%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT147^1 : 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 : n026.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 07:48:25 AM UTC 2026
% Result : Theorem 0.56s 0.42s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT147^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n026.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 18:04:27 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
% 0.21/0.29 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
% 0.56/0.42 % (958810)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.56/0.42 % (958819)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1476358127:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.56/0.42 % (958819)Instruction limit reached!
% 0.56/0.42 % (958819)------------------------------
% 0.56/0.42 % (958819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958819)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958819)Termination reason: Instruction limit
% 0.56/0.42 % (958819)Termination phase: Property scanning
% 0.56/0.42 % (958819)Time elapsed: 0.006 s
% 0.56/0.42 % (958819)Peak memory usage: 10 MB
% 0.56/0.42 % (958819)Instructions burned: 27 (million)
% 0.56/0.42 % (958816)lrs+10_16_si=on:nwc=1.5:random_seed=3485775231:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.56/0.42 % (958817)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=613165817:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.56/0.42 % (958818)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=3122662833: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)
% 0.56/0.42 % (958820)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3387112828:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.56/0.42 % (958821)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.56/0.42 % (958821)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
% 0.56/0.42 % (958817)Instruction limit reached!
% 0.56/0.42 % (958817)------------------------------
% 0.56/0.42 % (958817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958817)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958817)Termination reason: Instruction limit
% 0.56/0.42 % (958817)Termination phase: shuffling
% 0.56/0.42 % (958817)Time elapsed: 0.003 s
% 0.56/0.42 % (958817)Peak memory usage: 10 MB
% 0.56/0.42 % (958817)Instructions burned: 4 (million)
% 0.56/0.42 % (958821)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=279155717:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.56/0.42 % (958816)Instruction limit reached!
% 0.56/0.42 % (958816)------------------------------
% 0.56/0.42 % (958816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958816)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958816)Termination reason: Instruction limit
% 0.56/0.42 % (958816)Termination phase: Property scanning
% 0.56/0.42 % (958816)Time elapsed: 0.009 s
% 0.56/0.42 % (958816)Peak memory usage: 10 MB
% 0.56/0.42 % (958816)Instructions burned: 18 (million)
% 0.56/0.42 % (958823)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3802157463:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.56/0.42 % (958823)Instruction limit reached!
% 0.56/0.42 % (958823)------------------------------
% 0.56/0.42 % (958823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958823)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958823)Termination reason: Instruction limit
% 0.56/0.42 % (958823)Termination phase: shuffling
% 0.56/0.42 % (958823)Time elapsed: 0.001 s
% 0.56/0.42 % (958823)Peak memory usage: 10 MB
% 0.56/0.42 % (958823)Instructions burned: 5 (million)
% 0.56/0.42 % (958832)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4096045643:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.56/0.42 % (958828)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1305439674:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.56/0.42 % (958815)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2486663751:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.56/0.42 % (958831)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.56/0.42 % (958828)Instruction limit reached!
% 0.56/0.42 % (958828)------------------------------
% 0.56/0.42 % (958828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958828)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958828)Termination reason: Instruction limit
% 0.56/0.42 % (958828)Termination phase: shuffling
% 0.56/0.42 % (958828)Time elapsed: 0.003 s
% 0.56/0.42 % (958828)Peak memory usage: 10 MB
% 0.56/0.42 % (958828)Instructions burned: 5 (million)
% 0.56/0.42 % (958832)Instruction limit reached!
% 0.56/0.42 % (958832)------------------------------
% 0.56/0.42 % (958832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958832)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958832)Termination reason: Instruction limit
% 0.56/0.42 % (958832)Termination phase: shuffling
% 0.56/0.42 % (958832)Time elapsed: 0.003 s
% 0.56/0.42 % (958832)Peak memory usage: 10 MB
% 0.56/0.42 % (958832)Instructions burned: 13 (million)
% 0.56/0.42 % (958831)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3091709927:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.56/0.42 % (958831)Instruction limit reached!
% 0.56/0.42 % (958831)------------------------------
% 0.56/0.42 % (958831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958831)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958831)Termination reason: Instruction limit
% 0.56/0.42 % (958831)Termination phase: shuffling
% 0.56/0.42 % (958831)Time elapsed: 0.003 s
% 0.56/0.42 % (958831)Peak memory usage: 10 MB
% 0.56/0.42 % (958831)Instructions burned: 7 (million)
% 0.56/0.42 % (958837)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=4198723227:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.56/0.42 % (958820)Instruction limit reached!
