%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT133^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 0.40s 0.43s
% Output : Refutation 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT133^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:56:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.43 % (3723444)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.40/0.43 % (3723451)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=659960943:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.40/0.43 % (3723449)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3935196906:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.40/0.43 % (3723450)lrs+10_16_si=on:nwc=1.5:random_seed=106455573:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.40/0.43 % (3723452)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=2355929024: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)
% 0.40/0.43 % (3723451)Instruction limit reached!
% 0.40/0.43 % (3723451)------------------------------
% 0.40/0.43 % (3723451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723451)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723451)Termination reason: Instruction limit
% 0.40/0.43 % (3723451)Termination phase: shuffling
% 0.40/0.43 % (3723451)Time elapsed: 0.002 s
% 0.40/0.43 % (3723451)Peak memory usage: 10 MB
% 0.40/0.43 % (3723451)Instructions burned: 4 (million)
% 0.40/0.43 % (3723450)Instruction limit reached!
% 0.40/0.43 % (3723450)------------------------------
% 0.40/0.43 % (3723450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723450)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723450)Termination reason: Instruction limit
% 0.40/0.43 % (3723450)Termination phase: Property scanning
% 0.40/0.43 % (3723450)Time elapsed: 0.010 s
% 0.40/0.43 % (3723450)Peak memory usage: 10 MB
% 0.40/0.43 % (3723450)Instructions burned: 20 (million)
% 0.40/0.43 % (3723454)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3424291198:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.40/0.43 % (3723453)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2226338248:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.40/0.43 % (3723455)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.40/0.43 % (3723455)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
% 0.40/0.43 % (3723461)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3840137584:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.40/0.43 % (3723455)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=896429655:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.40/0.43 % (3723460)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1009711659:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.40/0.43 % (3723461)Instruction limit reached!
% 0.40/0.43 % (3723461)------------------------------
% 0.40/0.43 % (3723461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723461)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723461)Termination reason: Instruction limit
% 0.40/0.43 % (3723461)Termination phase: shuffling
% 0.40/0.43 % (3723461)Time elapsed: 0.003 s
% 0.40/0.43 % (3723461)Peak memory usage: 10 MB
% 0.40/0.43 % (3723461)Instructions burned: 6 (million)
% 0.40/0.43 % (3723460)Instruction limit reached!
% 0.40/0.43 % (3723460)------------------------------
% 0.40/0.43 % (3723460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723460)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723460)Termination reason: Instruction limit
% 0.40/0.43 % (3723460)Termination phase: shuffling
% 0.40/0.43 % (3723460)Time elapsed: 0.002 s
% 0.40/0.43 % (3723460)Peak memory usage: 10 MB
% 0.40/0.43 % (3723460)Instructions burned: 4 (million)
% 0.40/0.43 % (3723453)Instruction limit reached!
% 0.40/0.43 % (3723453)------------------------------
% 0.40/0.43 % (3723453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723453)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723453)Termination reason: Instruction limit
% 0.40/0.43 % (3723453)Termination phase: Property scanning
% 0.40/0.43 % (3723453)Time elapsed: 0.012 s
% 0.40/0.43 % (3723453)Peak memory usage: 10 MB
% 0.40/0.43 % (3723453)Instructions burned: 26 (million)
% 0.40/0.43 % (3723449)Instruction limit reached!
% 0.40/0.43 % (3723449)------------------------------
% 0.40/0.43 % (3723449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723449)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723449)Termination reason: Instruction limit
% 0.40/0.43 % (3723449)Termination phase: Property scanning
% 0.40/0.43 % (3723449)Time elapsed: 0.042 s
% 0.40/0.43 % (3723449)Peak memory usage: 12 MB
% 0.40/0.43 % (3723449)Instructions burned: 87 (million)
% 0.40/0.43 % (3723467)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.40/0.43 % (3723469)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
% 0.40/0.43 % (3723469)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.40/0.43 % (3723467)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2982671003:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.40/0.43 % (3723469)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3287270853:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.40/0.43 % (3723468)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1150703089:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.40/0.43 % (3723467)Instruction limit reached!
