/0.59 thf(type_def_5, type, paraco415392788lle_tv: $tType).
% 2.38/0.59 thf(type_def_6, type, paraco414474393lle_fm: $tType).
% 2.38/0.59 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.38/0.59 thf(type_def_8, type, char: $tType).
% 2.38/0.59 thf(type_def_9, type, list: $tType > $tType).
% 2.38/0.59 thf(type_def_10, type, set: $tType > $tType).
% 2.38/0.59 thf(type_def_11, type, nat: $tType).
% 2.38/0.59 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 2.38/0.59 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_6, type, order_top: !>[X0: $tType]:($o)).
% 2.38/0.59 thf(func_def_7, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 2.38/0.59 thf(func_def_8, type, the_inv_into: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 2.38/0.59 thf(func_def_9, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.38/0.59 thf(func_def_10, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.38/0.59 thf(func_def_11, type, top_top: !>[X0: $tType]:(X0)).
% 2.38/0.59 thf(func_def_12, type, paraco753463838ge_int: ((nat > nat) > (list @ char > paraco415392788lle_tv) > list @ char > paraco415392788lle_tv)).
% 2.38/0.59 thf(func_def_13, type, paraco1920534163nge_tv: ((nat > nat) > paraco415392788lle_tv > paraco415392788lle_tv)).
% 2.38/0.59 thf(func_def_14, type, paraco2077297190tv_rel: (product_prod @ (nat > nat) @ paraco415392788lle_tv > product_prod @ (nat > nat) @ paraco415392788lle_tv > $o)).
% 2.38/0.59 thf(func_def_15, type, paraco876059933e_eval: ((list @ char > paraco415392788lle_tv) > paraco414474393lle_fm > paraco415392788lle_tv)).
% 2.38/0.59 thf(func_def_16, type, paraco2100061555le_Con: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_17, type, paraco2084319816le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_18, type, paraco1628874225le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_19, type, paraco329115265le_Neg: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_20, type, paraco27778325le_Pro: (list @ char > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_21, type, paraco251304083_Truth: paraco414474393lle_fm).
% 2.38/0.59 thf(func_def_22, type, paraco1246693743ase_fm: !>[X0: $tType]:(((list @ char > X0) > X0 > (paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > paraco414474393lle_fm > X0))).
% 2.38/0.59 thf(func_def_23, type, paraco2040174112le_Det: ($o > paraco415392788lle_tv)).
% 2.38/0.59 thf(func_def_24, type, paraco676387099_Indet: (nat > paraco415392788lle_tv)).
% 2.38/0.59 thf(func_def_25, type, paraco490622181ase_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 2.38/0.59 thf(func_def_26, type, paraco152590079rec_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 2.38/0.59 thf(func_def_27, type, paraco769098683_valid: (paraco414474393lle_fm > $o)).
% 2.38/0.59 thf(func_def_28, type, paraco2086025920lid_in: (set @ nat > paraco414474393lle_fm > $o)).
% 2.38/0.59 thf(func_def_29, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 2.38/0.59 thf(func_def_30, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 2.38/0.59 thf(func_def_31, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 2.38/0.59 thf(func_def_32, type, product_case_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 2.38/0.59 thf(func_def_33, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 2.38/0.59 thf(func_def_34, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.38/0.59 thf(func_def_35, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 2.38/0.59 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.38/0.59 thf(func_def_37, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.38/0.59 thf(func_def_38, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.38/0.59 thf(func_def_39, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 2.38/0.59 thf(func_def_40, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 2.38/0.59 thf(func_def_41, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 2.38/0.59 thf(func_def_42, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 2.38/0.59 thf(func_def_43, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.38/0.59 thf(func_def_44, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 2.38/0.59 thf(func_def_45, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 2.38/0.59 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.38/0.59 thf(func_def_47, type, f: (nat > nat)).
% 2.38/0.59 thf(func_def_48, type, i: (list @ char > paraco415392788lle_tv)).
% 2.38/0.59 thf(func_def_49, type, p1: paraco414474393lle_fm).
% 2.38/0.59 thf(func_def_50, type, p2: paraco414474393lle_fm).
% 2.38/0.59 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.38/0.59 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 2.38/0.59 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 2.38/0.59 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 2.38/0.59 thf(func_def_58, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.38/0.59 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.38/0.59 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 2.38/0.59 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 2.38/0.59 thf(func_def_62, type, db3: !>[X0: $tType]:(X0)).
