%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP190^2 : 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 08:11:03 AM UTC 2026
% Result : Theorem 3.23s 0.78s
% Output : Refutation 3.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP190^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.17 % Computer : n019.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Tue Sep 29 20:09:48 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.20 Running first-order model finding
% 0.12/0.20 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
% 3.23/0.78 % (1284845)Will run a generic schedule for satisfiability detection.
% 3.23/0.78 % (1284876)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3605887202:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.23/0.78 % (1284873)% WARNING: option uhcvi not known.
% 3.23/0.78 % (1284872)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1320258561_2999 on theBenchmark for (2999ds/0Mi)
% 3.23/0.78 % (1284873)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3629016764:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.23/0.78 % (1284874)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4254125338:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.23/0.78 % (1284875)dis+10_1_sil=32000:sp=arity:random_seed=700738275:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.23/0.78 % (1284877)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=256079303:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.23/0.78 % (1284878)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2988275400:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.23/0.78 % (1284876)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.78 % (1284876)Instruction limit reached!
% 3.23/0.78 % (1284876)------------------------------
% 3.23/0.78 % (1284876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284873)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.78 % (1284876)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284876)Termination reason: Instruction limit
% 3.23/0.78 % (1284876)Termination phase: Property scanning
% 3.23/0.78 % (1284876)Time elapsed: 0.028 s
% 3.23/0.78 % (1284876)Peak memory usage: 12 MB
% 3.23/0.78 % (1284876)Instructions burned: 118 (million)
% 3.23/0.78 % (1284907)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3545393281:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.23/0.78 % (1284875)Instruction limit reached!
% 3.23/0.78 % (1284875)------------------------------
% 3.23/0.78 % (1284875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284875)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284875)Termination reason: Instruction limit
% 3.23/0.78 % (1284875)Termination phase: Property scanning
% 3.23/0.78 % (1284875)Time elapsed: 0.045 s
% 3.23/0.78 % (1284875)Peak memory usage: 12 MB
% 3.23/0.78 % (1284875)Instructions burned: 104 (million)
% 3.23/0.78 % (1284877)Instruction limit reached!
% 3.23/0.78 % (1284877)------------------------------
% 3.23/0.78 % (1284877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284877)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284877)Termination reason: Instruction limit
% 3.23/0.78 % (1284877)Termination phase: Property scanning
% 3.23/0.78 % (1284877)Time elapsed: 0.057 s
% 3.23/0.78 % (1284877)Peak memory usage: 12 MB
% 3.23/0.78 % (1284877)Instructions burned: 133 (million)
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1284873)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1284918)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=16793464:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.23/0.78 % (1284878)Instruction limit reached!
% 3.23/0.78 % (1284878)------------------------------
% 3.23/0.78 % (1284878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284878)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284878)Termination reason: Instruction limit
% 3.23/0.78 % (1284878)Termination phase: Saturation
% 3.23/0.78 % (1284878)Time elapsed: 0.069 s
% 3.23/0.78 % (1284878)Peak memory usage: 13 MB
% 3.23/0.78 % (1284878)Instructions burned: 160 (million)
% 3.23/0.78 % (1284925)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=440268825:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.23/0.78 % (1284922)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=1474763758:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.23/0.78 % (1284923)ott-21_1_sil=16000:fs=off:random_seed=3162814553:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.23/0.78 % (1284930)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3230431517:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.23/0.78 % (1284922)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.78 % (1284918)Instruction limit reached!
% 3.23/0.78 % (1284918)------------------------------
% 3.23/0.78 % (1284918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284918)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284918)Termination reason: Instruction limit
% 3.23/0.78 % (1284918)Termination phase: Property scanning
% 3.23/0.78 % (1284918)Time elapsed: 0.057 s
% 3.23/0.78 % (1284918)Peak memory usage: 12 MB
% 3.23/0.78 % (1284918)Instructions burned: 132 (million)
% 3.23/0.78 % (1284922)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.23/0.78 % (1284953)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3060264695:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1284923)Instruction limit reached!
% 3.23/0.78 % (1284923)------------------------------
% 3.23/0.78 % (1284923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284923)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284923)Termination reason: Instruction limit
% 3.23/0.78 % (1284923)Termination phase: Saturation
% 3.23/0.78 % (1284923)Time elapsed: 0.079 s
% 3.23/0.78 % (1284923)Peak memory usage: 13 MB
% 3.23/0.78 % (1284923)Instructions burned: 182 (million)
% 3.23/0.78 % (1284963)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1751223596:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.23/0.78 % (1284969)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=4087289548: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)
% 3.23/0.78 % (1284969)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.78 % (1284925)Instruction limit reached!
% 3.23/0.78 % (1284925)------------------------------
% 3.23/0.78 % (1284925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284925)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284925)Termination reason: Instruction limit
% 3.23/0.78 % (1284925)Termination phase: Saturation
% 3.23/0.78 % (1284925)Time elapsed: 0.125 s
% 3.23/0.78 % (1284925)Peak memory usage: 15 MB
% 3.23/0.78 % (1284925)Instructions burned: 478 (million)
% 3.23/0.78 % (1284990)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2876684776:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1284990)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.78 % (1285011)fmb+10_1_sil=64000:random_seed=1704670971:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.23/0.78 % (1285011)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1285018)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2856840951:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1285020)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2107835313:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.23/0.78 % (1284922)Instruction limit reached!
% 3.23/0.78 % (1284922)------------------------------
% 3.23/0.78 % (1284922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % (1284922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 % (1284922)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284922)Termination reason: Instruction limit
% 3.23/0.78 % (1284922)Termination phase: Saturation
% 3.23/0.78 % (1284922)Time elapsed: 0.327 s
% 3.23/0.78 % (1284922)Peak memory usage: 16 MB
% 3.23/0.78 % (1284922)Instructions burned: 686 (million)
% 3.23/0.78 % (1285022)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3767043670:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.23/0.78 % (1285022)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.23/0.78 % (1284990)Instruction limit reached!
