%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP137^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 1.68s 0.56s
% Output : Refutation 1.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP137^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 19:59:18 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.68/0.56 % (1275603)Will run a generic schedule for satisfiability detection.
% 1.68/0.56 % (1275609)% WARNING: option uhcvi not known.
% 1.68/0.56 % (1275608)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2814998726_2999 on theBenchmark for (2999ds/0Mi)
% 1.68/0.56 % (1275610)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4209877159:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.68/0.56 % (1275612)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1502601046:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.68/0.56 % (1275609)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4264787176:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.68/0.56 % (1275611)dis+10_1_sil=32000:sp=arity:random_seed=2130331119:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.68/0.56 % (1275614)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1562347715:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.68/0.56 % (1275613)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3586762596:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.68/0.56 % (1275612)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.68/0.56 % (1275609)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.68/0.56 % Exception at run slice level
% 1.68/0.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.68/0.56 % (1275609)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.68/0.56 % (1275612)Instruction limit reached!
% 1.68/0.56 % (1275612)------------------------------
% 1.68/0.56 % (1275612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275612)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275612)Termination reason: Instruction limit
% 1.68/0.56 % (1275612)Termination phase: Saturation
% 1.68/0.56 % (1275612)Time elapsed: 0.055 s
% 1.68/0.56 % (1275612)Peak memory usage: 13 MB
% 1.68/0.56 % (1275612)Instructions burned: 116 (million)
% 1.68/0.56 % (1275622)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2315592504:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.68/0.56 % (1275611)Instruction limit reached!
% 1.68/0.56 % (1275611)------------------------------
% 1.68/0.56 % (1275611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275611)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275611)Termination reason: Instruction limit
% 1.68/0.56 % (1275611)Termination phase: Saturation
% 1.68/0.56 % (1275611)Time elapsed: 0.062 s
% 1.68/0.56 % (1275611)Peak memory usage: 13 MB
% 1.68/0.56 % (1275611)Instructions burned: 103 (million)
% 1.68/0.56 % (1275623)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2137328281:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.68/0.56 % (1275613)Instruction limit reached!
% 1.68/0.56 % (1275613)------------------------------
% 1.68/0.56 % (1275613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275613)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275613)Termination reason: Instruction limit
% 1.68/0.56 % (1275613)Termination phase: Saturation
% 1.68/0.56 % (1275613)Time elapsed: 0.065 s
% 1.68/0.56 % (1275613)Peak memory usage: 13 MB
% 1.68/0.56 % (1275613)Instructions burned: 131 (million)
% 1.68/0.56 % (1275614)Instruction limit reached!
% 1.68/0.56 % (1275614)------------------------------
% 1.68/0.56 % (1275614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275614)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275614)Termination reason: Instruction limit
% 1.68/0.56 % (1275614)Termination phase: Saturation
% 1.68/0.56 % (1275614)Time elapsed: 0.079 s
% 1.68/0.56 % (1275614)Peak memory usage: 14 MB
% 1.68/0.56 % (1275614)Instructions burned: 160 (million)
% 1.68/0.56 % (1275625)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=2945468087:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.68/0.56 % (1275627)ott-21_1_sil=16000:fs=off:random_seed=3782229292:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.68/0.56 % Exception at run slice level
% 1.68/0.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.68/0.56 % (1275628)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=527398116:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.68/0.56 % (1275625)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.68/0.56 % (1275631)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=263008659:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.68/0.56 % (1275623)Instruction limit reached!
% 1.68/0.56 % (1275623)------------------------------
% 1.68/0.56 % (1275623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275623)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275623)Termination reason: Instruction limit
% 1.68/0.56 % (1275623)Termination phase: Saturation
% 1.68/0.56 % (1275623)Time elapsed: 0.067 s
% 1.68/0.56 % (1275623)Peak memory usage: 13 MB
% 1.68/0.56 % (1275623)Instructions burned: 132 (million)
% 1.68/0.56 % (1275625)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.68/0.56 % (1275634)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=106392948:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.68/0.56 % Exception at run slice level
% 1.68/0.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.68/0.56 % (1275636)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2344102971:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.68/0.56 % (1275627)Instruction limit reached!
% 1.68/0.56 % (1275627)------------------------------
% 1.68/0.56 % (1275627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275627)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275627)Termination reason: Instruction limit
% 1.68/0.56 % (1275627)Termination phase: Saturation
% 1.68/0.56 % (1275627)Time elapsed: 0.112 s
% 1.68/0.56 % (1275627)Peak memory usage: 14 MB
% 1.68/0.56 % (1275627)Instructions burned: 180 (million)
% 1.68/0.56 % Exception at run slice level
% 1.68/0.56 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.68/0.56 % (1275638)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=2644706893: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)
% 1.68/0.56 % (1275639)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=350080643:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.68/0.56 % (1275625) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1275603-1275625"...
