%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT138^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 07:48:24 AM UTC 2026
% Result : Theorem 0.50s 0.41s
% Output : Refutation 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT138^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:59:06 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.50/0.41 % (2452484)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.41 % (2452494)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=169149419:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.41 % (2452495)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.41 % (2452495)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.50/0.41 % (2452491)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=887070085:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.41 % (2452489)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1834402970:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.41 % (2452492)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1260873794:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.50/0.41 % (2452493)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1426672322:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.41 % (2452495)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=326798393:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.41 % (2452491)Instruction limit reached!
% 0.50/0.41 % (2452491)------------------------------
% 0.50/0.41 % (2452491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452491)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452491)Termination reason: Instruction limit
% 0.50/0.41 % (2452491)Termination phase: shuffling
% 0.50/0.41 % (2452491)Time elapsed: 0.003 s
% 0.50/0.41 % (2452491)Peak memory usage: 10 MB
% 0.50/0.41 % (2452491)Instructions burned: 6 (million)
% 0.50/0.41 % (2452490)lrs+10_16_si=on:nwc=1.5:random_seed=2173560082:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.41 % (2452493)Instruction limit reached!
% 0.50/0.41 % (2452493)------------------------------
% 0.50/0.41 % (2452493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452493)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452493)Termination reason: Instruction limit
% 0.50/0.41 % (2452493)Termination phase: Property scanning
% 0.50/0.41 % (2452493)Time elapsed: 0.011 s
% 0.50/0.41 % (2452493)Peak memory usage: 10 MB
% 0.50/0.41 % (2452493)Instructions burned: 24 (million)
% 0.50/0.41 % (2452494)Instruction limit reached!
% 0.50/0.41 % (2452494)------------------------------
% 0.50/0.41 % (2452494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452494)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452494)Termination reason: Instruction limit
% 0.50/0.41 % (2452494)Termination phase: Function definition elimination
% 0.50/0.41 % (2452494)Time elapsed: 0.019 s
% 0.50/0.41 % (2452494)Peak memory usage: 12 MB
% 0.50/0.41 % (2452494)Instructions burned: 77 (million)
% 0.50/0.41 % (2452490)Instruction limit reached!
% 0.50/0.41 % (2452490)------------------------------
% 0.50/0.41 % (2452490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452490)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452490)Termination reason: Instruction limit
% 0.50/0.41 % (2452490)Termination phase: Property scanning
% 0.50/0.41 % (2452490)Time elapsed: 0.016 s
% 0.50/0.41 % (2452490)Peak memory usage: 10 MB
% 0.50/0.41 % (2452490)Instructions burned: 19 (million)
% 0.50/0.41 % (2452505)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.41 % (2452505)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=787818901:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.50/0.41 % (2452503)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2554240142:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.41 % (2452505)Instruction limit reached!
% 0.50/0.41 % (2452505)------------------------------
% 0.50/0.41 % (2452505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452505)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452505)Termination reason: Instruction limit
% 0.50/0.41 % (2452505)Termination phase: shuffling
% 0.50/0.41 % (2452505)Time elapsed: 0.002 s
% 0.50/0.41 % (2452505)Peak memory usage: 10 MB
% 0.50/0.41 % (2452505)Instructions burned: 10 (million)
% 0.50/0.41 % (2452503)Instruction limit reached!
% 0.50/0.41 % (2452503)------------------------------
% 0.50/0.41 % (2452503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452503)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452503)Termination reason: Instruction limit
% 0.50/0.41 % (2452503)Termination phase: shuffling
% 0.50/0.41 % (2452503)Time elapsed: 0.002 s
% 0.50/0.41 % (2452503)Peak memory usage: 10 MB
% 0.50/0.41 % (2452503)Instructions burned: 4 (million)
% 0.50/0.41 % (2452509)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.50/0.41 % (2452509)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.41 % (2452509)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1291023652:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.50/0.41 % (2452506)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2690874234:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.50/0.41 % (2452504)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2425490564:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.50/0.41 % (2452489)Instruction limit reached!