% 3.23/0.78 % (1284990)------------------------------
% 3.23/0.78 % (1284990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.78 % Exception at run slice level
% 3.23/0.78 User error: % (1284990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.78 Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.23/0.78 % (1284990)CaDiCaL version: 2.1.3
% 3.23/0.78 % (1284990)Termination reason: Instruction limit
% 3.23/0.78 % (1284990)Termination phase: Saturation
% 3.23/0.78 % (1284990)Time elapsed: 0.242 s
% 3.23/0.78 % (1284990)Peak memory usage: 20 MB
% 3.23/0.78 % (1284990)Instructions burned: 881 (million)
% 3.23/0.78 % (1285025)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2076488495:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 3.23/0.78 % (1285024)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3819392009:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 3.23/0.78 % (1284969) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1284845-1284969"...
% 3.23/0.78 % (1284969)...printing done.
% 3.23/0.78 % (1284969)Refutation found. Thanks to Tanya!
% 3.23/0.78 % SZS status Theorem for theBenchmark
% 3.23/0.78 % SZS output start Proof for theBenchmark
% 3.23/0.78 thf(type_def_5, type, late_residual_Rep: $tType).
% 3.23/0.78 thf(type_def_6, type, late_subject_Rep: $tType).
% 3.23/0.78 thf(type_def_7, type, late_freeRes_Rep: $tType).
% 3.23/0.78 thf(type_def_8, type, late_residual: $tType).
% 3.23/0.78 thf(type_def_9, type, late_subject: $tType).
% 3.23/0.78 thf(type_def_10, type, late_freeRes: $tType).
% 3.23/0.78 thf(type_def_11, type, product_prod: ($tType * $tType) > $tType).
% 3.23/0.78 thf(type_def_12, type, noption: $tType > $tType).
% 3.23/0.78 thf(type_def_13, type, pi_Rep: $tType).
% 3.23/0.78 thf(type_def_14, type, name: $tType).
% 3.23/0.78 thf(type_def_15, type, list: $tType > $tType).
% 3.23/0.78 thf(type_def_16, type, pi: $tType).
% 3.23/0.78 thf(type_def_17, type, set: $tType > $tType).
% 3.23/0.78 thf(type_def_18, type, sTfun: ($tType * $tType) > $tType).
% 3.23/0.78 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 3.23/0.78 thf(func_def_1, type, fs_name: !>[X0: $tType]:($o)).
% 3.23/0.78 thf(func_def_2, type, pt_name: !>[X0: $tType]:($o)).
% 3.23/0.78 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 3.23/0.78 thf(func_def_4, type, cp_name_name: !>[X0: $tType]:($o)).
% 3.23/0.78 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 3.23/0.78 thf(func_def_6, type, input: (name > name > pi > pi)).
% 3.23/0.78 thf(func_def_7, type, par: (pi > pi > pi)).
% 3.23/0.78 thf(func_def_8, type, res: (name > pi > pi)).
% 3.23/0.78 thf(func_def_9, type, name_prm_name: (list @ product_prod @ name @ name > name > name)).
% 3.23/0.78 thf(func_def_10, type, swap_name: (product_prod @ name @ name > name > name)).
% 3.23/0.78 thf(func_def_11, type, subs: (pi > name > name > pi)).
% 3.23/0.78 thf(func_def_12, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 3.23/0.78 thf(func_def_13, type, late_OutputR: (name > name > late_freeRes)).
% 3.23/0.78 thf(func_def_14, type, late_TauR: late_freeRes).
% 3.23/0.78 thf(func_def_15, type, late_BoundR: (late_subject > name > pi > late_residual)).
% 3.23/0.78 thf(func_def_16, type, late_FreeR: (late_freeRes > pi > late_residual)).
% 3.23/0.78 thf(func_def_17, type, late_r347633188eR_Rep: (late_freeRes > pi > late_residual_Rep)).
% 3.23/0.78 thf(func_def_18, type, late_BoundOutputS: (name > late_subject)).
% 3.23/0.78 thf(func_def_19, type, late_InputS: (name > late_subject)).
% 3.23/0.78 thf(func_def_20, type, late_transitions: (pi > late_residual > $o)).
% 3.23/0.78 thf(func_def_21, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_22, type, nil: !>[X0: $tType]:(list @ X0)).
% 3.23/0.78 thf(func_def_23, type, product_lists: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 3.23/0.78 thf(func_def_24, type, abs_fun: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > noption @ X1))).
% 3.23/0.78 thf(func_def_25, type, fresh: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o))).
% 3.23/0.78 thf(func_def_26, type, perm: !>[X0: $tType, X1: $tType]:((list @ product_prod @ X0 @ X0 > X1 > X1))).
% 3.23/0.78 thf(func_def_27, type, supports: !>[X0: $tType, X1: $tType]:((set @ X0 > X1 > $o))).
% 3.23/0.78 thf(func_def_28, type, swap: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0 > X0))).
% 3.23/0.78 thf(func_def_29, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 3.23/0.78 thf(func_def_30, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 3.23/0.78 thf(func_def_31, type, eqvt: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 3.23/0.78 thf(func_def_32, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.23/0.78 thf(func_def_33, type, strong2129052853vative: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > $o)).
% 3.23/0.78 thf(func_def_34, type, strong743114133lation: (pi > set @ product_prod @ pi @ pi > pi > $o)).
% 3.23/0.78 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.23/0.78 thf(func_def_36, type, p: pi).