% 0.40/0.43 % (3723467)------------------------------
% 0.40/0.43 % (3723467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723467)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723467)Termination reason: Instruction limit
% 0.40/0.43 % (3723467)Termination phase: shuffling
% 0.40/0.43 % (3723467)Time elapsed: 0.004 s
% 0.40/0.43 % (3723467)Peak memory usage: 10 MB
% 0.40/0.43 % (3723467)Instructions burned: 8 (million)
% 0.40/0.43 % (3723470)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=497492218:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.40/0.43 % (3723468)Instruction limit reached!
% 0.40/0.43 % (3723468)------------------------------
% 0.40/0.43 % (3723468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723468)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723468)Termination reason: Instruction limit
% 0.40/0.43 % (3723468)Termination phase: shuffling
% 0.40/0.43 % (3723468)Time elapsed: 0.006 s
% 0.40/0.43 % (3723468)Peak memory usage: 10 MB
% 0.40/0.43 % (3723468)Instructions burned: 13 (million)
% 0.40/0.43 % (3723454)Instruction limit reached!
% 0.40/0.43 % (3723454)------------------------------
% 0.40/0.43 % (3723454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723454)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723454)Termination reason: Instruction limit
% 0.40/0.43 % (3723454)Termination phase: Equality resolution with deletion
% 0.40/0.43 % (3723454)Time elapsed: 0.041 s
% 0.40/0.43 % (3723454)Peak memory usage: 12 MB
% 0.40/0.43 % (3723454)Instructions burned: 77 (million)
% 0.40/0.43 % (3723469)Instruction limit reached!
% 0.40/0.43 % (3723469)------------------------------
% 0.40/0.43 % (3723469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723469)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723469)Termination reason: Instruction limit
% 0.40/0.43 % (3723469)Termination phase: shuffling
% 0.40/0.43 % (3723469)Time elapsed: 0.014 s
% 0.40/0.43 % (3723469)Peak memory usage: 10 MB
% 0.40/0.43 % (3723469)Instructions burned: 30 (million)
% 0.40/0.43 % (3723452) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3723444-3723452"...
% 0.40/0.43 % (3723474)lrs+10_1_si=on:cs=on:random_seed=1157044400:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.40/0.43 % (3723452)...printing done.
% 0.40/0.43 % (3723476)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.40/0.43 % (3723452)Refutation found. Thanks to Tanya!
% 0.40/0.43 % SZS status Theorem for theBenchmark
% 0.40/0.43 % SZS output start Proof for theBenchmark
% 0.40/0.43 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.40/0.43 thf(type_def_6, type, extended_enat: $tType).
% 0.40/0.43 thf(type_def_7, type, set: $tType > $tType).
% 0.40/0.43 thf(type_def_8, type, nat: $tType).
% 0.40/0.43 thf(type_def_9, type, itself: $tType > $tType).
% 0.40/0.43 thf(type_def_10, type, a: $tType).
% 0.40/0.43 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.40/0.43 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_1, type, one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_2, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_3, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_4, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_5, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_6, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_7, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_8, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_9, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_10, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_11, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_12, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_13, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_14, type, ordere223160158up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_15, type, strict2144017051up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.40/0.43 thf(func_def_16, type, coindu493225792length: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > extended_enat))).
% 0.40/0.43 thf(func_def_17, type, coindu191418589_ldrop: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_18, type, coindu438612276pWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_19, type, coindu531130065ldropn: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_20, type, coindu1889960678filter: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_21, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.40/0.43 thf(func_def_22, type, coindu2000965700_llast: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.40/0.43 thf(func_def_23, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 0.40/0.43 thf(func_def_24, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.40/0.43 thf(func_def_25, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.40/0.43 thf(func_def_26, type, coindu1112613586e_lset: !>[X0: $tType]:((coindu1593790203_llist @ X0 > set @ X0))).