% 0.50/0.41 % (2452489)------------------------------
% 0.50/0.41 % (2452489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452489)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452489)Termination reason: Instruction limit
% 0.50/0.41 % (2452489)Termination phase: Property scanning
% 0.50/0.41 % (2452489)Time elapsed: 0.041 s
% 0.50/0.41 % (2452489)Peak memory usage: 12 MB
% 0.50/0.41 % (2452489)Instructions burned: 89 (million)
% 0.50/0.41 % (2452504)Instruction limit reached!
% 0.50/0.41 % (2452504)------------------------------
% 0.50/0.41 % (2452504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452504)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452504)Termination reason: Instruction limit
% 0.50/0.41 % (2452504)Termination phase: shuffling
% 0.50/0.41 % (2452504)Time elapsed: 0.004 s
% 0.50/0.41 % (2452504)Peak memory usage: 10 MB
% 0.50/0.41 % (2452504)Instructions burned: 7 (million)
% 0.50/0.41 % (2452509)Instruction limit reached!
% 0.50/0.41 % (2452509)------------------------------
% 0.50/0.41 % (2452509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452509)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452509)Termination reason: Instruction limit
% 0.50/0.41 % (2452509)Termination phase: shuffling
% 0.50/0.41 % (2452509)Time elapsed: 0.007 s
% 0.50/0.41 % (2452509)Peak memory usage: 10 MB
% 0.50/0.41 % (2452509)Instructions burned: 31 (million)
% 0.50/0.41 % (2452506)Instruction limit reached!
% 0.50/0.41 % (2452506)------------------------------
% 0.50/0.41 % (2452506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452506)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452506)Termination reason: Instruction limit
% 0.50/0.41 % (2452506)Termination phase: shuffling
% 0.50/0.41 % (2452506)Time elapsed: 0.006 s
% 0.50/0.41 % (2452506)Peak memory usage: 10 MB
% 0.50/0.41 % (2452506)Instructions burned: 13 (million)
% 0.50/0.41 % (2452510)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2922513304:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.50/0.41 % (2452516)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2732332402:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.50/0.41 % (2452515)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.50/0.41 % (2452514)lrs+10_1_si=on:cs=on:random_seed=1008352621:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.50/0.41 % (2452492) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2452484-2452492"...
% 0.50/0.41 % (2452515)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=456667743:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.41 % (2452492)...printing done.
% 0.50/0.41 % (2452514)Instruction limit reached!
% 0.50/0.41 % (2452514)------------------------------
% 0.50/0.41 % (2452514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452514)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452514)Termination reason: Instruction limit
% 0.50/0.41 % (2452514)Termination phase: shuffling
% 0.50/0.41 % (2452514)Time elapsed: 0.004 s
% 0.50/0.41 % (2452514)Peak memory usage: 10 MB
% 0.50/0.41 % (2452514)Instructions burned: 9 (million)
% 0.50/0.41 % (2452492)Refutation found. Thanks to Tanya!
% 0.50/0.41 % SZS status Theorem for theBenchmark
% 0.50/0.41 % SZS output start Proof for theBenchmark
% 0.50/0.41 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.50/0.41 thf(type_def_6, type, list: $tType > $tType).
% 0.50/0.41 thf(type_def_7, type, nat: $tType).
% 0.50/0.41 thf(type_def_8, type, itself: $tType > $tType).
% 0.50/0.41 thf(type_def_9, type, a: $tType).
% 0.50/0.41 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.50/0.41 thf(func_def_0, type, coindu1571841457prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.50/0.41 thf(func_def_1, type, coindu288502823_llist: !>[X0: $tType]:(((nat > X0) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_2, type, coindu1529956631erates: !>[X0: $tType]:(((X0 > X0) > X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_3, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_4, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.50/0.41 thf(func_def_5, type, coindu1736001939ist_of: !>[X0: $tType]:((coindu1593790203_llist @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_6, type, coindu1542816657of_aux: !>[X0: $tType]:((list @ X0 > coindu1593790203_llist @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_7, type, coindu2000965700_llast: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.50/0.41 thf(func_def_8, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_9, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 0.50/0.41 thf(func_def_10, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.50/0.41 thf(func_def_11, type, coindu1079202755ist_of: !>[X0: $tType]:((list @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_12, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 0.50/0.41 thf(func_def_13, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.50/0.41 thf(func_def_14, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.50/0.41 thf(func_def_15, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.50/0.41 thf(func_def_16, type, undefined: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_17, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.50/0.41 thf(func_def_18, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_19, type, bind: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > list @ X1) > list @ X1))).