% 3.23/0.78 thf(func_def_37, type, p2: pi).
% 3.23/0.78 thf(func_def_38, type, pxQ: pi).
% 3.23/0.78 thf(func_def_39, type, q: pi).
% 3.23/0.78 thf(func_def_40, type, q2: pi).
% 3.23/0.78 thf(func_def_41, type, q_a: pi).
% 3.23/0.78 thf(func_def_42, type, rel: set @ product_prod @ pi @ pi).
% 3.23/0.78 thf(func_def_43, type, alpha: late_freeRes).
% 3.23/0.78 thf(func_def_44, type, aa: name).
% 3.23/0.78 thf(func_def_45, type, b: name).
% 3.23/0.78 thf(func_def_46, type, x: name).
% 3.23/0.78 thf(func_def_47, type, y: name).
% 3.23/0.78 thf(func_def_48, type, z: name).
% 3.23/0.78 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 3.23/0.78 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_55, type, db0: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_56, type, vNOT: ($o > $o)).
% 3.23/0.78 thf(func_def_57, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.23/0.78 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 3.23/0.78 thf(func_def_59, type, vOR: ($o > $o > $o)).
% 3.23/0.78 thf(func_def_60, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.23/0.78 thf(func_def_61, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.23/0.78 thf(func_def_62, type, db3: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_64, type, db5: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_65, type, db6: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_66, type, db4: !>[X0: $tType]:(X0)).
% 3.23/0.78 thf(func_def_67, type, sP0: (pi > late_freeRes > (pi > $o) > name > $o)).
% 3.23/0.78 thf(func_def_68, type, sP1: (name > pi > late_freeRes > pi > $o)).
% 3.23/0.78 thf(func_def_69, type, sP2: (late_residual > pi > name > name > $o)).
% 3.23/0.78 thf(func_def_70, type, sP3: (name > pi > late_residual > $o)).
% 3.23/0.78 thf(func_def_71, type, sP4: (name > pi > late_residual > $o)).
% 3.23/0.78 thf(func_def_72, type, sP5: (late_subject > name > pi > pi > name > name > $o)).
% 3.23/0.78 thf(func_def_73, type, sP6: (name > pi > late_subject > name > pi > $o)).
% 3.23/0.78 thf(func_def_74, type, sP7: !>[X0: $tType]:(((X0 > late_residual > $o) > $o))).
% 3.23/0.78 thf(func_def_75, type, sP8: !>[X0: $tType]:(((X0 > late_residual > $o) > $o))).
% 3.23/0.78 thf(func_def_76, type, sP9: (pi > late_subject > (late_subject > pi > $o) > name > name > $o)).
% 3.23/0.78 thf(func_def_77, type, sP10: (pi > name > (late_subject > pi > $o) > late_subject > name > $o)).
% 3.23/0.78 thf(func_def_78, type, sP11: !>[X0: $tType]:(((list @ X0 > $o) > $o))).
% 3.23/0.78 thf(func_def_79, type, sP12: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > $o))).
% 3.23/0.78 thf(func_def_80, type, sP13: !>[X0: $tType]:(((list @ X0 > $o) > $o))).
% 3.23/0.78 thf(func_def_81, type, sP14: !>[X0: $tType]:(((list @ X0 > $o) > $o))).
% 3.23/0.78 thf(func_def_82, type, sP15: (pi > late_subject > name > (pi > $o) > pi > $o)).
% 3.23/0.78 thf(func_def_83, type, sP16: (pi > pi > late_subject > name > pi > $o)).
% 3.23/0.78 thf(func_def_84, type, sP17: (pi > pi > late_subject > name > pi > $o)).
% 3.23/0.78 thf(func_def_85, type, sP18: (late_subject > pi > (late_subject > name > pi > $o) > name > name > name > pi > $o)).
% 3.23/0.78 thf(func_def_86, type, sP19: (pi > pi > name > set @ product_prod @ pi @ pi > $o)).
% 3.23/0.78 thf(func_def_87, type, sP20: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > $o))).
% 3.23/0.78 thf(func_def_88, type, sP21: (pi > pi > name > set @ product_prod @ pi @ pi > $o)).
% 3.23/0.78 thf(func_def_89, type, sP22: (pi > pi > set @ product_prod @ pi @ pi > $o)).
% 3.23/0.78 thf(func_def_90, type, sP23: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > $o))).
% 3.23/0.78 thf(func_def_91, type, sP24: (set @ product_prod @ pi @ pi > $o)).
% 3.23/0.78 thf(func_def_92, type, sP25: (set @ product_prod @ pi @ pi > $o)).
% 3.23/0.78 thf(func_def_93, type, sK26: !>[X0: $tType]:((X0 > name))).
% 3.23/0.78 thf(func_def_94, type, sK27: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_95, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.23/0.78 thf(func_def_96, type, sK29: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 3.23/0.78 thf(func_def_97, type, sK30: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 3.23/0.78 thf(func_def_98, type, sK31: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 3.23/0.78 thf(func_def_99, type, sK32: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 3.23/0.78 thf(func_def_100, type, sK33: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 3.23/0.78 thf(func_def_101, type, sK34: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 3.23/0.78 thf(func_def_102, type, sK35: !>[X0: $tType]:(((X0 > late_freeRes > $o) > name))).
% 3.23/0.78 thf(func_def_103, type, sK36: !>[X0: $tType]:(((X0 > late_freeRes > $o) > X0))).
% 3.23/0.78 thf(func_def_104, type, sK37: (late_freeRes > name)).
% 3.23/0.78 thf(func_def_105, type, sK38: (late_freeRes > name)).
% 3.23/0.78 thf(func_def_106, type, sK39: ((late_freeRes > $o) > name)).