% 2.38/0.59 thf(func_def_63, type, vNOT: ($o > $o)).
% 2.38/0.59 thf(func_def_64, type, vOR: ($o > $o > $o)).
% 2.38/0.59 thf(func_def_65, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.38/0.59 thf(func_def_66, type, sP0: ((paraco414474393lle_fm > $o) > $o)).
% 2.38/0.59 thf(func_def_67, type, sP1: ((paraco414474393lle_fm > $o) > $o)).
% 2.38/0.59 thf(func_def_68, type, sP2: ((paraco414474393lle_fm > $o) > $o)).
% 2.38/0.59 thf(func_def_69, type, sP3: ((paraco414474393lle_fm > $o) > $o)).
% 2.38/0.59 thf(func_def_70, type, sP4: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > $o)).
% 2.38/0.59 thf(func_def_71, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.38/0.59 thf(func_def_72, type, sP6: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.38/0.59 thf(func_def_73, type, sP7: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 2.38/0.59 thf(func_def_74, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.59 thf(func_def_75, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.59 thf(func_def_76, type, sK10: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_77, type, sK11: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_78, type, sK12: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_79, type, sK13: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_80, type, sK14: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_81, type, sK15: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_82, type, sK16: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_83, type, sK17: ((paraco414474393lle_fm > $o) > list @ char)).
% 2.38/0.59 thf(func_def_84, type, sK18: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_85, type, sK19: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_86, type, sK20: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_87, type, sK21: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_88, type, sK22: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_89, type, sK23: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_90, type, sK24: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_91, type, sK25: (paraco414474393lle_fm > list @ char)).
% 2.38/0.59 thf(func_def_92, type, sK26: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.38/0.59 thf(func_def_93, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.38/0.59 thf(func_def_94, type, sK28: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_95, type, sK29: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.59 thf(func_def_96, type, sK30: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_97, type, sK31: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_98, type, sK32: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_99, type, sK33: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_100, type, sK34: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_101, type, sK35: (paraco414474393lle_fm > list @ char)).
% 2.38/0.60 thf(func_def_102, type, sK36: !>[X0: $tType]:(X0)).
% 2.38/0.60 thf(func_def_103, type, sK37: !>[X0: $tType]:((set @ X0 > X0))).
% 2.38/0.60 thf(func_def_104, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_105, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_106, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_107, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_108, type, sK42: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_109, type, sK43: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_110, type, sK44: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_111, type, sK45: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_112, type, sK46: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_113, type, sK47: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_114, type, sK48: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_115, type, sK49: ((paraco414474393lle_fm > $o) > list @ char)).
% 2.38/0.60 thf(func_def_116, type, sK50: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_117, type, sK51: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_118, type, sK52: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_119, type, sK53: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_120, type, sK54: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_121, type, sK55: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_122, type, sK56: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_123, type, sK57: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_124, type, sK58: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_125, type, sK59: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_126, type, sK60: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 2.38/0.60 thf(func_def_127, type, sK61: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_128, type, sK62: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_129, type, sK63: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char)).
% 2.38/0.60 thf(func_def_130, type, sK64: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > nat)).
% 2.38/0.60 thf(func_def_131, type, sK65: (paraco415392788lle_tv > paraco415392788lle_tv > $o)).
% 2.38/0.60 thf(func_def_132, type, sK66: ((paraco415392788lle_tv > $o) > nat)).
% 2.38/0.60 thf(func_def_133, type, sK67: (((nat > nat) > paraco415392788lle_tv > $o) > nat > nat)).
% 2.38/0.60 thf(func_def_134, type, sK68: (((nat > nat) > paraco415392788lle_tv > $o) > nat)).
% 2.38/0.60 thf(func_def_135, type, sK69: (((nat > nat) > paraco415392788lle_tv > $o) > nat > nat)).
% 2.38/0.60 thf(func_def_136, type, sK70: (((nat > nat) > paraco415392788lle_tv > $o) > $o)).
% 2.38/0.60 thf(func_def_137, type, sK71: (paraco415392788lle_tv > nat)).
% 2.38/0.60 thf(func_def_138, type, sK72: (paraco415392788lle_tv > nat)).
% 2.38/0.60 thf(func_def_139, type, sK73: (paraco415392788lle_tv > $o)).