% 0.50/0.41 thf(func_def_20, type, butlast: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_21, type, insert: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_22, type, last: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_23, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_24, type, nil: !>[X0: $tType]:(list @ X0)).
% 0.50/0.41 thf(func_def_25, type, map: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1))).
% 0.50/0.41 thf(func_def_26, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.50/0.41 thf(func_def_27, type, map_tailrec: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1))).
% 0.50/0.41 thf(func_def_28, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > list @ X1))).
% 0.50/0.41 thf(func_def_29, type, maps: !>[X0: $tType, X1: $tType]:(((X0 > list @ X1) > list @ X0 > list @ X1))).
% 0.50/0.41 thf(func_def_30, type, nth: !>[X0: $tType]:((list @ X0 > nat > X0))).
% 0.50/0.41 thf(func_def_31, type, lexordp_eq: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o))).
% 0.50/0.41 thf(func_def_32, type, product_lists: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.50/0.41 thf(func_def_33, type, rev: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_34, type, rotate1: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_35, type, sublists: !>[X0: $tType]:((list @ X0 > list @ list @ X0))).
% 0.50/0.41 thf(func_def_36, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.50/0.41 thf(func_def_37, type, type: !>[X0: $tType]:(itself @ X0)).
% 0.50/0.41 thf(func_def_38, type, prefixes: !>[X0: $tType]:((list @ X0 > list @ list @ X0))).
% 0.50/0.41 thf(func_def_39, type, prefixes_rel: !>[X0: $tType]:((list @ X0 > list @ X0 > $o))).
% 0.50/0.41 thf(func_def_40, type, strict_suffix: !>[X0: $tType]:((list @ X0 > list @ X0 > $o))).
% 0.50/0.41 thf(func_def_41, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.50/0.41 thf(func_def_42, type, f: (nat > a)).
% 0.50/0.41 thf(func_def_43, type, xs: coindu1593790203_llist @ a).
% 0.50/0.41 thf(func_def_47, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.50/0.41 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_49, type, db0: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.50/0.41 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.50/0.41 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.50/0.41 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.50/0.41 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 0.50/0.41 thf(func_def_56, type, db4: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_57, type, db3: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_58, type, db5: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_59, type, db6: !>[X0: $tType]:(X0)).
% 0.50/0.41 thf(func_def_60, type, vIMP: ($o > $o > $o)).
% 0.50/0.41 thf(func_def_61, type, sP0: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o))).
% 0.50/0.41 thf(func_def_62, type, sK1: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_63, type, sK2: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_64, type, sK3: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_65, type, sK4: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_66, type, sK5: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_67, type, sK6: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_68, type, sK7: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_69, type, sK8: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_70, type, sK9: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_71, type, sK10: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_72, type, sK11: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_73, type, sK12: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_74, type, sK13: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_75, type, sK14: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_76, type, sK15: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_77, type, sK16: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_78, type, sK17: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_79, type, sK18: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_80, type, sK19: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_81, type, sK20: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_82, type, sK21: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_83, type, sK22: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_84, type, sK23: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_85, type, sK24: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_86, type, sK25: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_87, type, sK26: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 0.50/0.41 thf(func_def_88, type, sK27: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.50/0.41 thf(func_def_89, type, sK28: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_90, type, sK29: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_91, type, sK30: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.50/0.41 thf(func_def_92, type, sK31: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 0.50/0.41 thf(func_def_93, type, sK32: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_94, type, sK33: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > X0))).
% 0.50/0.41 thf(func_def_95, type, sK34: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.50/0.41 thf(func_def_96, type, sK35: !>[X0: $tType]:((coindu1593790203_llist @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_97, type, sK36: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_98, type, sK37: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_99, type, sK38: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > (X0 > X1) > list @ X1 > list @ X0))).
% 0.50/0.41 thf(func_def_100, type, sK39: !>[X0: $tType, X1: $tType]:((list @ X1 > list @ X0 > (X0 > X1) > list @ X1 > X0))).
% 0.50/0.41 thf(func_def_101, type, sK40: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_102, type, sK41: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_103, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_104, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_105, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_106, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_107, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_108, type, sK47: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_109, type, sK48: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_110, type, sK49: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_111, type, sK50: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > X0))).