% 3.23/0.78 thf(func_def_107, type, sK40: ((late_freeRes > $o) > name)).
% 3.23/0.78 thf(func_def_108, type, sK41: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_109, type, sK42: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_110, type, sK43: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1))).
% 3.23/0.78 thf(func_def_111, type, sK44: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0))).
% 3.23/0.78 thf(func_def_112, type, sK45: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X0))).
% 3.23/0.78 thf(func_def_113, type, sK46: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1))).
% 3.23/0.78 thf(func_def_114, type, sK47: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > X0 > X1))).
% 3.23/0.78 thf(func_def_115, type, sK48: !>[X0: $tType, X1: $tType]:((product_prod @ (X0 > X1) @ product_prod @ list @ X0 @ list @ X1 > list @ X1))).
% 3.23/0.78 thf(func_def_116, type, sK49: (pi > late_freeRes > (pi > $o) > name > pi)).
% 3.23/0.78 thf(func_def_117, type, sK50: (name > pi > late_freeRes > pi > pi)).
% 3.23/0.78 thf(func_def_118, type, sK51: (name > pi > late_freeRes > pi > late_freeRes)).
% 3.23/0.78 thf(func_def_119, type, sK52: (name > pi > late_freeRes > pi > pi)).
% 3.23/0.78 thf(func_def_120, type, sK53: (name > pi > late_freeRes > pi > name)).
% 3.23/0.78 thf(func_def_121, type, sK54: ((late_residual > $o) > late_freeRes)).
% 3.23/0.78 thf(func_def_122, type, sK55: ((late_residual > $o) > pi)).
% 3.23/0.78 thf(func_def_123, type, sK56: ((late_residual > $o) > late_subject)).
% 3.23/0.78 thf(func_def_124, type, sK57: ((late_residual > $o) > name)).
% 3.23/0.78 thf(func_def_125, type, sK58: ((late_residual > $o) > pi)).
% 3.23/0.78 thf(func_def_126, type, sK59: (name > pi > late_residual > pi)).
% 3.23/0.78 thf(func_def_127, type, sK60: (name > pi > late_residual > late_freeRes)).
% 3.23/0.78 thf(func_def_128, type, sK61: (name > pi > late_residual > pi)).
% 3.23/0.78 thf(func_def_129, type, sK62: (name > pi > late_residual > name)).
% 3.23/0.78 thf(func_def_130, type, sK63: (name > pi > late_residual > pi)).
% 3.23/0.78 thf(func_def_131, type, sK64: (name > pi > late_residual > late_subject)).
% 3.23/0.78 thf(func_def_132, type, sK65: (name > pi > late_residual > name)).
% 3.23/0.78 thf(func_def_133, type, sK66: (name > pi > late_residual > pi)).
% 3.23/0.78 thf(func_def_134, type, sK67: (name > pi > late_residual > name)).
% 3.23/0.78 thf(func_def_135, type, sK68: (late_residual > pi > name > name > pi)).
% 3.23/0.78 thf(func_def_136, type, sK69: (late_residual > pi > name > pi)).
% 3.23/0.78 thf(func_def_137, type, sK70: (late_residual > pi > name > name)).
% 3.23/0.78 thf(func_def_138, type, sK71: (late_residual > pi > name > name)).
% 3.23/0.78 thf(func_def_139, type, sK72: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1 > X0))).
% 3.23/0.78 thf(func_def_140, type, sK73: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1 > X0))).
% 3.23/0.78 thf(func_def_141, type, sK74: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1))).
% 3.23/0.78 thf(func_def_142, type, sK75: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1))).
% 3.23/0.78 thf(func_def_143, type, sK76: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > list @ X1))).
% 3.23/0.78 thf(func_def_144, type, sK77: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1 > X0))).
% 3.23/0.78 thf(func_def_145, type, sK78: !>[X0: $tType, X1: $tType]:((product_prod @ (X1 > X0) @ list @ X1 > X1))).
% 3.23/0.78 thf(func_def_146, type, sK79: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_147, type, sK80: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_148, type, sK81: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_149, type, sK82: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_150, type, sK83: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_151, type, sK84: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_152, type, sK85: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_153, type, sK86: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_154, type, sK87: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_155, type, sK88: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_156, type, sK89: !>[X0: $tType]:((product_prod @ (X0 > X0 > $o) @ list @ X0 > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_157, type, sK90: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_158, type, sK91: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_159, type, sK92: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_160, type, sK93: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_161, type, sK94: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_162, type, sK95: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_163, type, sK96: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_164, type, sK97: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_165, type, sK98: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_166, type, sK99: !>[X0: $tType]:((product_prod @ list @ X0 @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_167, type, sK100: (name > pi > late_subject > name > pi > pi)).
% 3.23/0.78 thf(func_def_168, type, sK101: (name > pi > late_subject > name > pi > late_subject)).
% 3.23/0.78 thf(func_def_169, type, sK102: (name > pi > late_subject > name > pi > name)).
% 3.23/0.78 thf(func_def_170, type, sK103: (name > pi > late_subject > name > pi > pi)).
% 3.23/0.78 thf(func_def_171, type, sK104: (name > pi > late_subject > name > pi > name)).
% 3.23/0.78 thf(func_def_172, type, sK105: (late_subject > name > pi > pi > name > name > pi)).
% 3.23/0.78 thf(func_def_173, type, sK106: (pi > name > late_subject > pi > name > pi)).
% 3.23/0.78 thf(func_def_174, type, sK107: (pi > name > late_subject > pi > name > name)).
% 3.23/0.78 thf(func_def_175, type, sK108: (pi > name > late_subject > pi > name > name)).
% 3.23/0.78 thf(func_def_176, type, sK109: !>[X0: $tType]:(((X0 > late_residual > $o) > late_subject))).