% 1.68/0.56 % (1275625)...printing done.
% 1.68/0.56 % (1275625)Refutation found. Thanks to Tanya!
% 1.68/0.56 % SZS status Theorem for theBenchmark
% 1.68/0.56 % SZS output start Proof for theBenchmark
% 1.68/0.56 thf(type_def_5, type, paraco415392788lle_tv: $tType).
% 1.68/0.56 thf(type_def_6, type, paraco414474393lle_fm: $tType).
% 1.68/0.56 thf(type_def_7, type, product_unit: $tType).
% 1.68/0.56 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 1.68/0.56 thf(type_def_9, type, char: $tType).
% 1.68/0.56 thf(type_def_10, type, list: $tType > $tType).
% 1.68/0.56 thf(type_def_11, type, set: $tType > $tType).
% 1.68/0.56 thf(type_def_12, type, nat: $tType).
% 1.68/0.56 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 1.68/0.56 thf(func_def_0, type, fun_reduction_pair: !>[X0: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > $o))).
% 1.68/0.56 thf(func_def_1, type, fun_rp_inv_image: !>[X0: $tType, X1: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > (X1 > X0) > product_prod @ set @ product_prod @ X1 @ X1 @ set @ product_prod @ X1 @ X1))).
% 1.68/0.56 thf(func_def_2, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_3, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.68/0.56 thf(func_def_4, type, order_above: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > set @ X0))).
% 1.68/0.56 thf(func_def_5, type, order_aboveS: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > set @ X0))).
% 1.68/0.56 thf(func_def_6, type, order_relation_of: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > set @ product_prod @ X0 @ X0))).
% 1.68/0.56 thf(func_def_7, type, bot_bot: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_8, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.68/0.56 thf(func_def_9, type, top_top: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_10, type, paraco876059933e_eval: ((list @ char > paraco415392788lle_tv) > paraco414474393lle_fm > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_11, type, paraco2100061555le_Con: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_12, type, paraco2084319816le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_13, type, paraco1628874225le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_14, type, paraco329115265le_Neg: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_15, type, paraco27778325le_Pro: (list @ char > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_16, type, paraco251304083_Truth: paraco414474393lle_fm).
% 1.68/0.56 thf(func_def_17, type, paraco1246693743ase_fm: !>[X0: $tType]:(((list @ char > X0) > X0 > (paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > paraco414474393lle_fm > X0))).
% 1.68/0.56 thf(func_def_18, type, paraco2040174112le_Det: ($o > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_19, type, paraco676387099_Indet: (nat > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_20, type, paraco490622181ase_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 1.68/0.56 thf(func_def_21, type, paraco152590079rec_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 1.68/0.56 thf(func_def_22, type, paraco769098683_valid: (paraco414474393lle_fm > $o)).
% 1.68/0.56 thf(func_def_23, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 1.68/0.56 thf(func_def_24, type, product_Sigma: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ product_prod @ X0 @ X1))).
% 1.68/0.56 thf(func_def_25, type, product_case_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 1.68/0.56 thf(func_def_26, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 1.68/0.56 thf(func_def_27, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.68/0.56 thf(func_def_28, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 1.68/0.56 thf(func_def_29, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.68/0.56 thf(func_def_30, type, product_rec_set_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2 > $o))).
% 1.68/0.56 thf(func_def_31, type, product_rec_set_unit: !>[X0: $tType]:((X0 > product_unit > X0 > $o))).
% 1.68/0.56 thf(func_def_32, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 1.68/0.56 thf(func_def_33, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 1.68/0.56 thf(func_def_34, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.68/0.56 thf(func_def_35, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.68/0.56 thf(func_def_36, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 1.68/0.56 thf(func_def_37, type, product_product: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ product_prod @ X0 @ X1))).
% 1.68/0.56 thf(func_def_38, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 1.68/0.56 thf(func_def_39, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 1.68/0.56 thf(func_def_40, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 1.68/0.56 thf(func_def_41, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.68/0.56 thf(func_def_42, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 1.68/0.56 thf(func_def_43, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 1.68/0.56 thf(func_def_44, 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))).
% 1.68/0.56 thf(func_def_45, 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))).
% 1.68/0.56 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.68/0.56 thf(func_def_47, type, p: paraco414474393lle_fm).
% 1.68/0.56 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.68/0.56 thf(func_def_52, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.68/0.56 thf(func_def_53, type, db0: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.68/0.56 thf(func_def_56, type, vAND: ($o > $o > $o)).
% 1.68/0.56 thf(func_def_57, type, vNOT: ($o > $o)).