% 0.56/0.42 % (958820)------------------------------
% 0.56/0.42 % (958820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958820)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958820)Termination reason: Instruction limit
% 0.56/0.42 % (958820)Termination phase: Property scanning
% 0.56/0.42 % (958820)Time elapsed: 0.036 s
% 0.56/0.42 % (958820)Peak memory usage: 12 MB
% 0.56/0.42 % (958820)Instructions burned: 77 (million)
% 0.56/0.42 % (958836)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
% 0.56/0.42 % (958836)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.56/0.42 % (958836)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=888262649:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.56/0.42 % (958839)lrs+10_1_si=on:cs=on:random_seed=4163991030:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.56/0.42 % (958841)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.56/0.42 % (958837)Instruction limit reached!
% 0.56/0.42 % (958837)------------------------------
% 0.56/0.42 % (958837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958837)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958837)Termination reason: Instruction limit
% 0.56/0.42 % (958837)Termination phase: Property scanning
% 0.56/0.42 % (958837)Time elapsed: 0.019 s
% 0.56/0.42 % (958837)Peak memory usage: 11 MB
% 0.56/0.42 % (958837)Instructions burned: 86 (million)
% 0.56/0.42 % (958841)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=1910699402:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.56/0.42 % (958839)Instruction limit reached!
% 0.56/0.42 % (958839)------------------------------
% 0.56/0.42 % (958839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958839)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958839)Termination reason: Instruction limit
% 0.56/0.42 % (958839)Termination phase: shuffling
% 0.56/0.42 % (958839)Time elapsed: 0.005 s
% 0.56/0.42 % (958839)Peak memory usage: 10 MB
% 0.56/0.42 % (958839)Instructions burned: 10 (million)
% 0.56/0.42 % (958836)Instruction limit reached!
% 0.56/0.42 % (958836)------------------------------
% 0.56/0.42 % (958836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958836)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958836)Termination reason: Instruction limit
% 0.56/0.42 % (958836)Termination phase: shuffling
% 0.56/0.42 % (958836)Time elapsed: 0.014 s
% 0.56/0.42 % (958836)Peak memory usage: 10 MB
% 0.56/0.42 % (958836)Instructions burned: 30 (million)
% 0.56/0.42 % (958841)Instruction limit reached!
% 0.56/0.42 % (958841)------------------------------
% 0.56/0.42 % (958841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958841)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958841)Termination reason: Instruction limit
% 0.56/0.42 % (958841)Termination phase: shuffling
% 0.56/0.42 % (958841)Time elapsed: 0.002 s
% 0.56/0.42 % (958841)Peak memory usage: 10 MB
% 0.56/0.42 % (958841)Instructions burned: 3 (million)
% 0.56/0.42 % (958818) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-958810-958818"...
% 0.56/0.42 % (958818)...printing done.
% 0.56/0.42 % (958818)Refutation found. Thanks to Tanya!
% 0.56/0.42 % SZS status Theorem for theBenchmark
% 0.56/0.42 % SZS output start Proof for theBenchmark
% 0.56/0.42 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.56/0.42 thf(type_def_6, type, stream: $tType > $tType).
% 0.56/0.42 thf(type_def_7, type, set: $tType > $tType).
% 0.56/0.42 thf(type_def_8, type, itself: $tType > $tType).
% 0.56/0.42 thf(type_def_9, type, a: $tType).
% 0.56/0.42 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.56/0.42 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_2, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_3, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_4, type, distrib_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_5, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_6, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_7, type, bounded_lattice_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_8, type, bounde1808546759up_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.56/0.42 thf(func_def_9, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.56/0.42 thf(func_def_10, type, coinductive_lappend: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_11, type, coinductive_lconcat: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_12, type, coindu351974385stinct: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.56/0.42 thf(func_def_13, type, coindu218763757pWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_14, type, coinductive_lfilter: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_15, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.56/0.42 thf(func_def_16, type, coinductive_llast: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_17, type, coinductive_LCons: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_18, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 0.56/0.42 thf(func_def_19, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0))).
% 0.56/0.42 thf(func_def_20, type, coinductive_lhd: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_21, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.56/0.42 thf(func_def_22, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.56/0.42 thf(func_def_23, type, coinductive_ltl: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_24, type, coinductive_lmember: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o))).
% 0.56/0.42 thf(func_def_25, type, coinductive_lsetp: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_26, type, coindu1478340336prefix: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o))).
% 0.56/0.42 thf(func_def_27, type, coindu501562517eWhile: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_28, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1))).
% 0.56/0.42 thf(func_def_29, type, coindu1724414836stream: !>[X0: $tType]:((stream @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_30, type, coindu1183105481stream: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0 > $o))).