% 3.23/0.78 thf(func_def_177, type, sK110: !>[X0: $tType]:(((X0 > late_residual > $o) > name))).
% 3.23/0.78 thf(func_def_178, type, sK111: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 3.23/0.78 thf(func_def_179, type, sK112: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 3.23/0.78 thf(func_def_180, type, sK113: !>[X0: $tType]:(((X0 > late_residual > $o) > late_freeRes))).
% 3.23/0.78 thf(func_def_181, type, sK114: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 3.23/0.78 thf(func_def_182, type, sK115: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 3.23/0.78 thf(func_def_183, type, sK116: !>[X0: $tType]:(((X0 > late_residual > $o) > late_subject))).
% 3.23/0.78 thf(func_def_184, type, sK117: !>[X0: $tType]:(((X0 > late_residual > $o) > name))).
% 3.23/0.78 thf(func_def_185, type, sK118: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 3.23/0.78 thf(func_def_186, type, sK119: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 3.23/0.78 thf(func_def_187, type, sK120: !>[X0: $tType]:(((X0 > late_residual > $o) > late_freeRes))).
% 3.23/0.78 thf(func_def_188, type, sK121: !>[X0: $tType]:(((X0 > late_residual > $o) > pi))).
% 3.23/0.78 thf(func_def_189, type, sK122: !>[X0: $tType]:(((X0 > late_residual > $o) > X0))).
% 3.23/0.78 thf(func_def_190, type, sK123: (pi > name > (late_subject > pi > $o) > late_subject > name > pi)).
% 3.23/0.78 thf(func_def_191, type, sK124: (pi > late_subject > (late_subject > pi > $o) > name > name > name)).
% 3.23/0.78 thf(func_def_192, type, sK125: (pi > late_subject > (late_subject > pi > $o) > name > name > pi)).
% 3.23/0.78 thf(func_def_193, type, sK126: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.23/0.78 thf(func_def_194, type, sK127: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.23/0.78 thf(func_def_195, type, sK128: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 3.23/0.78 thf(func_def_196, type, sK129: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_197, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 3.23/0.78 thf(func_def_198, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 3.23/0.78 thf(func_def_199, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 3.23/0.78 thf(func_def_200, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 3.23/0.78 thf(func_def_201, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 3.23/0.78 thf(func_def_202, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 3.23/0.78 thf(func_def_203, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 3.23/0.78 thf(func_def_204, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 3.23/0.78 thf(func_def_205, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 3.23/0.78 thf(func_def_206, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 3.23/0.78 thf(func_def_207, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 3.23/0.78 thf(func_def_208, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 3.23/0.78 thf(func_def_209, type, sK142: !>[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))).
% 3.23/0.78 thf(func_def_210, type, sK143: !>[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))).
% 3.23/0.78 thf(func_def_211, type, sK144: !>[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))).
% 3.23/0.78 thf(func_def_212, type, sK145: !>[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))).
% 3.23/0.78 thf(func_def_213, type, sK146: !>[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))).
% 3.23/0.78 thf(func_def_214, type, sK147: !>[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))).
% 3.23/0.78 thf(func_def_215, type, sK148: !>[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))).
% 3.23/0.78 thf(func_def_216, type, sK149: !>[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))).
% 3.23/0.78 thf(func_def_217, type, sK150: !>[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))).
% 3.23/0.78 thf(func_def_218, type, sK151: !>[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))).
% 3.23/0.78 thf(func_def_219, type, sK152: !>[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))).
% 3.23/0.78 thf(func_def_220, type, sK153: !>[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))).
% 3.23/0.78 thf(func_def_221, type, sK154: !>[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))).
% 3.23/0.78 thf(func_def_222, type, sK155: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.23/0.78 thf(func_def_223, type, sK156: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.23/0.78 thf(func_def_224, type, sK157: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_225, type, sK158: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.23/0.78 thf(func_def_226, type, sK159: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.23/0.78 thf(func_def_227, type, sK160: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.23/0.78 thf(func_def_228, type, sK161: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_229, type, sK162: !>[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))).
% 3.23/0.78 thf(func_def_230, type, sK163: !>[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))).
% 3.23/0.78 thf(func_def_231, type, sK164: !>[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))).
% 3.23/0.78 thf(func_def_232, type, sK165: !>[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))).
% 3.23/0.78 thf(func_def_233, type, sK166: !>[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))).
% 3.23/0.78 thf(func_def_234, type, sK167: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 3.23/0.78 thf(func_def_235, type, sK168: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 3.23/0.78 thf(func_def_236, type, sK169: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 3.23/0.78 thf(func_def_237, type, sK170: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 3.23/0.78 thf(func_def_238, type, sK171: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 3.23/0.78 thf(func_def_239, type, sK172: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_240, type, sK173: !>[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))).
% 3.23/0.78 thf(func_def_241, type, sK174: !>[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))).
% 3.23/0.78 thf(func_def_242, type, sK175: !>[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))).
% 3.23/0.78 thf(func_def_243, type, sK176: !>[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))).
% 3.23/0.78 thf(func_def_244, type, sK177: !>[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))).
% 3.23/0.78 thf(func_def_245, type, sK178: !>[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))).
% 3.23/0.78 thf(func_def_246, type, sK179: !>[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))).