% 0.50/0.41 thf(func_def_112, type, sK51: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_113, type, sK52: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 0.50/0.41 thf(func_def_114, type, sK53: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_115, type, sK54: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_116, type, sK55: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 0.50/0.41 thf(func_def_117, type, sK56: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.50/0.41 thf(func_def_118, type, sK57: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1))).
% 0.50/0.41 thf(func_def_119, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_120, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > X1))).
% 0.50/0.41 thf(func_def_121, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > X2))).
% 0.50/0.41 thf(func_def_122, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > list @ X3))).
% 0.50/0.41 thf(func_def_123, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > X3))).
% 0.50/0.41 thf(func_def_124, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > list @ X1))).
% 0.50/0.41 thf(func_def_125, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_126, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((list @ X1 > list @ X2 > list @ X3 > list @ X0 > $o) > list @ X2))).
% 0.50/0.41 thf(func_def_127, type, sK66: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_128, type, sK67: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_129, type, sK68: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_130, type, sK69: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_131, type, sK70: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_132, type, sK71: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_133, type, sK72: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_134, type, sK73: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_135, type, sK74: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_136, type, sK75: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.50/0.41 thf(func_def_137, type, sK76: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_138, type, sK77: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.50/0.41 thf(func_def_139, type, sK78: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_140, type, sK79: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_141, type, sK80: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > list @ X0 > X0))).
% 0.50/0.41 thf(func_def_142, type, sK81: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_143, type, sK82: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > list @ X0 > X0))).
% 0.50/0.41 thf(func_def_144, type, sK83: !>[X0: $tType]:((list @ X0 > (X0 > X0 > $o) > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_145, type, sK84: !>[X0: $tType]:((X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_146, type, sK85: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_147, type, sK86: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_148, type, sK87: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_149, type, sK88: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_150, type, sK89: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_151, type, sK90: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_152, type, sK91: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_153, type, sK92: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_154, type, sK93: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_155, type, sK94: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_156, type, sK95: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_157, type, sK96: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.50/0.41 thf(func_def_158, type, sK97: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.50/0.41 thf(func_def_159, type, sK98: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_160, type, sK99: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_161, type, sK100: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_162, type, sK101: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_163, type, sK102: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_164, type, sK103: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_165, type, sK104: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_166, type, sK105: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.50/0.41 thf(func_def_167, type, sK106: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_168, type, sK107: !>[X0: $tType, X1: $tType]:((list @ X1 > X1 > list @ X0 > (X0 > X1) > X0))).
% 0.50/0.41 thf(func_def_169, type, sK108: !>[X0: $tType, X1: $tType]:((list @ X1 > X1 > list @ X0 > (X0 > X1) > list @ X0))).
% 0.50/0.41 thf(func_def_170, type, sK109: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_171, type, sK110: !>[X0: $tType, X1: $tType]:((list @ X0 > X0 > (X1 > X0) > list @ X1 > list @ X1))).
% 0.50/0.41 thf(func_def_172, type, sK111: !>[X0: $tType, X1: $tType]:((list @ X0 > X0 > (X1 > X0) > list @ X1 > X1))).
% 0.50/0.41 thf(func_def_173, type, sK112: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > list @ X0 > list @ X1 > list @ X1))).
% 0.50/0.41 thf(func_def_174, type, sK113: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > list @ X0 > list @ X1 > X1))).
% 0.50/0.41 thf(func_def_175, type, sK114: !>[X0: $tType]:((list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_176, type, sK115: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.50/0.41 thf(func_def_177, type, sK116: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_178, type, sK117: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_179, type, sK118: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_180, type, sK119: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_181, type, sK120: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_182, type, sK121: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0))).
% 0.50/0.41 thf(func_def_183, type, sK122: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_184, type, sK123: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_185, type, sK124: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_186, type, sK125: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_187, type, sK126: !>[X0: $tType]:((list @ X0 > X0))).
% 0.50/0.41 thf(func_def_188, type, sK127: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.50/0.41 thf(func_def_189, type, sK128: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_190, type, sK129: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.50/0.41 thf(func_def_191, type, sK130: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 0.50/0.41 thf(func_def_192, type, sK131: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0))).
% 0.50/0.41 thf(func_def_193, type, sK132: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > X0))).