% 2.38/0.60 thf(func_def_140, type, sK74: ((paraco415392788lle_tv > $o) > nat)).
% 2.38/0.60 thf(func_def_141, type, sK75: ((paraco415392788lle_tv > $o) > $o)).
% 2.38/0.60 thf(func_def_142, type, sK76: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.38/0.60 thf(func_def_143, type, sK77: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.38/0.60 thf(func_def_144, type, sK78: (product_prod @ (nat > nat) @ paraco415392788lle_tv > nat > nat)).
% 2.38/0.60 thf(func_def_145, type, sK79: (product_prod @ (nat > nat) @ paraco415392788lle_tv > nat)).
% 2.38/0.60 thf(func_def_146, type, sK80: (product_prod @ (nat > nat) @ paraco415392788lle_tv > nat > nat)).
% 2.38/0.60 thf(func_def_147, type, sK81: (product_prod @ (nat > nat) @ paraco415392788lle_tv > $o)).
% 2.38/0.60 thf(func_def_148, type, sK82: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.38/0.60 thf(func_def_149, type, sK83: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_150, type, sK84: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.38/0.60 thf(func_def_151, type, sK85: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.38/0.60 thf(func_def_152, type, sK86: !>[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))).
% 2.38/0.60 thf(func_def_153, type, sK87: !>[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))).
% 2.38/0.60 thf(func_def_154, type, sK88: !>[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))).
% 2.38/0.60 thf(func_def_155, type, sK89: !>[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))).
% 2.38/0.60 thf(func_def_156, type, sK90: !>[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))).
% 2.38/0.60 thf(func_def_157, type, sK91: !>[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))).
% 2.38/0.60 thf(func_def_158, type, sK92: !>[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))).
% 2.38/0.60 thf(func_def_159, type, sK93: !>[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))).
% 2.38/0.60 thf(func_def_160, type, sK94: !>[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))).
% 2.38/0.60 thf(func_def_161, type, sK95: !>[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))).
% 2.38/0.60 thf(func_def_162, type, sK96: !>[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))).
% 2.38/0.60 thf(func_def_163, type, sK97: !>[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))).
% 2.38/0.60 thf(func_def_164, type, sK98: !>[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))).
% 2.38/0.60 thf(func_def_165, type, sK99: !>[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))).
% 2.38/0.60 thf(func_def_166, type, sK100: !>[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))).
% 2.38/0.60 thf(func_def_167, type, sK101: !>[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))).
% 2.38/0.60 thf(func_def_168, type, sK102: !>[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))).
% 2.38/0.60 thf(func_def_169, type, sK103: !>[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))).
% 2.38/0.60 thf(func_def_170, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 2.38/0.60 thf(func_def_171, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.38/0.60 thf(func_def_172, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.38/0.60 thf(func_def_173, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_174, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.38/0.60 thf(func_def_175, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.38/0.60 thf(func_def_176, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_177, type, sK111: !>[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))).
% 2.38/0.60 thf(func_def_178, type, sK112: !>[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))).
% 2.38/0.60 thf(func_def_179, type, sK113: !>[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))).
% 2.38/0.60 thf(func_def_180, type, sK114: !>[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))).
% 2.38/0.60 thf(func_def_181, type, sK115: !>[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))).
% 2.38/0.60 thf(func_def_182, type, sK116: !>[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))).
% 2.38/0.60 thf(func_def_183, type, sK117: !>[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))).
% 2.38/0.60 thf(func_def_184, type, sK118: !>[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))).
% 2.38/0.60 thf(func_def_185, type, sK119: !>[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))).
% 2.38/0.60 thf(func_def_186, type, sK120: !>[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))).
% 2.38/0.60 thf(func_def_187, type, sK121: !>[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))).
% 2.38/0.60 thf(func_def_188, type, sK122: !>[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))).
% 2.38/0.60 thf(func_def_189, type, sK123: !>[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))).
% 2.38/0.60 thf(func_def_190, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 2.38/0.60 thf(func_def_191, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 2.38/0.60 thf(func_def_192, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 2.38/0.60 thf(func_def_193, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 2.38/0.60 thf(func_def_194, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 2.38/0.60 thf(func_def_195, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 2.38/0.60 thf(func_def_196, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 2.38/0.60 thf(func_def_197, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 2.38/0.60 thf(func_def_198, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 2.38/0.60 thf(func_def_199, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 2.38/0.60 thf(func_def_200, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 2.38/0.60 thf(func_def_201, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 2.38/0.60 thf(func_def_202, type, sK136: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.38/0.60 thf(func_def_203, type, sK137: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_204, type, sK138: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > $o)).