% 3.23/0.78 thf(func_def_247, type, sK180: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 3.23/0.78 thf(func_def_248, type, sK181: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 3.23/0.78 thf(func_def_249, type, sK182: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 3.23/0.78 thf(func_def_250, type, sK183: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_251, type, sK184: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_252, type, sK185: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.78 thf(func_def_253, type, sK186: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_254, type, sK187: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_255, type, sK188: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_256, type, sK189: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 3.23/0.78 thf(func_def_257, type, sK190: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_258, type, sK191: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 3.23/0.78 thf(func_def_259, type, sK192: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 3.23/0.78 thf(func_def_260, type, sK193: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 3.23/0.78 thf(func_def_261, type, sK194: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 3.23/0.78 thf(func_def_262, type, sK195: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 3.23/0.78 thf(func_def_263, type, sK196: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_264, type, sK197: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_265, type, sK198: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_266, type, sK199: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_267, type, sK200: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_268, type, sK201: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_269, type, sK202: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_270, type, sK203: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_271, type, sK204: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_272, type, sK205: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.78 thf(func_def_273, type, sK206: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_274, type, sK207: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_275, type, sK208: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_276, type, sK209: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_277, type, sK210: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_278, type, sK211: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_279, type, sK212: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_280, type, sK213: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_281, type, sK214: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_282, type, sK215: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 3.23/0.78 thf(func_def_283, type, sK216: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_284, type, sK217: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 3.23/0.78 thf(func_def_285, type, sK218: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 3.23/0.78 thf(func_def_286, type, sK219: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.78 thf(func_def_287, type, sK220: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.78 thf(func_def_288, type, sK221: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 3.23/0.78 thf(func_def_289, type, sK222: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.78 thf(func_def_290, type, sK223: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_291, type, sK224: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_292, type, sK225: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_293, type, sK226: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 3.23/0.78 thf(func_def_294, type, sK227: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_295, type, sK228: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_296, type, sK229: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.78 thf(func_def_297, type, sK230: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.78 thf(func_def_298, type, sK231: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 3.23/0.78 thf(func_def_299, type, sK232: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 3.23/0.78 thf(func_def_300, type, sK233: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 3.23/0.79 thf(func_def_301, type, sK234: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 3.23/0.79 thf(func_def_302, type, sK235: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > list @ X1))).
% 3.23/0.79 thf(func_def_303, type, sK236: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 3.23/0.79 thf(func_def_304, type, sK237: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 3.23/0.79 thf(func_def_305, type, sK238: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 3.23/0.79 thf(func_def_306, type, sK239: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 3.23/0.79 thf(func_def_307, type, sK240: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 3.23/0.79 thf(func_def_308, type, sK241: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 3.23/0.79 thf(func_def_309, type, sK242: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 3.23/0.79 thf(func_def_310, type, sK243: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 3.23/0.79 thf(func_def_311, type, sK244: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 3.23/0.79 thf(func_def_312, type, sK245: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.79 thf(func_def_313, type, sK246: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 3.23/0.79 thf(func_def_314, type, sK247: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 3.23/0.79 thf(func_def_315, type, sK248: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1))).
% 3.23/0.79 thf(func_def_316, type, sK249: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0))).
% 3.23/0.79 thf(func_def_317, type, sK250: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0))).
% 3.23/0.79 thf(func_def_318, type, sK251: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1))).
% 3.23/0.79 thf(func_def_319, type, sK252: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1))).
% 3.23/0.79 thf(func_def_320, type, sK253: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1))).
% 3.23/0.79 thf(func_def_321, type, sK254: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.79 thf(func_def_322, type, sK255: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 3.23/0.79 thf(func_def_323, type, sK256: ((late_subject > $o) > name)).
% 3.23/0.79 thf(func_def_324, type, sK257: ((late_subject > $o) > name)).
% 3.23/0.79 thf(func_def_325, type, sK258: (late_subject > name)).
% 3.23/0.79 thf(func_def_326, type, sK259: (late_subject > name)).
% 3.23/0.79 thf(func_def_327, type, sK260: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 3.23/0.79 thf(func_def_328, type, sK261: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 3.23/0.79 thf(func_def_329, type, sK262: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 3.23/0.79 thf(func_def_330, type, sK263: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 3.23/0.79 thf(func_def_331, type, sK264: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 3.23/0.79 thf(func_def_332, type, sK265: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 3.23/0.79 thf(func_def_333, type, sK266: !>[X0: $tType]:(((X0 > late_subject > $o) > name))).
% 3.23/0.79 thf(func_def_334, type, sK267: !>[X0: $tType]:(((X0 > late_subject > $o) > X0))).
% 3.23/0.79 thf(func_def_335, type, sK268: (pi > late_subject > name > (pi > $o) > pi > pi)).
% 3.23/0.79 thf(func_def_336, type, sK269: ((pi > $o) > name > late_subject > pi > pi > pi)).
% 3.23/0.79 thf(func_def_337, type, sK270: (pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_338, type, sK271: (pi > pi > late_subject > name > pi > late_subject)).
% 3.23/0.79 thf(func_def_339, type, sK272: (pi > pi > late_subject > name > pi > name)).
% 3.23/0.79 thf(func_def_340, type, sK273: (pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_341, type, sK274: (pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_342, type, sK275: (pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_343, type, sK276: (pi > pi > late_subject > name > pi > late_subject)).
% 3.23/0.79 thf(func_def_344, type, sK277: (pi > pi > late_subject > name > pi > name)).
% 3.23/0.79 thf(func_def_345, type, sK278: (pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_346, type, sK279: (pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_347, type, sK280: (pi > pi > name > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_348, type, sK281: (pi > pi > name > set @ product_prod @ pi @ pi > late_freeRes)).
% 3.23/0.79 thf(func_def_349, type, sK282: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > pi))).
% 3.23/0.79 thf(func_def_350, type, sK283: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > late_subject))).
% 3.23/0.79 thf(func_def_351, type, sK284: !>[X0: $tType]:((pi > X0 > pi > name > set @ product_prod @ pi @ pi > name))).