% 1.68/0.56 thf(func_def_58, type, vOR: ($o > $o > $o)).
% 1.68/0.56 thf(func_def_59, type, db2: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_60, type, vIMP: ($o > $o > $o)).
% 1.68/0.56 thf(func_def_61, type, db4: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_62, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.68/0.56 thf(func_def_63, type, db3: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_64, type, db5: !>[X0: $tType]:(X0)).
% 1.68/0.56 thf(func_def_65, type, sP0: ((paraco414474393lle_fm > $o) > $o)).
% 1.68/0.56 thf(func_def_66, type, sP1: ((paraco414474393lle_fm > $o) > $o)).
% 1.68/0.56 thf(func_def_67, type, sK2: ((paraco415392788lle_tv > $o) > nat)).
% 1.68/0.56 thf(func_def_68, type, sK3: ((paraco415392788lle_tv > $o) > $o)).
% 1.68/0.56 thf(func_def_69, type, sK4: (paraco415392788lle_tv > nat)).
% 1.68/0.56 thf(func_def_70, type, sK5: (paraco415392788lle_tv > $o)).
% 1.68/0.56 thf(func_def_71, type, sK6: ((paraco415392788lle_tv > $o) > nat)).
% 1.68/0.56 thf(func_def_72, type, sK7: (paraco415392788lle_tv > nat)).
% 1.68/0.56 thf(func_def_73, type, sK8: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_74, type, sK9: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_75, type, sK10: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_76, type, sK11: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_77, type, sK12: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_78, type, sK13: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_79, type, sK14: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_80, type, sK15: ((paraco414474393lle_fm > $o) > list @ char)).
% 1.68/0.56 thf(func_def_81, type, sK16: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_82, type, sK17: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_83, type, sK18: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_84, type, sK19: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_85, type, sK20: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_86, type, sK21: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_87, type, sK22: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_88, type, sK23: (paraco414474393lle_fm > list @ char)).
% 1.68/0.56 thf(func_def_89, type, sK24: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_90, type, sK25: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_91, type, sK26: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_92, type, sK27: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_93, type, sK28: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_94, type, sK29: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_95, type, sK30: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_96, type, sK31: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_97, type, sK32: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_98, type, sK33: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_99, type, sK34: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 1.68/0.56 thf(func_def_100, type, sK35: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_101, type, sK36: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 1.68/0.56 thf(func_def_102, type, sK37: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char)).
% 1.68/0.56 thf(func_def_103, type, sK38: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_104, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.68/0.56 thf(func_def_105, type, sK40: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.68/0.56 thf(func_def_106, type, sK41: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.68/0.56 thf(func_def_107, type, sK42: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.68/0.56 thf(func_def_108, type, sK43: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_109, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 1.68/0.56 thf(func_def_110, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 1.68/0.56 thf(func_def_111, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 1.68/0.56 thf(func_def_112, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 1.68/0.56 thf(func_def_113, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 1.68/0.56 thf(func_def_114, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 1.68/0.56 thf(func_def_115, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 1.68/0.56 thf(func_def_116, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 1.68/0.56 thf(func_def_117, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 1.68/0.56 thf(func_def_118, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 1.68/0.56 thf(func_def_119, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 1.68/0.56 thf(func_def_120, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 1.68/0.56 thf(func_def_121, 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))).
% 1.68/0.56 thf(func_def_122, 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))).
% 1.68/0.56 thf(func_def_123, 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))).
% 1.68/0.56 thf(func_def_124, 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))).
% 1.68/0.56 thf(func_def_125, 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))).
% 1.68/0.56 thf(func_def_126, 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))).
% 1.68/0.56 thf(func_def_127, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 1.68/0.56 thf(func_def_128, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 1.68/0.56 thf(func_def_129, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 1.68/0.56 thf(func_def_130, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 1.68/0.56 thf(func_def_131, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 1.68/0.56 thf(func_def_132, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 1.68/0.56 thf(func_def_133, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 1.68/0.56 thf(func_def_134, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.68/0.56 thf(func_def_135, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.68/0.56 thf(func_def_136, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_137, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.68/0.56 thf(func_def_138, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.68/0.56 thf(func_def_139, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.68/0.56 thf(func_def_140, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_141, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 1.68/0.56 thf(func_def_142, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.68/0.56 thf(func_def_143, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.68/0.56 thf(func_def_144, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.68/0.56 thf(func_def_145, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_146, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 1.68/0.56 thf(func_def_147, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 1.68/0.56 thf(func_def_148, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 1.68/0.56 thf(func_def_149, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 1.68/0.56 thf(func_def_150, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 1.68/0.56 thf(func_def_151, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_152, 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) > X6))).
% 1.68/0.56 thf(func_def_153, 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) > X5))).