% 0.50/0.41 thf(func_def_194, type, sK133: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > X1) > X1 > list @ X1 > X0))).
% 0.50/0.41 thf(func_def_195, type, sK134: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > X1) > X1 > list @ X1 > list @ X0))).
% 0.50/0.41 thf(func_def_196, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X2 > list @ X0 > list @ X1 > $o) > list @ X2))).
% 0.50/0.41 thf(func_def_197, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X2 > list @ X0 > list @ X1 > $o) > X1))).
% 0.50/0.41 thf(func_def_198, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X2 > list @ X0 > list @ X1 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_199, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X2 > list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.50/0.41 thf(func_def_200, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X2 > list @ X0 > list @ X1 > $o) > X0))).
% 0.50/0.41 thf(func_def_201, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType]:(((list @ X2 > list @ X0 > list @ X1 > $o) > X2))).
% 0.50/0.41 thf(func_def_202, type, sK141: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.50/0.41 thf(func_def_203, type, sK142: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 0.50/0.41 thf(func_def_204, type, sK143: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.50/0.41 thf(func_def_205, type, sK144: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 0.50/0.41 thf(func_def_206, type, sK145: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.50/0.41 thf(func_def_207, type, sK146: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.50/0.41 thf(func_def_209, type, inv_coindu288502823_llist_148: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.50/0.41 thf(f72,axiom,(
% 0.50/0.41 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (~(coindu1213758845finite @ X0 @ X1) => (((coindu268472904append @ X0 @ X1 @ X2)) = X1))),
% 0.50/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_lappend__inf)).
% 0.50/0.41 thf(f85,axiom,(
% 0.50/0.41 ! [X0 : $tType,X1 : (nat > X0)] : ~(coindu1213758845finite @ X0 @ (coindu288502823_llist @ X0 @ X1))),
% 0.50/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_lfinite__inf__llist)).
% 0.50/0.41 thf(f257,conjecture,(
% 0.50/0.41 (((coindu268472904append @ a @ (coindu288502823_llist @ a @ f) @ xs)) = ((coindu288502823_llist @ a @ f)))),
% 0.50/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.50/0.41 thf(f258,negated_conjecture,(
% 0.50/0.41 ~ (((coindu268472904append @ a @ (coindu288502823_llist @ a @ f) @ xs)) = ((coindu288502823_llist @ a @ f)))),
% 0.50/0.41 inference(negated_conjecture,[status(cth)],[f257])).
% 0.50/0.41 thf(f410,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : (nat > X0)] : ~(coindu1213758845finite @ X0 @ (coindu288502823_llist @ X0 @ X1))),
% 0.50/0.41 inference(rectify,[],[f85])).
% 0.50/0.41 thf(f411,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : (nat > X0)] : ~ (((coindu1213758845finite @ X0 @ (coindu288502823_llist @ X0 @ X1))) = $true)),
% 0.50/0.41 inference(fool_elimination,[],[f410])).
% 0.50/0.41 thf(f557,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~(coindu1213758845finite @ X0 @ X2) => (((coindu268472904append @ X0 @ X2 @ X1)) = X2))),
% 0.50/0.41 inference(rectify,[],[f72])).
% 0.50/0.41 thf(f558,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~ (((coindu1213758845finite @ X0 @ X2)) = $true) => (((coindu268472904append @ X0 @ X2 @ X1)) = X2))),
% 0.50/0.41 inference(fool_elimination,[],[f557])).
% 0.50/0.41 thf(f599,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : (nat > X0)] : (((coindu1213758845finite @ X0 @ (coindu288502823_llist @ X0 @ X1))) != $true)),
% 0.50/0.41 inference(flattening,[],[f411])).
% 0.50/0.41 thf(f618,plain,(
% 0.50/0.41 (((coindu288502823_llist @ a @ f)) != ((coindu268472904append @ a @ (coindu288502823_llist @ a @ f) @ xs)))),
% 0.50/0.41 inference(flattening,[],[f258])).
% 0.50/0.41 thf(f641,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : ((((coindu1213758845finite @ X0 @ X2)) != $true) => (((coindu268472904append @ X0 @ X2 @ X1)) = X2))),
% 0.50/0.41 inference(flattening,[],[f558])).