% 0.40/0.43 thf(func_def_27, type, coindu1047225960le_ltl: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_28, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.40/0.43 thf(func_def_29, type, coindu721411036eWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_30, type, coindu1491768222unfold: !>[X0: $tType]:(((X0 > $o) > (X0 > X0) > X0 > extended_enat))).
% 0.40/0.43 thf(func_def_31, type, extended_enat2: (nat > extended_enat)).
% 0.40/0.43 thf(func_def_32, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.40/0.43 thf(func_def_33, type, extended_the_enat: (extended_enat > nat)).
% 0.40/0.43 thf(func_def_34, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.40/0.43 thf(func_def_35, type, one_one: !>[X0: $tType]:(X0)).
% 0.40/0.43 thf(func_def_36, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.40/0.43 thf(func_def_37, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.40/0.43 thf(func_def_38, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.40/0.43 thf(func_def_39, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.40/0.43 thf(func_def_40, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.40/0.43 thf(func_def_41, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.40/0.43 thf(func_def_42, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.40/0.43 thf(func_def_43, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.40/0.43 thf(func_def_44, type, p: (a > $o)).
% 0.40/0.43 thf(func_def_45, type, n: nat).
% 0.40/0.43 thf(func_def_46, type, xs: coindu1593790203_llist @ a).
% 0.40/0.43 thf(func_def_47, type, xsa: coindu1593790203_llist @ a).
% 0.40/0.43 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.40/0.43 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.40/0.43 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.40/0.43 thf(func_def_54, type, db2: !>[X0: $tType]:(X0)).
% 0.40/0.43 thf(func_def_55, type, db1: !>[X0: $tType]:(X0)).
% 0.40/0.43 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.40/0.43 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.40/0.43 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.40/0.43 thf(func_def_59, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.40/0.43 thf(func_def_60, type, vNOT: ($o > $o)).
% 0.40/0.43 thf(func_def_61, type, vOR: ($o > $o > $o)).
% 0.40/0.43 thf(func_def_62, type, sK0: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.40/0.43 thf(func_def_63, type, sK1: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_64, type, sK2: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_65, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.40/0.43 thf(func_def_66, type, sK4: (extended_enat > extended_enat > nat)).
% 0.40/0.43 thf(func_def_67, type, sK5: ((nat > $o) > nat)).
% 0.40/0.43 thf(func_def_68, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.40/0.43 thf(func_def_69, type, sK7: (nat > set @ nat > nat)).
% 0.40/0.43 thf(func_def_70, type, sK8: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_71, type, sK9: !>[X0: $tType]:((((nat > X0 > X0) > nat > nat > X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_72, type, sK10: !>[X0: $tType]:((((nat > X0 > X0) > nat > nat > X0 > $o) > nat > X0 > X0))).
% 0.40/0.43 thf(func_def_73, type, sK11: !>[X0: $tType]:((((nat > X0 > X0) > nat > nat > X0 > $o) > nat))).
% 0.40/0.43 thf(func_def_74, type, sK12: !>[X0: $tType]:((((nat > X0 > X0) > nat > nat > X0 > $o) > nat))).
% 0.40/0.43 thf(func_def_75, type, sK13: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_76, type, sK14: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_77, type, sK15: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.40/0.43 thf(func_def_78, type, sK16: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_79, type, sK17: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_80, type, sK18: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_81, type, sK19: (extended_enat > nat > nat)).
% 0.40/0.43 thf(func_def_82, type, sK20: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_83, type, sK21: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > nat))).
% 0.40/0.43 thf(func_def_84, type, sK22: ((extended_enat > $o) > extended_enat)).
% 0.40/0.43 thf(func_def_85, type, sK23: (extended_enat > nat)).
% 0.40/0.43 thf(func_def_86, type, sK24: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_87, type, sK25: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_88, type, sK26: (nat > set @ nat > nat)).
% 0.40/0.43 thf(func_def_89, type, sK27: (set @ nat > nat)).
% 0.40/0.43 thf(func_def_90, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > set @ X0 > X0))).
% 0.40/0.43 thf(func_def_91, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X1 > set @ X0 > X1))).