% 2.38/0.60 thf(func_def_205, type, sK139: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > nat)).
% 2.38/0.60 thf(func_def_206, type, sK140: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 2.38/0.60 thf(func_def_207, type, sK141: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_208, type, sK142: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_209, type, sK143: !>[X0: $tType, X1: $tType]:(((X1 > X1) > (X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_210, type, sK144: !>[X0: $tType, X1: $tType]:(((X1 > X1) > (X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_211, type, sK145: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_212, type, sK146: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_213, type, sK147: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 2.38/0.60 thf(func_def_214, type, sK148: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 2.38/0.60 thf(func_def_215, type, sK149: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 2.38/0.60 thf(func_def_216, type, sK150: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_217, type, sK151: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 2.38/0.60 thf(func_def_218, type, sK152: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_219, type, sK153: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 2.38/0.60 thf(func_def_220, type, sK154: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 2.38/0.60 thf(func_def_221, type, sK155: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_222, type, sK156: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_223, type, sK157: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_224, type, sK158: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_225, type, sK159: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_226, type, sK160: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_227, type, sK161: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_228, type, sK162: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_229, type, sK163: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_230, type, sK164: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_231, type, sK165: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_232, type, sK166: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_233, type, sK167: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_234, type, sK168: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_235, type, sK169: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_236, type, sK170: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_237, type, sK171: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 2.38/0.60 thf(func_def_238, type, sK172: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_239, type, sK173: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_240, type, sK174: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_241, type, sK175: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_242, type, sK176: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_243, type, sK177: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_244, type, sK178: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_245, type, sK179: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_246, type, sK180: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_247, type, sK181: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_248, type, sK182: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_249, type, sK183: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_250, type, sK184: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_251, type, sK185: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_252, type, sK186: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.38/0.60 thf(func_def_253, type, sK187: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_254, type, sK188: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_255, type, sK189: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_256, type, sK190: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_257, type, sK191: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_258, type, sK192: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 2.38/0.60 thf(func_def_259, type, sK193: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_260, type, sK194: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_261, type, sK195: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.38/0.60 thf(func_def_262, type, sK196: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_263, type, sK197: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_264, type, sK198: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 2.38/0.60 thf(func_def_265, type, sK199: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_266, type, sK200: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_267, type, sK201: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_268, type, sK202: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_269, type, sK203: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_270, type, sK204: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_271, type, sK205: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_272, type, sK206: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_273, type, sK207: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_274, type, sK208: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_275, type, sK209: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_276, type, sK210: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_277, type, sK211: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_278, type, sK212: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_279, type, sK213: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_280, type, sK214: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_281, type, sK215: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_282, type, sK216: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_283, type, sK217: !>[X0: $tType, X1: $tType]:((X0 > X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_284, type, sK218: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_285, type, sK219: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_286, type, sK220: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 2.38/0.60 thf(func_def_287, type, sK221: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_288, type, sK222: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_289, type, sK223: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_290, type, sK224: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_291, type, sK225: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_292, type, sK226: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_293, type, sK227: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_294, type, sK228: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_295, type, sK229: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_296, type, sK230: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_297, type, sK231: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_298, type, sK232: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_299, type, sK233: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_300, type, sK234: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_301, type, sK235: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_302, type, sK236: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_303, type, sK237: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_304, type, sK238: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_305, type, sK239: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_306, type, sK240: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_307, type, sK241: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_308, type, sK242: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_309, type, sK243: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_310, type, sK244: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_311, type, sK245: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_312, type, sK246: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_313, type, sK247: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_314, type, sK248: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_315, type, sK249: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_316, type, sK250: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_317, type, sK251: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_318, type, sK252: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_319, type, sK253: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_320, type, sK254: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_321, type, sK255: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_322, type, sK256: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_323, type, sK257: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_324, type, sK258: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_325, type, sK259: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0))).
% 2.38/0.60 thf(func_def_326, type, sK260: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X1) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_327, type, sK261: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 2.38/0.60 thf(func_def_328, type, sK262: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_329, type, sK263: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_330, type, sK264: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_331, type, sK265: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_332, type, sK266: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_333, type, sK267: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_334, type, sK268: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_335, type, sK269: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_336, type, sK270: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_337, type, sK271: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2) > product_prod @ X1 @ X0))).