% 0.50/0.41 thf(f678,plain,(
% 0.50/0.41 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : ((((coindu268472904append @ X0 @ X2 @ X1)) = X2) | (((coindu1213758845finite @ X0 @ X2)) = $true))),
% 0.50/0.41 inference(ennf_transformation,[],[f641])).
% 0.50/0.41 thf(f1123,plain,(
% 0.50/0.41 (((coindu288502823_llist @ a @ f)) != ((coindu268472904append @ a @ (coindu288502823_llist @ a @ f) @ xs)))),
% 0.50/0.41 inference(cnf_transformation,[],[f618])).
% 0.50/0.41 thf(f1137,plain,(
% 0.50/0.41 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((coindu268472904append @ X0 @ X2 @ X1)) = X2) | (((coindu1213758845finite @ X0 @ X2)) = $true)) )),
% 0.50/0.41 inference(cnf_transformation,[],[f678])).
% 0.50/0.41 thf(f1344,plain,(
% 0.50/0.41 ( ! [X0 : $tType,X1 : (nat > X0)] : ((((coindu1213758845finite @ X0 @ (coindu288502823_llist @ X0 @ X1))) != $true)) )),
% 0.50/0.41 inference(cnf_transformation,[],[f599])).
% 0.50/0.41 thf(f1632,definition,(
% 0.50/0.41 spl147_1 <=> (((coindu288502823_llist @ a @ f)) = ((coindu268472904append @ a @ (coindu288502823_llist @ a @ f) @ xs)))),
% 0.50/0.41 introduced(definition,[new_symbols(definition,[spl147_1])],[avatar_definition])).
% 0.50/0.41 thf(f1634,plain,(
% 0.50/0.41 (((coindu288502823_llist @ a @ f)) != ((coindu268472904append @ a @ (coindu288502823_llist @ a @ f) @ xs))) | spl147_1),
% 0.50/0.41 inference(avatar_component_clause,[],[f1632])).
% 0.50/0.41 thf(f1635,plain,(
% 0.50/0.41 ~spl147_1),
% 0.50/0.41 inference(avatar_split_clause,[],[f1123,f1632])).
% 0.50/0.41 thf(f1646,plain,(
% 0.50/0.41 (((coindu288502823_llist @ a @ f)) != ((coindu288502823_llist @ a @ f))) | ($true = ((coindu1213758845finite @ a @ (coindu288502823_llist @ a @ f)))) | spl147_1),
% 0.50/0.41 inference(superposition,[],[f1634,f1137])).
% 0.50/0.41 thf(f1647,plain,(
% 0.50/0.41 ($true = ((coindu1213758845finite @ a @ (coindu288502823_llist @ a @ f)))) | spl147_1),
% 0.50/0.41 inference(trivial_inequality_removal,[],[f1646])).
% 0.50/0.41 thf(f1648,plain,(
% 0.50/0.41 $false | spl147_1),
% 0.50/0.41 inference(forward_subsumption_resolution,[],[f1647,f1344])).
% 0.50/0.41 thf(f1649,plain,(
% 0.50/0.41 spl147_1),
% 0.50/0.41 inference(avatar_contradiction_clause,[],[f1648])).
% 0.50/0.41 cnf(s1, plain, ~spl147_1, inference(sat_conversion,[],[f1635])).
% 0.50/0.41 cnf(s2, plain, spl147_1, inference(sat_conversion,[],[f1649])).
% 0.50/0.41 cnf(s3, plain, $false, inference(rat,[],[s1,s2])).
% 0.50/0.41 thf(f1650,plain,(
% 0.50/0.41 $false),
% 0.50/0.41 inference(avatar_sat_refutation,[],[s3])).
% 0.50/0.41 % SZS output end Proof for theBenchmark
% 0.50/0.41 % (2452492)------------------------------
% 0.50/0.41 % (2452492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (2452492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (2452492)CaDiCaL version: 2.1.3
% 0.50/0.41 % (2452492)Termination reason: Refutation
% 0.50/0.41 % (2452492)Time elapsed: 0.063 s
% 0.50/0.41 % (2452492)Peak memory usage: 14 MB
% 0.50/0.41 % (2452492)Instructions burned: 129 (million)
% 0.50/0.41 % (2452484)Success in time 0.118 s
% 0.50/0.41 % Vampire exiting
%------------------------------------------------------------------------------