% 1.68/0.56 thf(func_def_154, 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) > X4))).
% 1.68/0.56 thf(func_def_155, 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) > X3))).
% 1.68/0.56 thf(func_def_156, 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) > X2))).
% 1.68/0.56 thf(func_def_157, 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) > X1))).
% 1.68/0.56 thf(func_def_158, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_159, type, sK94: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 1.68/0.56 thf(func_def_160, type, sK95: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 1.68/0.56 thf(func_def_161, type, sK96: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 1.68/0.56 thf(func_def_162, type, sK97: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_163, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2))).
% 1.68/0.56 thf(func_def_164, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1))).
% 1.68/0.56 thf(func_def_165, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0))).
% 1.68/0.56 thf(func_def_166, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2))).
% 1.68/0.56 thf(func_def_167, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 1.68/0.56 thf(func_def_168, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 1.68/0.56 thf(func_def_169, type, sK104: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 1.68/0.56 thf(func_def_170, type, sK105: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 1.68/0.56 thf(func_def_171, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2))).
% 1.68/0.56 thf(func_def_172, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1))).
% 1.68/0.56 thf(func_def_173, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0))).
% 1.68/0.56 thf(func_def_174, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1))).
% 1.68/0.56 thf(func_def_175, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 1.68/0.56 thf(func_def_176, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 1.68/0.56 thf(func_def_177, type, sK112: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 1.68/0.56 thf(func_def_178, type, sK113: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 1.68/0.56 thf(func_def_179, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1))).
% 1.68/0.56 thf(func_def_180, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0))).
% 1.68/0.56 thf(func_def_181, type, sK116: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.68/0.56 thf(func_def_182, type, sK117: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.68/0.56 thf(func_def_183, type, sK118: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 1.68/0.56 thf(func_def_184, type, sK119: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.68/0.56 thf(func_def_185, type, sK120: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 1.68/0.56 thf(func_def_186, type, sK121: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 1.68/0.56 thf(func_def_187, type, sK122: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 1.68/0.56 thf(func_def_188, type, sK123: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > product_prod @ X0 @ X1 > X0))).
% 1.68/0.56 thf(func_def_189, type, sK124: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > product_prod @ X0 @ X1 > X1))).
% 1.68/0.56 thf(func_def_190, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 1.68/0.56 thf(func_def_191, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 1.68/0.56 thf(func_def_192, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 1.68/0.56 thf(func_def_193, type, sK128: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_194, type, sK129: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_195, type, sK130: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_196, type, sK131: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_197, type, sK132: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_198, type, sK133: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_199, type, sK134: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_200, type, sK135: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.68/0.56 thf(func_def_201, type, sK136: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 1.68/0.56 thf(func_def_202, type, sK137: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 1.68/0.56 thf(func_def_203, type, sK138: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 1.68/0.56 thf(func_def_204, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X2))).
% 1.68/0.56 thf(func_def_205, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X1))).
% 1.68/0.56 thf(func_def_206, type, sK141: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0) > set @ X1 > X1))).
% 1.68/0.56 thf(func_def_207, type, sK142: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 1.68/0.56 thf(func_def_208, type, sK143: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 1.68/0.56 thf(func_def_209, type, sK144: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > set @ X0) > X1))).
% 1.68/0.56 thf(func_def_210, type, sK145: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 1.68/0.56 thf(func_def_211, type, sK146: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 1.68/0.56 thf(func_def_212, type, sK147: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 1.68/0.56 thf(func_def_213, type, sK148: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 1.68/0.56 thf(func_def_214, type, sK149: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 1.68/0.56 thf(f1,axiom,(
% 1.68/0.56 ! [X5 : $o,X6 : $o] : ((((paraco2040174112le_Det @ X5)) = ((paraco2040174112le_Det @ X6))) = (X5 = X6))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tv_Oinject_I1_J)).
% 1.68/0.56 thf(f2,axiom,(
% 1.68/0.56 (paraco769098683_valid @ (paraco329115265le_Neg @ p))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms)).
% 1.68/0.56 thf(f3,axiom,(
% 1.68/0.56 (paraco769098683_valid = (^[X0 : paraco414474393lle_fm] : (! [X1 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X1 @ X0)) = ((paraco2040174112le_Det @ $true))))))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_valid__def)).
% 1.68/0.56 thf(f9,axiom,(
% 1.68/0.56 ! [X0 : (list @ char > paraco415392788lle_tv),X1 : paraco414474393lle_fm] : (((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $false))) => (((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $true))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco876059933e_eval @ X0 @ X1)))) & ((((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $true))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $false)))))) & ((((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $false))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $true)))))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_eval__negation)).