% 0.56/0.42 thf(func_def_31, type, coindu2010755910_llist: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0))).
% 0.56/0.42 thf(func_def_32, type, coindu139217191stream: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X0) > X0 > stream @ X1))).
% 0.56/0.42 thf(func_def_33, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_34, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_35, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_36, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_37, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.56/0.42 thf(func_def_38, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.56/0.42 thf(func_def_39, type, disjnt: !>[X0: $tType]:((set @ X0 > set @ X0 > $o))).
% 0.56/0.42 thf(func_def_40, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.56/0.42 thf(func_def_41, type, sinterleave: !>[X0: $tType]:((stream @ X0 > stream @ X0 > stream @ X0))).
% 0.56/0.42 thf(func_def_42, type, smember: !>[X0: $tType]:((X0 > stream @ X0 > $o))).
% 0.56/0.42 thf(func_def_43, type, shd: !>[X0: $tType]:((stream @ X0 > X0))).
% 0.56/0.42 thf(func_def_44, type, sset: !>[X0: $tType]:((stream @ X0 > set @ X0))).
% 0.56/0.42 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.56/0.42 thf(func_def_46, type, x: a).
% 0.56/0.42 thf(func_def_47, type, xs: stream @ a).
% 0.56/0.42 thf(func_def_48, type, xsa: stream @ a).
% 0.56/0.42 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_53, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.56/0.42 thf(func_def_54, type, db2: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_55, type, db1: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.56/0.42 thf(func_def_57, type, vNOT: ($o > $o)).
% 0.56/0.42 thf(func_def_58, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.56/0.42 thf(func_def_59, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.56/0.42 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 0.56/0.42 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.56/0.42 thf(func_def_62, type, db3: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_63, type, db4: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_64, type, sK0: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.56/0.42 thf(func_def_65, type, sK1: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_66, type, sK2: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_67, type, sK3: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_68, type, sK4: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_69, type, sK5: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_70, type, sK6: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_71, type, sK7: !>[X0: $tType]:((set @ X0 > X0))).
% 0.56/0.42 thf(func_def_72, type, sK8: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_73, type, sK9: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_74, type, sK10: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_75, type, sK11: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_76, type, sK12: !>[X0: $tType]:((coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_77, type, sK13: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_78, type, sK14: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_79, type, sK15: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_80, type, sK16: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > X0 > X0))).
% 0.56/0.42 thf(func_def_81, type, sK17: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_82, type, sK18: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_83, type, sK19: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_84, type, sK20: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_85, type, sK21: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_86, type, sK22: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_87, type, sK23: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_88, type, sK24: !>[X0: $tType]:((set @ X0 > X0))).
% 0.56/0.42 thf(func_def_89, type, sK25: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_90, type, sK26: !>[X0: $tType]:(((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_91, type, sK27: !>[X0: $tType]:((set @ X0 > X0))).
% 0.56/0.42 thf(func_def_92, type, sK28: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_93, type, sK29: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_94, type, sK30: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_95, type, sK31: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_96, type, sK32: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_97, type, sK33: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_98, type, sK34: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_99, type, sK35: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_100, type, sK36: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_101, type, sK37: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_102, type, sK38: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_103, type, sK39: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_104, type, sK40: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_105, type, sK41: !>[X0: $tType]:(X0)).
% 0.56/0.42 thf(func_def_106, type, sK42: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_107, type, sK43: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_108, type, sK44: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_109, type, sK45: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_110, type, sK46: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_111, type, sK47: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_112, type, sK48: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_113, type, sK49: !>[X0: $tType]:((coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_114, type, sK50: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_115, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.56/0.42 thf(func_def_116, type, sK52: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_117, type, sK53: !>[X0: $tType]:(((coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_118, type, sK54: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_119, type, sK55: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_120, type, sK56: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_121, type, sK57: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_122, type, sK58: !>[X0: $tType]:((coinductive_llist @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_123, type, sK59: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_124, type, sK60: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_125, type, sK61: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_126, type, sK62: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_127, type, sK63: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_128, type, sK64: !>[X0: $tType]:(((coinductive_llist @ X0 > X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_129, type, sK65: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_130, type, sK66: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > X0))).
% 0.56/0.42 thf(func_def_131, type, sK67: !>[X0: $tType]:((coinductive_llist @ X0 > X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_132, type, sK68: !>[X0: $tType]:(((X0 > $o) > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_133, type, sK69: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_134, type, sK70: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_135, type, sK71: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_136, type, sK72: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_137, type, sK73: !>[X0: $tType]:(((X0 > coinductive_llist @ X0 > $o) > X0))).