% 0.40/0.43 thf(func_def_92, type, sK30: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_93, type, sK31: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_94, type, sK32: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.40/0.43 thf(func_def_95, type, sK33: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_96, type, sK34: a).
% 0.40/0.43 thf(func_def_97, type, sK35: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.40/0.43 thf(func_def_98, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (X1 > $o) > X0))).
% 0.40/0.43 thf(func_def_99, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_100, type, sK38: ((nat > $o) > nat)).
% 0.40/0.43 thf(func_def_101, type, sK39: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_102, type, sK40: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat))).
% 0.40/0.43 thf(func_def_103, type, sK41: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.40/0.43 thf(func_def_104, type, sK42: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.40/0.43 thf(func_def_105, type, sK43: nat).
% 0.40/0.43 thf(func_def_106, type, sK44: (set @ nat > nat > nat)).
% 0.40/0.43 thf(func_def_107, type, sK45: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0 > X1))).
% 0.40/0.43 thf(func_def_108, type, sK46: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0))).
% 0.40/0.43 thf(func_def_109, type, sK47: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_110, type, sK48: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_111, type, sK49: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_112, type, sK50: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_113, type, sK51: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_114, type, sK52: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_115, type, sK53: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.40/0.43 thf(func_def_116, type, sK54: !>[X0: $tType]:((coindu1593790203_llist @ X0 > (X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_117, type, sK55: !>[X0: $tType]:(((X0 > extended_enat) > nat > X0))).
% 0.40/0.43 thf(func_def_118, type, sK56: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 0.40/0.43 thf(func_def_119, type, sK57: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_120, type, sK58: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.40/0.43 thf(func_def_121, type, sK59: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.40/0.43 thf(func_def_122, type, sK60: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.40/0.43 thf(func_def_123, type, sK61: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.40/0.43 thf(func_def_124, type, sK62: !>[X0: $tType, X1: $tType]:((X0 > set @ X1 > (X1 > X0) > X1))).
% 0.40/0.43 thf(func_def_126, type, inv_extended_enat2_64: (extended_enat > nat)).
% 0.40/0.43 thf(func_def_127, type, inv_plus_plus_65: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.40/0.43 thf(func_def_128, type, inv_plus_plus_66: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.40/0.43 thf(f1,axiom,(
% 0.40/0.43 (finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[X3 : nat] : ((ord_less @ extended_enat @ (extended_enat2 @ X3) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X4 : a] : (~(p @ X4))) @ xsa))))))) @ (collect @ nat @ (^[X3 : nat] : ((p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X4 : a] : (~(p @ X4))) @ xsa)) @ X3)))))))),
% 0.40/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062finite_A_I_123n_O_Aenat_An_A_060_Allength_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_125_A_092_060inter_062_A_123n_O_AP_A_Ilnth_A_Iltl_A_IldropWhile_A_I_092_060lambda_062x_O_A_092_060not_062_AP_Ax_J_Axs_J_J_An_J_125_J_092_060close_062)).
% 0.40/0.43 thf(f5,axiom,(
% 0.40/0.43 ! [X1 : $tType,X0 : $tType,X3 : (X1 > X0),X2 : set @ X1] : ((finite_finite2 @ X1 @ X2) => (finite_finite2 @ X0 @ (image @ X1 @ X0 @ X3 @ X2)))),
% 0.40/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__imageI)).
% 0.40/0.43 thf(f281,conjecture,(
% 0.40/0.43 (finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[X0 : nat] : ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X1 : a] : (~(p @ X1))) @ xsa))))))) @ (collect @ nat @ (^[X0 : nat] : ((p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X1 : a] : (~(p @ X1))) @ xsa)) @ X0))))))))),
% 0.40/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.40/0.43 thf(f282,negated_conjecture,(
% 0.40/0.43 ~(finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[X0 : nat] : ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X1 : a] : (~(p @ X1))) @ xsa))))))) @ (collect @ nat @ (^[X0 : nat] : ((p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X1 : a] : (~(p @ X1))) @ xsa)) @ X0))))))))),
% 0.40/0.43 inference(negated_conjecture,[status(cth)],[f281])).