% 1.68/0.56 thf(f65,axiom,(
% 1.68/0.56 ! [X0 : $tType,X1 : $tType,X2 : (product_prod @ X1 @ X0 > $o),X3 : product_prod @ X1 @ X0] : (! [X4 : X1,X5 : X0] : (X2 @ (product_Pair @ X1 @ X0 @ X4 @ X5)) => (X2 @ X3))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_prod__cases)).
% 1.68/0.56 thf(f257,axiom,(
% 1.68/0.56 ! [X0 : $o] : ((X0 = $false) | (X0 = $true))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T)).
% 1.68/0.56 thf(f260,conjecture,(
% 1.68/0.56 ? [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) != ((paraco2040174112le_Det @ $true)))),
% 1.68/0.56 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.68/0.56 thf(f261,negated_conjecture,(
% 1.68/0.56 ~ ? [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) != ((paraco2040174112le_Det @ $true)))),
% 1.68/0.56 inference(negated_conjecture,[status(cth)],[f260])).
% 1.68/0.56 thf(f262,plain,(
% 1.68/0.56 ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) = ((paraco2040174112le_Det @ X1))) = (X0 = X1))),
% 1.68/0.56 inference(rectify,[],[f1])).
% 1.68/0.56 thf(f263,plain,(
% 1.68/0.56 ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0) = (paraco2040174112le_Det @ X1))) = ((X0 = X1)))),
% 1.68/0.56 inference(fool_elimination,[],[f262])).
% 1.68/0.56 thf(f264,plain,(
% 1.68/0.56 (paraco769098683_valid @ (paraco329115265le_Neg @ p))),
% 1.68/0.56 inference(rectify,[],[f2])).
% 1.68/0.56 thf(f265,plain,(
% 1.68/0.56 (((paraco769098683_valid @ (paraco329115265le_Neg @ p))) = $true)),
% 1.68/0.56 inference(fool_elimination,[],[f264])).
% 1.68/0.56 thf(f266,plain,(
% 1.68/0.56 (paraco769098683_valid = (^[X0 : paraco414474393lle_fm] : (! [X1 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X1 @ X0)) = ((paraco2040174112le_Det @ $true))))))),
% 1.68/0.56 inference(rectify,[],[f3])).
% 1.68/0.56 thf(f267,plain,(
% 1.68/0.56 (paraco769098683_valid = (^[Y0 : paraco414474393lle_fm]: (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y1 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y1 @ Y0) = (paraco2040174112le_Det @ $true))))))),
% 1.68/0.56 inference(fool_elimination,[],[f266])).
% 1.68/0.56 thf(f276,plain,(
% 1.68/0.56 ! [X0 : (list @ char > paraco415392788lle_tv),X1 : paraco414474393lle_fm] : (((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $false))) => (((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $true))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco876059933e_eval @ X0 @ X1)))) & ((((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $true))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $false)))))) & ((((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $false))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $true)))))),
% 1.68/0.56 inference(rectify,[],[f9])).
% 1.68/0.56 thf(f277,plain,(
% 1.68/0.56 ! [X0 : (list @ char > paraco415392788lle_tv),X1 : paraco414474393lle_fm] : (((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $false))) => (((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $true))) => (((paraco876059933e_eval @ X0 @ X1)) = ((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))))) & ((((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $true))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $false)))))) & ((((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $false))) => (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $true)))))),
% 1.68/0.56 inference(fool_elimination,[],[f276])).
% 1.68/0.56 thf(f310,plain,(
% 1.68/0.56 ! [X0 : $tType,X1 : $tType,X2 : (product_prod @ X1 @ X0 > $o),X3 : product_prod @ X1 @ X0] : (! [X4 : X1,X5 : X0] : (X2 @ (product_Pair @ X1 @ X0 @ X4 @ X5)) => (X2 @ X3))),
% 1.68/0.56 inference(rectify,[],[f65])).
% 1.68/0.56 thf(f311,plain,(
% 1.68/0.56 ! [X0 : $tType,X1 : $tType,X2 : (product_prod @ X1 @ X0 > $o),X3 : product_prod @ X1 @ X0] : (! [X4 : X1,X5 : X0] : (((X2 @ (product_Pair @ X1 @ X0 @ X4 @ X5))) = $true) => (((X2 @ X3)) = $true))),
% 1.68/0.56 inference(fool_elimination,[],[f310])).
% 1.68/0.56 thf(f577,plain,(
% 1.68/0.56 ! [X0 : $o] : (($false = X0) | ($true = X0))),
% 1.68/0.56 inference(fool_elimination,[],[f257])).
% 1.68/0.56 thf(f582,plain,(
% 1.68/0.56 ~ ? [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) != ((paraco2040174112le_Det @ $true)))),
% 1.68/0.56 inference(rectify,[],[f261])).