% 0.56/0.42 thf(func_def_138, type, sK74: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_139, type, sK75: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.56/0.42 thf(func_def_140, type, sK76: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_141, type, sK77: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_142, type, sK78: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > X0))).
% 0.56/0.42 thf(func_def_143, type, sK79: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_144, type, sK80: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > coinductive_llist @ X0))).
% 0.56/0.42 thf(func_def_146, type, inv_coindu1724414836stream_82: !>[X0: $tType]:((coinductive_llist @ X0 > stream @ X0))).
% 0.56/0.42 thf(f1,axiom,(
% 0.56/0.42 ~(coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa)) => (member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060not_062_Alnull_A_Illist__of__stream_Axs_J_A_092_060Longrightarrow_062_Alhd_A_Illist__of__stream_Axs_J_A_092_060in_062_Alset_A_Illist__of__stream_Axs_J_092_060close_062)).
% 0.56/0.42 thf(f3,axiom,(
% 0.56/0.42 ! [X0 : $tType,X1 : stream @ X0] : (((coinductive_lhd @ X0 @ (coindu1724414836stream @ X0 @ X1))) = ((shd @ X0 @ X1)))),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_lhd__llist__of__stream)).
% 0.56/0.42 thf(f4,axiom,(
% 0.56/0.42 ! [X0 : $tType,X1 : stream @ X0] : ~(coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_lnull__llist__of__stream)).
% 0.56/0.42 thf(f282,conjecture,(
% 0.56/0.42 (member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.56/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.56/0.42 thf(f283,negated_conjecture,(
% 0.56/0.42 ~(member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.56/0.42 inference(negated_conjecture,[status(cth)],[f282])).
% 0.56/0.42 thf(f374,plain,(
% 0.56/0.42 ! [X0 : $tType,X1 : stream @ X0] : ~(coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))),
% 0.56/0.42 inference(rectify,[],[f4])).
% 0.56/0.42 thf(f375,plain,(
% 0.56/0.42 ! [X0 : $tType,X1 : stream @ X0] : ~ (((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) = $true)),
% 0.56/0.42 inference(fool_elimination,[],[f374])).
% 0.56/0.42 thf(f630,plain,(
% 0.56/0.42 ~(coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa)) => (member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.56/0.42 inference(rectify,[],[f1])).
% 0.56/0.42 thf(f631,plain,(
% 0.56/0.42 ~ (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true) => (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 inference(fool_elimination,[],[f630])).
% 0.56/0.42 thf(f671,plain,(
% 0.56/0.42 ~(member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))),
% 0.56/0.42 inference(rectify,[],[f283])).
% 0.56/0.42 thf(f672,plain,(
% 0.56/0.42 ~ (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 inference(fool_elimination,[],[f671])).
% 0.56/0.42 thf(f748,plain,(
% 0.56/0.42 ! [X0 : $tType,X1 : stream @ X0] : (((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) != $true)),
% 0.56/0.42 inference(flattening,[],[f375])).
% 0.56/0.42 thf(f818,plain,(
% 0.56/0.42 (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) != $true) => (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 inference(flattening,[],[f631])).
% 0.56/0.42 thf(f831,plain,(
% 0.56/0.42 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) != $true)),
% 0.56/0.42 inference(flattening,[],[f672])).
% 0.56/0.42 thf(f924,plain,(
% 0.56/0.42 (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true) | (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 inference(ennf_transformation,[],[f818])).
% 0.56/0.42 thf(f1376,plain,(
% 0.56/0.42 ( ! [X0 : $tType,X1 : stream @ X0] : ((((coinductive_lnull @ X0 @ (coindu1724414836stream @ X0 @ X1))) != $true)) )),
% 0.56/0.42 inference(cnf_transformation,[],[f748])).
% 0.56/0.42 thf(f1506,plain,(
% 0.56/0.42 ( ! [X0 : $tType,X1 : stream @ X0] : ((((coinductive_lhd @ X0 @ (coindu1724414836stream @ X0 @ X1))) = ((shd @ X0 @ X1)))) )),
% 0.56/0.42 inference(cnf_transformation,[],[f3])).
% 0.56/0.42 thf(f1644,plain,(
% 0.56/0.42 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) != $true)),
% 0.56/0.42 inference(cnf_transformation,[],[f831])).
% 0.56/0.42 thf(f1679,plain,(
% 0.56/0.42 (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true) | (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 inference(cnf_transformation,[],[f924])).
% 0.56/0.42 thf(f1794,definition,(
% 0.56/0.42 spl81_3 <=> (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true)),
% 0.56/0.42 introduced(definition,[new_symbols(definition,[spl81_3])],[avatar_definition])).