% 0.40/0.43 thf(f625,plain,(
% 0.40/0.43 ~(finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[X0 : nat] : ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X1 : a] : (~(p @ X1))) @ xsa))))))) @ (collect @ nat @ (^[X2 : nat] : ((p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X3 : a] : (~(p @ X3))) @ xsa)) @ X2))))))))),
% 0.40/0.43 inference(rectify,[],[f282])).
% 0.40/0.43 thf(f626,plain,(
% 0.40/0.43 ~ ($true = ((finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0)))))))))),
% 0.40/0.43 inference(fool_elimination,[],[f625])).
% 0.40/0.43 thf(f654,plain,(
% 0.40/0.43 ! [X0 : $tType,X1 : $tType,X2 : (X0 > X1),X3 : set @ X0] : ((finite_finite2 @ X0 @ X3) => (finite_finite2 @ X1 @ (image @ X0 @ X1 @ X2 @ X3)))),
% 0.40/0.43 inference(rectify,[],[f5])).
% 0.40/0.43 thf(f655,plain,(
% 0.40/0.43 ! [X1 : $tType,X0 : $tType,X3 : set @ X0,X2 : (X0 > X1)] : ((((finite_finite2 @ X0 @ X3)) = $true) => ($true = ((finite_finite2 @ X1 @ (image @ X0 @ X1 @ X2 @ X3)))))),
% 0.40/0.43 inference(fool_elimination,[],[f654])).
% 0.40/0.43 thf(f676,plain,(
% 0.40/0.43 (finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[X0 : nat] : ((ord_less @ extended_enat @ (extended_enat2 @ X0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X1 : a] : (~(p @ X1))) @ xsa))))))) @ (collect @ nat @ (^[X2 : nat] : ((p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[X3 : a] : (~(p @ X3))) @ xsa)) @ X2)))))))),
% 0.40/0.43 inference(rectify,[],[f1])).
% 0.40/0.43 thf(f677,plain,(
% 0.40/0.43 ($true = ((finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0))))))))),
% 0.40/0.43 inference(fool_elimination,[],[f676])).
% 0.40/0.43 thf(f827,plain,(
% 0.40/0.43 ($true != ((finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0)))))))))),
% 0.40/0.43 inference(flattening,[],[f626])).
% 0.40/0.43 thf(f968,plain,(
% 0.40/0.43 ! [X1 : $tType,X0 : $tType,X3 : set @ X0,X2 : (X0 > X1)] : ((((finite_finite2 @ X0 @ X3)) != $true) | ($true = ((finite_finite2 @ X1 @ (image @ X0 @ X1 @ X2 @ X3)))))),
% 0.40/0.43 inference(ennf_transformation,[],[f655])).
% 0.40/0.43 thf(f1126,plain,(
% 0.40/0.43 ! [X0 : $tType,X1 : $tType,X2 : set @ X1,X3 : (X1 > X0)] : ((((finite_finite2 @ X1 @ X2)) != $true) | (((finite_finite2 @ X0 @ (image @ X1 @ X0 @ X3 @ X2))) = $true))),
% 0.40/0.43 inference(rectify,[],[f968])).
% 0.40/0.43 thf(f1396,plain,(
% 0.40/0.43 ( ! [X1 : $tType,X0 : $tType,X2 : set @ X1,X3 : (X1 > X0)] : ((((finite_finite2 @ X0 @ (image @ X1 @ X0 @ X3 @ X2))) = $true) | (((finite_finite2 @ X1 @ X2)) != $true)) )),
% 0.40/0.43 inference(cnf_transformation,[],[f1126])).
% 0.40/0.43 thf(f1426,plain,(
% 0.40/0.43 ($true = ((finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0))))))))),
% 0.40/0.43 inference(cnf_transformation,[],[f677])).