% 1.68/0.56 thf(f583,plain,(
% 1.68/0.56 ~ ? [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) != ((paraco2040174112le_Det @ $true)))),
% 1.68/0.56 inference(fool_elimination,[],[f582])).
% 1.68/0.56 thf(f596,plain,(
% 1.68/0.56 ! [X0 : (list @ char > paraco415392788lle_tv),X1 : paraco414474393lle_fm] : (((((((paraco876059933e_eval @ X0 @ X1)) = ((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1)))) | (((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $true)))) & ((((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $false))) | (((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $true))))) | (((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $false)))) & ((((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $true))) | (((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $false)))))),
% 1.68/0.56 inference(ennf_transformation,[],[f277])).
% 1.68/0.56 thf(f613,plain,(
% 1.68/0.56 ! [X0 : $tType,X1 : $tType,X2 : (product_prod @ X1 @ X0 > $o),X3 : product_prod @ X1 @ X0] : ((((X2 @ X3)) = $true) | ? [X4 : X1,X5 : X0] : (((X2 @ (product_Pair @ X1 @ X0 @ X4 @ X5))) != $true))),
% 1.68/0.56 inference(ennf_transformation,[],[f311])).
% 1.68/0.56 thf(f720,plain,(
% 1.68/0.56 ! [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))),
% 1.68/0.56 inference(ennf_transformation,[],[f583])).
% 1.68/0.56 thf(f745,plain,(
% 1.68/0.56 ! [X0 : $tType,X1 : $tType,X2 : (product_prod @ X1 @ X0 > $o),X3 : product_prod @ X1 @ X0] : ((((X2 @ X3)) = $true) | ($true != ((X2 @ (product_Pair @ X1 @ X0 @ (sK42 @ X0 @ X1 @ X2) @ (sK43 @ X0 @ X1 @ X2))))))),
% 1.68/0.56 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK3 @ X0),skolemize(X3,sK3 @ X0)],[f613])).
% 1.68/0.56 thf(f793,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : (((((paraco2040174112le_Det @ X0) = (paraco2040174112le_Det @ X1))) = ((X0 = X1)))) )),
% 1.68/0.56 inference(cnf_transformation,[],[f263])).
% 1.68/0.56 thf(f794,plain,(
% 1.68/0.56 (((paraco769098683_valid @ (paraco329115265le_Neg @ p))) = $true)),
% 1.68/0.56 inference(cnf_transformation,[],[f265])).
% 1.68/0.56 thf(f795,plain,(
% 1.68/0.56 (paraco769098683_valid = (^[Y0 : paraco414474393lle_fm]: (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y1 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y1 @ Y0) = (paraco2040174112le_Det @ $true))))))),
% 1.68/0.56 inference(cnf_transformation,[],[f267])).
% 1.68/0.56 thf(f806,plain,(
% 1.68/0.56 ( ! [X0 : (list @ char > paraco415392788lle_tv),X1 : paraco414474393lle_fm] : ((((paraco876059933e_eval @ X0 @ X1)) != ((paraco2040174112le_Det @ $true))) | (((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ X1))) = ((paraco2040174112le_Det @ $false))) | (((paraco876059933e_eval @ X0 @ X1)) = ((paraco2040174112le_Det @ $false)))) )),
% 1.68/0.56 inference(cnf_transformation,[],[f596])).
% 1.68/0.56 thf(f879,plain,(
% 1.68/0.56 ( ! [X1 : $tType,X0 : $tType,X2 : (product_prod @ X1 @ X0 > $o),X3 : product_prod @ X1 @ X0] : (($true != ((X2 @ (product_Pair @ X1 @ X0 @ (sK42 @ X0 @ X1 @ X2) @ (sK43 @ X0 @ X1 @ X2))))) | (((X2 @ X3)) = $true)) )),
% 1.68/0.56 inference(cnf_transformation,[],[f745])).
% 1.68/0.56 thf(f1112,plain,(
% 1.68/0.56 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.68/0.56 inference(cnf_transformation,[],[f577])).
% 1.68/0.56 thf(f1115,plain,(
% 1.68/0.56 ( ! [X0 : (list @ char > paraco415392788lle_tv)] : ((((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))) )),
% 1.68/0.56 inference(cnf_transformation,[],[f720])).
% 1.68/0.56 thf(f1129,plain,(
% 1.68/0.56 ($true = (((^[Y0 : paraco414474393lle_fm]: (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y1 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y1 @ Y0) = (paraco2040174112le_Det @ $true))))) @ (paraco329115265le_Neg @ p))))),
% 1.68/0.56 inference(definition_unfolding,[],[f794,f795])).