% 0.56/0.42 thf(f1796,plain,(
% 0.56/0.42 (((coinductive_lnull @ a @ (coindu1724414836stream @ a @ xsa))) = $true) | ~spl81_3),
% 0.56/0.42 inference(avatar_component_clause,[],[f1794])).
% 0.56/0.42 thf(f1798,definition,(
% 0.56/0.42 spl81_4 <=> (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 introduced(definition,[new_symbols(definition,[spl81_4])],[avatar_definition])).
% 0.56/0.42 thf(f1800,plain,(
% 0.56/0.42 (((member @ a @ (coinductive_lhd @ a @ (coindu1724414836stream @ a @ xsa)) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true) | ~spl81_4),
% 0.56/0.42 inference(avatar_component_clause,[],[f1798])).
% 0.56/0.42 thf(f1801,plain,(
% 0.56/0.42 spl81_3 | spl81_4),
% 0.56/0.42 inference(avatar_split_clause,[],[f1679,f1798,f1794])).
% 0.56/0.42 thf(f1823,definition,(
% 0.56/0.42 spl81_9 <=> (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true)),
% 0.56/0.42 introduced(definition,[new_symbols(definition,[spl81_9])],[avatar_definition])).
% 0.56/0.42 thf(f1825,plain,(
% 0.56/0.42 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) != $true) | spl81_9),
% 0.56/0.42 inference(avatar_component_clause,[],[f1823])).
% 0.56/0.42 thf(f1826,plain,(
% 0.56/0.42 ~spl81_9),
% 0.56/0.42 inference(avatar_split_clause,[],[f1644,f1823])).
% 0.56/0.42 thf(f1856,plain,(
% 0.56/0.42 (((member @ a @ (shd @ a @ xsa) @ (coinductive_lset @ a @ (coindu1724414836stream @ a @ xsa)))) = $true) | ~spl81_4),
% 0.56/0.42 inference(superposition,[],[f1800,f1506])).
% 0.56/0.42 thf(f1857,plain,(
% 0.56/0.42 $false | (~spl81_4 | spl81_9)),
% 0.56/0.42 inference(forward_subsumption_resolution,[],[f1856,f1825])).
% 0.56/0.42 thf(f1858,plain,(
% 0.56/0.42 ~spl81_4 | spl81_9),
% 0.56/0.42 inference(avatar_contradiction_clause,[],[f1857])).
% 0.56/0.42 thf(f1865,plain,(
% 0.56/0.42 ($true != $true) | ~spl81_3),
% 0.56/0.42 inference(superposition,[],[f1376,f1796])).
% 0.56/0.42 thf(f1866,plain,(
% 0.56/0.42 $false | ~spl81_3),
% 0.56/0.42 inference(trivial_inequality_removal,[],[f1865])).
% 0.56/0.42 thf(f1867,plain,(
% 0.56/0.42 ~spl81_3),
% 0.56/0.42 inference(avatar_contradiction_clause,[],[f1866])).
% 0.56/0.42 cnf(s3, plain, spl81_3 | spl81_4, inference(sat_conversion,[],[f1801])).
% 0.56/0.42 cnf(s8, plain, ~spl81_9, inference(sat_conversion,[],[f1826])).
% 0.56/0.42 cnf(s12, plain, ~spl81_4 | spl81_9, inference(sat_conversion,[],[f1858])).
% 0.56/0.42 cnf(s13, plain, ~spl81_3, inference(sat_conversion,[],[f1867])).
% 0.56/0.42 cnf(s14, plain, ~spl81_4, inference(rat,[],[s12,s8])).
% 0.56/0.42 cnf(s15, plain, $false, inference(rat,[],[s3,s14,s13])).
% 0.56/0.42 thf(f1868,plain,(
% 0.56/0.42 $false),
% 0.56/0.42 inference(avatar_sat_refutation,[],[s15])).
% 0.56/0.42 % SZS output end Proof for theBenchmark
% 0.56/0.42 % (958818)------------------------------
% 0.56/0.42 % (958818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.42 % (958818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.42 % (958818)CaDiCaL version: 2.1.3
% 0.56/0.42 % (958818)Termination reason: Refutation
% 0.56/0.42 % (958818)Time elapsed: 0.063 s
% 0.56/0.42 % (958818)Peak memory usage: 14 MB
% 0.56/0.42 % (958818)Instructions burned: 127 (million)
% 0.56/0.42 % (958810)Success in time 0.121 s
% 0.56/0.42 % Vampire exiting
%------------------------------------------------------------------------------