% 2.38/0.60 thf(func_def_338, type, sK272: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2) > product_prod @ X1 @ X0))).
% 2.38/0.60 thf(func_def_339, type, sK273: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2) > product_prod @ X0 @ X1))).
% 2.38/0.60 thf(func_def_340, type, sK274: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X2) > product_prod @ X0 @ X1))).
% 2.38/0.60 thf(func_def_341, type, sK275: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_342, type, sK276: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 2.38/0.60 thf(func_def_343, type, sK277: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_344, type, sK278: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_345, type, sK279: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_346, type, sK280: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_347, type, sK281: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_348, type, sK282: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_349, type, sK283: (paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_350, type, sK284: (paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_351, type, sK285: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_352, type, sK286: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_353, type, sK287: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_354, type, sK288: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_355, type, sK289: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_356, type, sK290: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_357, type, sK291: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_358, type, sK292: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_359, type, sK293: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_360, type, sK294: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 2.38/0.60 thf(func_def_361, type, sK295: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_362, type, sK296: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_363, type, sK297: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_364, type, sK298: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_365, type, sK299: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_366, type, sK300: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_367, type, sK301: ((nat > nat) > nat)).
% 2.38/0.60 thf(func_def_368, type, sK302: ((nat > nat) > nat)).
% 2.38/0.60 thf(func_def_369, type, sK303: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_370, type, sK304: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_371, type, sK305: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_372, type, sK306: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_373, type, sK307: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_374, type, sK308: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_375, type, sK309: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_376, type, sK310: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_377, type, sK311: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_378, type, sK312: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 2.38/0.60 thf(func_def_379, type, sK313: (paraco414474393lle_fm > paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_380, type, sK314: (paraco414474393lle_fm > paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_381, type, sK315: (paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_382, type, sK316: (paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 2.38/0.60 thf(func_def_384, type, db4: !>[X0: $tType]:(X0)).
% 2.38/0.60 thf(f1,axiom,(
% 2.38/0.60 (((paraco876059933e_eval @ i @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_a)).
% 2.38/0.60 thf(f3,axiom,(
% 2.38/0.60 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))))),
% 2.38/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_ih2)).
% 2.38/0.60 thf(f8,axiom,(
% 2.38/0.60 (paraco753463838ge_int = (^[X0 : (nat > nat), X1 : (list @ char > paraco415392788lle_tv), X2 : list @ char] : ((paraco1920534163nge_tv @ X0 @ (X1 @ X2)))))),
% 2.38/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_change__int__def)).
% 2.38/0.60 thf(f9,axiom,(
% 2.38/0.60 ! [X0 : (nat > nat),X1 : $o] : (((paraco1920534163nge_tv @ X0 @ (paraco2040174112le_Det @ X1))) = ((paraco2040174112le_Det @ X1)))),
% 2.38/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_change__tv_Osimps_I1_J)).
% 2.38/0.60 thf(f280,conjecture,(
% 2.38/0.60 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 2.38/0.60 thf(f281,negated_conjecture,(
% 2.38/0.60 ~ (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(negated_conjecture,[status(cth)],[f280])).
% 2.38/0.60 thf(f282,plain,(
% 2.38/0.60 (((paraco876059933e_eval @ i @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(rectify,[],[f1])).
% 2.38/0.60 thf(f283,plain,(
% 2.38/0.60 (((paraco876059933e_eval @ i @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(fool_elimination,[],[f282])).
% 2.38/0.60 thf(f289,plain,(
% 2.38/0.60 (paraco753463838ge_int = (^[Y0 : nat > nat]: ((^[Y1 : list @ char > paraco415392788lle_tv]: ((^[Y2 : list @ char]: (paraco1920534163nge_tv @ Y0 @ (Y1 @ Y2))))))))),
% 2.38/0.60 inference(fool_elimination,[],[f8])).
% 2.38/0.60 thf(f638,plain,(
% 2.38/0.60 ~ (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(rectify,[],[f281])).
% 2.38/0.60 thf(f639,plain,(
% 2.38/0.60 ~ (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(fool_elimination,[],[f638])).
% 2.38/0.60 thf(f649,plain,(
% 2.38/0.60 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) != ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(flattening,[],[f639])).