% 1.68/0.56 thf(f1662,plain,(
% 1.68/0.56 ($true = ((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ (paraco329115265le_Neg @ p)) = (paraco2040174112le_Det @ $true))))))),
% 1.68/0.56 inference(beta-eta_normalization,[],[f1129])).
% 1.68/0.56 thf(f1663,plain,(
% 1.68/0.56 ( ! [X1 : (list @ char > paraco415392788lle_tv)] : (($true = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ (paraco329115265le_Neg @ p)) = (paraco2040174112le_Det @ $true))) @ X1)))) )),
% 1.68/0.56 inference(pi_proxy_clausification,[],[f1662])).
% 1.68/0.56 thf(f1664,plain,(
% 1.68/0.56 ( ! [X1 : (list @ char > paraco415392788lle_tv)] : (($true = (((paraco876059933e_eval @ X1 @ (paraco329115265le_Neg @ p)) = (paraco2040174112le_Det @ $true))))) )),
% 1.68/0.56 inference(beta-eta_normalization,[],[f1663])).
% 1.68/0.56 thf(f1665,plain,(
% 1.68/0.56 ( ! [X1 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X1 @ (paraco329115265le_Neg @ p))))) )),
% 1.68/0.56 inference(equality_proxy_clausification,[],[f1664])).
% 1.68/0.56 thf(f1666,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : (((((paraco2040174112le_Det @ X0) = (paraco2040174112le_Det @ X1))) = $true) | (((X0 = X1)) = $false)) )),
% 1.68/0.56 inference(iff_proxy_clausification,[],[f793])).
% 1.68/0.56 thf(f1667,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : (((((paraco2040174112le_Det @ X0) = (paraco2040174112le_Det @ X1))) = $false) | (((X0 = X1)) = $true)) )),
% 1.68/0.56 inference(iff_proxy_clausification,[],[f793])).
% 1.68/0.56 thf(f1668,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) != ((paraco2040174112le_Det @ X1))) | (((X0 = X1)) = $true)) )),
% 1.68/0.56 inference(equality_proxy_clausification,[],[f1667])).
% 1.68/0.56 thf(f1669,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) != ((paraco2040174112le_Det @ X1))) | (X0 = X1)) )),
% 1.68/0.56 inference(equality_proxy_clausification,[],[f1668])).
% 1.68/0.56 thf(f1670,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) != ((paraco2040174112le_Det @ X1))) | ($true = X0) | ($false = X1)) )),
% 1.68/0.56 inference(iff_proxy_clausification,[],[f1669])).
% 1.68/0.56 thf(f1672,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) = ((paraco2040174112le_Det @ X1))) | (((X0 = X1)) = $false)) )),
% 1.68/0.56 inference(equality_proxy_clausification,[],[f1666])).
% 1.68/0.56 thf(f1673,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) = ((paraco2040174112le_Det @ X1))) | (X0 != X1)) )),
% 1.68/0.56 inference(equality_proxy_clausification,[],[f1672])).
% 1.68/0.56 thf(f1675,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) = ((paraco2040174112le_Det @ X1))) | ($false = X0) | ($false = X1)) )),
% 1.68/0.56 inference(xor_proxy_clausification,[],[f1673])).
% 1.68/0.56 thf(f3481,plain,(
% 1.68/0.56 ( ! [X0 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $true)) != ((paraco2040174112le_Det @ $true))) | (((paraco2040174112le_Det @ $false)) = ((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ p)))) | (((paraco2040174112le_Det @ $true)) = ((paraco2040174112le_Det @ $false)))) )),
% 1.68/0.56 inference(constrained_superposition,[],[f806,f1115])).
% 1.68/0.56 thf(f3511,plain,(
% 1.68/0.56 ( ! [X0 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $false)) = ((paraco876059933e_eval @ X0 @ (paraco329115265le_Neg @ p)))) | (((paraco2040174112le_Det @ $true)) = ((paraco2040174112le_Det @ $false)))) )),
% 1.68/0.56 inference(trivial_inequality_removal,[],[f3481])).
% 1.68/0.56 thf(f3542,plain,(
% 1.68/0.56 (((paraco2040174112le_Det @ $true)) = ((paraco2040174112le_Det @ $false))) | (((paraco2040174112le_Det @ $true)) = ((paraco2040174112le_Det @ $false)))),
% 1.68/0.56 inference(forward_demodulation,[],[f3511,f1665])).
% 1.68/0.56 thf(f3543,plain,(
% 1.68/0.56 (((paraco2040174112le_Det @ $true)) = ((paraco2040174112le_Det @ $false)))),
% 1.68/0.56 inference(duplicate_literal_removal,[],[f3542])).