% 3.23/0.79 thf(func_def_352, type, sK285: (pi > pi > name > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_353, type, sK286: (pi > pi > name > set @ product_prod @ pi @ pi > name)).
% 3.23/0.79 thf(func_def_354, type, sK287: (pi > late_freeRes > set @ product_prod @ pi @ pi > pi > pi)).
% 3.23/0.79 thf(func_def_355, type, sK288: (pi > name > late_subject > set @ product_prod @ pi @ pi > pi > pi)).
% 3.23/0.79 thf(func_def_356, type, sK289: (pi > pi > set @ product_prod @ pi @ pi > late_subject)).
% 3.23/0.79 thf(func_def_357, type, sK290: (pi > pi > set @ product_prod @ pi @ pi > name)).
% 3.23/0.79 thf(func_def_358, type, sK291: (pi > pi > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_359, type, sK292: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 3.23/0.79 thf(func_def_360, type, sK293: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_361, type, sK294: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_362, type, sK295: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_363, type, sK296: (set @ product_prod @ pi @ pi > name)).
% 3.23/0.79 thf(func_def_364, type, sK297: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_365, type, sK298: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_366, type, sK299: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > late_subject))).
% 3.23/0.79 thf(func_def_367, type, sK300: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > name))).
% 3.23/0.79 thf(func_def_368, type, sK301: !>[X0: $tType]:((pi > X0 > pi > set @ product_prod @ pi @ pi > pi))).
% 3.23/0.79 thf(func_def_369, type, sK302: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes)).
% 3.23/0.79 thf(func_def_370, type, sK303: (pi > pi > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_371, type, sK304: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_372, type, sK305: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_373, type, sK306: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_374, type, sK307: (set @ product_prod @ pi @ pi > name)).
% 3.23/0.79 thf(func_def_375, type, sK308: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_376, type, sK309: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_377, type, sK310: (set @ product_prod @ pi @ pi > name)).
% 3.23/0.79 thf(func_def_378, type, sK311: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_379, type, sK312: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_380, type, sK313: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_381, type, sK314: (set @ product_prod @ pi @ pi > name)).
% 3.23/0.79 thf(func_def_382, type, sK315: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_383, type, sK316: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_384, type, sK317: (set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_385, type, sK318: (pi > pi > late_subject > set @ product_prod @ pi @ pi > pi > pi > name > pi)).
% 3.23/0.79 thf(func_def_386, type, sK319: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes > pi > pi > pi)).
% 3.23/0.79 thf(func_def_387, type, sK320: (pi > pi > set @ product_prod @ pi @ pi > name > pi > late_subject > pi > pi)).
% 3.23/0.79 thf(func_def_388, type, sK321: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes > pi > pi > pi)).
% 3.23/0.79 thf(func_def_389, type, sK322: (set @ product_prod @ pi @ pi > pi > late_subject > name > pi > pi)).
% 3.23/0.79 thf(func_def_390, type, sK323: (set @ product_prod @ pi @ pi > pi > late_freeRes > pi > pi)).
% 3.23/0.79 thf(func_def_391, type, sK324: (set @ product_prod @ pi @ pi > pi > pi > late_subject > name > pi)).
% 3.23/0.79 thf(func_def_392, type, sK325: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes > pi)).
% 3.23/0.79 thf(func_def_393, type, sK326: (pi > late_subject > set @ product_prod @ pi @ pi > name > pi > pi > pi)).
% 3.23/0.79 thf(func_def_394, type, sK327: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes > pi > pi)).
% 3.23/0.79 thf(func_def_395, type, sK328: (pi > late_subject > set @ product_prod @ pi @ pi > name > pi > pi > pi)).
% 3.23/0.79 thf(func_def_396, type, sK329: (pi > pi > set @ product_prod @ pi @ pi > late_freeRes > pi > pi)).
% 3.23/0.79 thf(func_def_397, type, sK330: (pi > late_subject > name > pi > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_398, type, sK331: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_399, type, sK332: (pi > pi > late_subject > name > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_400, type, sK333: (pi > pi > late_freeRes > set @ product_prod @ pi @ pi > pi)).
% 3.23/0.79 thf(func_def_401, type, sK334: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_402, type, sK335: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_403, type, sK336: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 3.23/0.79 thf(func_def_404, type, sK337: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 3.23/0.79 thf(func_def_405, type, sK338: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_406, type, sK339: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_407, type, sK340: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_408, type, sK341: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_409, type, sK342: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 3.23/0.79 thf(func_def_410, type, sK343: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 3.23/0.79 thf(func_def_411, type, sK344: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_412, type, sK345: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_413, type, sK346: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_414, type, sK347: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_415, type, sK348: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 3.23/0.79 thf(func_def_416, type, sK349: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 3.23/0.79 thf(func_def_417, type, sK350: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_418, type, sK351: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_419, type, sK352: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_420, type, sK353: (set @ product_prod @ pi @ pi > pi > pi > pi)).
% 3.23/0.79 thf(func_def_421, type, sK354: (set @ product_prod @ pi @ pi > pi > pi > late_freeRes)).
% 3.23/0.79 thf(func_def_422, type, sK355: (set @ product_prod @ pi @ pi > pi > pi > name)).
% 3.23/0.79 thf(func_def_423, type, sK356: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_424, type, sK357: (set @ product_prod @ pi @ pi > pi > pi > late_subject)).
% 3.23/0.79 thf(func_def_425, type, sK358: (set @ product_prod @ pi @ pi > late_subject > pi > name > pi > pi)).
% 3.23/0.79 thf(func_def_426, type, sK359: (set @ product_prod @ pi @ pi > pi > late_freeRes > pi > pi)).
% 3.23/0.79 thf(func_def_427, type, sK360: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 3.23/0.79 thf(func_def_428, type, sK361: !>[X0: $tType]:((list @ X0 > X0))).