% 2.38/0.60 thf(f945,plain,(
% 2.38/0.60 (((paraco876059933e_eval @ i @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(cnf_transformation,[],[f283])).
% 2.38/0.60 thf(f947,plain,(
% 2.38/0.60 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)))),
% 2.38/0.60 inference(cnf_transformation,[],[f3])).
% 2.38/0.60 thf(f952,plain,(
% 2.38/0.60 (paraco753463838ge_int = (^[Y0 : nat > nat]: ((^[Y1 : list @ char > paraco415392788lle_tv]: ((^[Y2 : list @ char]: (paraco1920534163nge_tv @ Y0 @ (Y1 @ Y2))))))))),
% 2.38/0.60 inference(cnf_transformation,[],[f289])).
% 2.38/0.60 thf(f953,plain,(
% 2.38/0.60 ( ! [X0 : (nat > nat),X1 : $o] : ((((paraco2040174112le_Det @ X1)) = ((paraco1920534163nge_tv @ X0 @ (paraco2040174112le_Det @ X1))))) )),
% 2.38/0.60 inference(cnf_transformation,[],[f9])).
% 2.38/0.60 thf(f1309,plain,(
% 2.38/0.60 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) != ((paraco2040174112le_Det @ $true)))),
% 2.38/0.60 inference(cnf_transformation,[],[f649])).
% 2.38/0.60 thf(f1312,plain,(
% 2.38/0.60 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco876059933e_eval @ ((^[Y0 : nat > nat]: ((^[Y1 : list @ char > paraco415392788lle_tv]: ((^[Y2 : list @ char]: (paraco1920534163nge_tv @ Y0 @ (Y1 @ Y2))))))) @ f @ i) @ p2)))),
% 2.38/0.60 inference(definition_unfolding,[],[f947,f952])).
% 2.38/0.60 thf(f1379,plain,(
% 2.38/0.60 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ ((^[Y0 : nat > nat]: ((^[Y1 : list @ char > paraco415392788lle_tv]: ((^[Y2 : list @ char]: (paraco1920534163nge_tv @ Y0 @ (Y1 @ Y2))))))) @ f @ i) @ p2)))),
% 2.38/0.60 inference(definition_unfolding,[],[f1309,f952])).
% 2.38/0.60 thf(f1408,plain,(
% 2.38/0.60 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ (^[Y0 : list @ char]: (paraco1920534163nge_tv @ f @ (i @ Y0))) @ p2)))),
% 2.38/0.60 inference(beta-eta_normalization,[],[f1379])).
% 2.38/0.60 thf(f4050,plain,(
% 2.38/0.60 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco876059933e_eval @ (^[Y0 : list @ char]: (paraco1920534163nge_tv @ f @ (i @ Y0))) @ p2)))),
% 2.38/0.60 inference(beta-eta_normalization,[],[f1312])).
% 2.38/0.60 thf(f12807,plain,(
% 2.38/0.60 (((paraco876059933e_eval @ (^[Y0 : list @ char]: (paraco1920534163nge_tv @ f @ (i @ Y0))) @ p2)) = ((paraco1920534163nge_tv @ f @ (paraco2040174112le_Det @ $true))))),
% 2.38/0.60 inference(forward_demodulation,[],[f4050,f945])).
% 2.38/0.60 thf(f12808,plain,(
% 2.38/0.60 (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ (^[Y0 : list @ char]: (paraco1920534163nge_tv @ f @ (i @ Y0))) @ p2)))),
% 2.38/0.60 inference(forward_demodulation,[],[f12807,f953])).
% 2.38/0.60 thf(f12809,plain,(
% 2.38/0.60 $false),
% 2.38/0.60 inference(forward_subsumption_resolution,[],[f12808,f1408])).
% 2.38/0.60 % SZS output end Proof for theBenchmark
% 2.38/0.60 % (1776433)------------------------------
% 2.38/0.60 % (1776433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.38/0.60 % (1776433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/0.60 % (1776433)CaDiCaL version: 2.1.3
% 2.38/0.60 % (1776433)Termination reason: Refutation
% 2.38/0.60 % (1776433)Time elapsed: 0.337 s
% 2.38/0.60 % (1776433)Peak memory usage: 21 MB
% 2.38/0.60 % (1776433)Instructions burned: 1262 (million)
% 2.38/0.60 % (1776424)Success in time 0.37 s
% 2.38/0.60 % Vampire exiting
%------------------------------------------------------------------------------