% 1.68/0.56 thf(f3560,plain,(
% 1.68/0.56 ( ! [X0 : $o] : ((((paraco2040174112le_Det @ X0)) = ((paraco2040174112le_Det @ $false))) | ($false = X0)) )),
% 1.68/0.56 inference(constrained_superposition,[],[f3543,f1112])).
% 1.68/0.56 thf(f3600,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) != ((paraco2040174112le_Det @ X1))) | ($true = $false) | ($false = X1) | ($false = X0)) )),
% 1.68/0.56 inference(constrained_superposition,[],[f1670,f3560])).
% 1.68/0.56 thf(f3605,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : ((((paraco2040174112le_Det @ X0)) != ((paraco2040174112le_Det @ X1))) | ($false = X1) | ($false = X0)) )),
% 1.68/0.56 inference(trivial_inequality_removal,[],[f3600])).
% 1.68/0.56 thf(f3615,plain,(
% 1.68/0.56 ( ! [X0 : $o,X1 : $o] : (($false = X1) | ($false = X0)) )),
% 1.68/0.56 inference(forward_subsumption_resolution,[],[f3605,f1675])).
% 1.68/0.56 thf(f3617,definition,(
% 1.68/0.56 spl150_19 <=> ! [X1 : $o] : ($false = X1)),
% 1.68/0.56 introduced(definition,[new_symbols(definition,[spl150_19])],[avatar_definition])).
% 1.68/0.56 thf(f3618,plain,(
% 1.68/0.56 ( ! [X1 : $o] : (($false = X1)) ) | ~spl150_19),
% 1.68/0.56 inference(avatar_component_clause,[],[f3617])).
% 1.68/0.56 thf(f3630,plain,(
% 1.68/0.56 spl150_19 | spl150_19),
% 1.68/0.56 inference(avatar_split_clause,[],[f3615,f3617,f3617])).
% 1.68/0.56 thf(f3637,plain,(
% 1.68/0.56 ( ! [X1 : $tType,X2 : $tType,X3 : product_prod @ X1 @ X2,X0 : $o] : (($true != X0) | ($true = (((^[Y0 : product_prod @ X1 @ X2]: ($false)) @ X3)))) ) | ~spl150_19),
% 1.68/0.56 inference(constrained_superposition,[],[f879,f3618])).
% 1.68/0.56 thf(f3651,plain,(
% 1.68/0.56 ( ! [X0 : $o] : (($true != X0) | ($true = $false)) ) | ~spl150_19),
% 1.68/0.56 inference(beta-eta_normalization,[],[f3637])).
% 1.68/0.56 thf(f3652,plain,(
% 1.68/0.56 ( ! [X0 : $o] : (($true != X0)) ) | ~spl150_19),
% 1.68/0.56 inference(trivial_inequality_removal,[],[f3651])).
% 1.68/0.56 thf(f3660,plain,(
% 1.68/0.56 ( ! [X0 : $o] : (($false != X0)) ) | ~spl150_19),
% 1.68/0.56 inference(forward_demodulation,[],[f3652,f3618])).
% 1.68/0.56 thf(f3663,plain,(
% 1.68/0.56 $false | ~spl150_19),
% 1.68/0.56 inference(forward_subsumption_resolution,[],[f3660,f3618])).
% 1.68/0.56 thf(f3664,plain,(
% 1.68/0.56 ~spl150_19),
% 1.68/0.56 inference(avatar_contradiction_clause,[],[f3663])).
% 1.68/0.56 cnf(s20, plain, spl150_19 | spl150_19, inference(sat_conversion,[],[f3630])).
% 1.68/0.56 cnf(s21, plain, spl150_19, inference(rat,[],[s20])).
% 1.68/0.56 cnf(s26, plain, ~spl150_19, inference(sat_conversion,[],[f3664])).
% 1.68/0.56 cnf(s28, plain, $false, inference(rat,[],[s21,s26])).
% 1.68/0.56 thf(f3665,plain,(
% 1.68/0.56 $false),
% 1.68/0.56 inference(avatar_sat_refutation,[],[s28])).
% 1.68/0.56 % SZS output end Proof for theBenchmark
% 1.68/0.56 % (1275625)------------------------------
% 1.68/0.56 % (1275625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.68/0.56 % (1275625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/0.56 % (1275625)CaDiCaL version: 2.1.3
% 1.68/0.56 % (1275625)Termination reason: Refutation
% 1.68/0.56 % (1275625)Time elapsed: 0.172 s
% 1.68/0.56 % (1275625)Peak memory usage: 15 MB
% 1.68/0.56 % (1275625)Instructions burned: 357 (million)
% 1.68/0.56 % (1275603)Success in time 0.325 s
% 1.68/0.56 % Vampire exiting
%------------------------------------------------------------------------------