% 3.23/0.79 thf(f1,axiom,(
% 3.23/0.79 (aa = b)),
% 3.23/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062a_A_061_Ab_092_060close_062)).
% 3.23/0.79 thf(f7,axiom,(
% 3.23/0.79 (late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))),
% 3.23/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_cOpen_Ohyps_I1_J)).
% 3.23/0.79 thf(f18,axiom,(
% 3.23/0.79 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : ((late_transitions @ X0 @ X1) => (late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1)))),
% 3.23/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_eqvt)).
% 3.23/0.79 thf(f301,conjecture,(
% 3.23/0.79 (late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 3.23/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 3.23/0.79 thf(f302,negated_conjecture,(
% 3.23/0.79 ~(late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 3.23/0.79 inference(negated_conjecture,[status(cth)],[f301])).
% 3.23/0.79 thf(f303,plain,(
% 3.23/0.79 (late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))),
% 3.23/0.79 inference(rectify,[],[f7])).
% 3.23/0.79 thf(f304,plain,(
% 3.23/0.79 (((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))) = $true)),
% 3.23/0.79 inference(fool_elimination,[],[f303])).
% 3.23/0.79 thf(f319,plain,(
% 3.23/0.79 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : ((late_transitions @ X0 @ X1) => (late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1)))),
% 3.23/0.79 inference(rectify,[],[f18])).
% 3.23/0.79 thf(f320,plain,(
% 3.23/0.79 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : ((((late_transitions @ X0 @ X1)) = $true) => (((late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1))) = $true))),
% 3.23/0.79 inference(fool_elimination,[],[f319])).
% 3.23/0.79 thf(f725,plain,(
% 3.23/0.79 ~(late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))),
% 3.23/0.79 inference(rectify,[],[f302])).
% 3.23/0.79 thf(f726,plain,(
% 3.23/0.79 ~ (((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))) = $true)),
% 3.23/0.79 inference(fool_elimination,[],[f725])).
% 3.23/0.79 thf(f749,plain,(
% 3.23/0.79 (((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))) != $true)),
% 3.23/0.79 inference(flattening,[],[f726])).
% 3.23/0.79 thf(f756,plain,(
% 3.23/0.79 ! [X0 : pi,X1 : late_residual,X2 : list @ product_prod @ name @ name] : ((((late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1))) = $true) | (((late_transitions @ X0 @ X1)) != $true))),
% 3.23/0.79 inference(ennf_transformation,[],[f320])).
% 3.23/0.79 thf(f1199,plain,(
% 3.23/0.79 (aa = b)),
% 3.23/0.79 inference(cnf_transformation,[],[f1])).
% 3.23/0.79 thf(f1205,plain,(
% 3.23/0.79 (((late_transitions @ q @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a))) = $true)),
% 3.23/0.79 inference(cnf_transformation,[],[f304])).
% 3.23/0.79 thf(f1216,plain,(
% 3.23/0.79 ( ! [X2 : list @ product_prod @ name @ name,X0 : pi,X1 : late_residual] : ((((late_transitions @ X0 @ X1)) != $true) | (((late_transitions @ (perm @ name @ pi @ X2 @ X0) @ (perm @ name @ late_residual @ X2 @ X1))) = $true)) )),
% 3.23/0.79 inference(cnf_transformation,[],[f756])).
% 3.23/0.79 thf(f1621,plain,(
% 3.23/0.79 (((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ aa @ x) @ q_a)))) != $true)),
% 3.23/0.79 inference(cnf_transformation,[],[f749])).
% 3.23/0.79 thf(f1648,plain,(
% 3.23/0.79 ($true != ((late_transitions @ (perm @ name @ pi @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ q) @ (perm @ name @ late_residual @ (cons @ product_prod @ name @ name @ (product_Pair @ name @ name @ z @ x) @ nil @ product_prod @ name @ name) @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)))))),
% 3.23/0.79 inference(definition_unfolding,[],[f1621,f1199])).
% 3.23/0.79 thf(f7830,plain,(
% 3.23/0.79 ( ! [X0 : list @ product_prod @ name @ name] : (($true != $true) | ($true = ((late_transitions @ (perm @ name @ pi @ X0 @ q) @ (perm @ name @ late_residual @ X0 @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)))))) )),
% 3.23/0.79 inference(constrained_superposition,[],[f1216,f1205])).
% 3.23/0.79 thf(f7837,plain,(
% 3.23/0.79 ( ! [X0 : list @ product_prod @ name @ name] : (($true = ((late_transitions @ (perm @ name @ pi @ X0 @ q) @ (perm @ name @ late_residual @ X0 @ (late_FreeR @ (late_OutputR @ b @ x) @ q_a)))))) )),
% 3.23/0.79 inference(trivial_inequality_removal,[],[f7830])).
% 3.23/0.79 thf(f7839,plain,(
% 3.23/0.79 $false),
% 3.23/0.79 inference(backward_subsumption_resolution,[],[f1648,f7837])).
% 3.23/0.79 % SZS output end Proof for theBenchmark
% 3.23/0.79 % (1284969)------------------------------
% 3.23/0.79 % (1284969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.23/0.79 % (1284969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.23/0.79 % (1284969)CaDiCaL version: 2.1.3
% 3.23/0.79 % (1284969)Termination reason: Refutation
% 3.23/0.79 % (1284969)Time elapsed: 0.320 s
% 3.23/0.79 % (1284969)Peak memory usage: 19 MB
% 3.23/0.79 % (1284969)Instructions burned: 636 (million)
% 3.23/0.79 % (1284845)Success in time 0.571 s
% 3.23/0.79 % Vampire exiting
%------------------------------------------------------------------------------