% 0.40/0.43 thf(f1560,plain,(
% 0.40/0.43 ($true != ((finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0)))))))))),
% 0.40/0.43 inference(cnf_transformation,[],[f827])).
% 0.40/0.43 thf(f1887,definition,(
% 0.40/0.43 spl63_22 <=> ($true = ((finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0)))))))))),
% 0.40/0.43 introduced(definition,[new_symbols(definition,[spl63_22])],[avatar_definition])).
% 0.40/0.43 thf(f1889,plain,(
% 0.40/0.43 ($true != ((finite_finite2 @ nat @ (image @ nat @ nat @ (plus_plus @ nat @ (plus_plus @ nat @ n @ one_one @ nat)) @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0))))))))) | spl63_22),
% 0.40/0.43 inference(avatar_component_clause,[],[f1887])).
% 0.40/0.43 thf(f1890,plain,(
% 0.40/0.43 ~spl63_22),
% 0.40/0.43 inference(avatar_split_clause,[],[f1560,f1887])).
% 0.40/0.43 thf(f1937,definition,(
% 0.40/0.43 spl63_32 <=> ($true = ((finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0))))))))),
% 0.40/0.43 introduced(definition,[new_symbols(definition,[spl63_32])],[avatar_definition])).
% 0.40/0.43 thf(f1940,plain,(
% 0.40/0.43 spl63_32),
% 0.40/0.43 inference(avatar_split_clause,[],[f1426,f1937])).
% 0.40/0.43 thf(f2201,plain,(
% 0.40/0.43 ($true != ((finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0)))))))) | ($true != $true) | spl63_22),
% 0.40/0.43 inference(superposition,[],[f1889,f1396])).
% 0.40/0.43 thf(f2202,plain,(
% 0.40/0.43 ($true != ((finite_finite2 @ nat @ (inf_inf @ set @ nat @ (collect @ nat @ (^[Y0 : nat]: (ord_less @ extended_enat @ (extended_enat2 @ Y0) @ (coindu1018505716length @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)))))) @ (collect @ nat @ (^[Y0 : nat]: (p @ (coindu749330388e_lnth @ a @ (coindu1047225960le_ltl @ a @ (coindu438612276pWhile @ a @ (^[Y1 : a]: (~ (p @ Y1))) @ xsa)) @ Y0)))))))) | spl63_22),
% 0.40/0.43 inference(trivial_inequality_removal,[],[f2201])).
% 0.40/0.43 thf(f2203,plain,(
% 0.40/0.43 ~spl63_32 | spl63_22),
% 0.40/0.43 inference(avatar_split_clause,[],[f2202,f1887,f1937])).
% 0.40/0.43 cnf(s22, plain, ~spl63_22, inference(sat_conversion,[],[f1890])).
% 0.40/0.43 cnf(s33, plain, spl63_32, inference(sat_conversion,[],[f1940])).
% 0.40/0.43 cnf(s42, plain, spl63_22 | ~spl63_32, inference(sat_conversion,[],[f2203])).
% 0.40/0.43 cnf(s43, plain, spl63_22, inference(rat,[],[s42,s33])).
% 0.40/0.43 cnf(s49, plain, $false, inference(rat,[],[s22,s43])).
% 0.40/0.43 thf(f2204,plain,(
% 0.40/0.43 $false),
% 0.40/0.43 inference(avatar_sat_refutation,[],[s49])).
% 0.40/0.43 % SZS output end Proof for theBenchmark
% 0.40/0.43 % (3723452)------------------------------
% 0.40/0.43 % (3723452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.40/0.43 % (3723452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.40/0.43 % (3723452)CaDiCaL version: 2.1.3
% 0.40/0.43 % (3723452)Termination reason: Refutation
% 0.40/0.43 % (3723452)Time elapsed: 0.075 s
% 0.40/0.43 % (3723452)Peak memory usage: 15 MB
% 0.40/0.43 % (3723452)Instructions burned: 155 (million)
% 0.40/0.43 % (3723444)Success in time 0.13 s
% 0.40/0.43 % Vampire exiting
%------------------------------------------------------------------------------