%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT129^1 : 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 07:48:23 AM UTC 2026
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT129^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n007.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:56:41 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 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
% 0.21/0.38 % (3722984)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.38 % (3722992)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=2027233101: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)
% 0.21/0.38 % (3722989)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=295396538:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.38 % (3722991)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2210922144:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (3722991)Instruction limit reached!
% 0.21/0.38 % (3722991)------------------------------
% 0.21/0.38 % (3722991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (3722991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (3722991)CaDiCaL version: 2.1.3
% 0.21/0.38 % (3722991)Termination reason: Instruction limit
% 0.21/0.38 % (3722991)Termination phase: shuffling
% 0.21/0.38 % (3722991)Time elapsed: 0.003 s
% 0.21/0.38 % (3722991)Peak memory usage: 10 MB
% 0.21/0.38 % (3722991)Instructions burned: 5 (million)
% 0.21/0.38 % (3722993)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2227738883:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.38 % (3722995)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.38 % (3722995)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
% 0.21/0.38 % (3722994)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2123762057:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.38 % (3722995)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=191427875:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.38 % (3722990)lrs+10_16_si=on:nwc=1.5:random_seed=1529177004:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (3722993)Instruction limit reached!
% 0.21/0.38 % (3722993)------------------------------
% 0.21/0.38 % (3722993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (3722993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (3722993)CaDiCaL version: 2.1.3
% 0.21/0.38 % (3722993)Termination reason: Instruction limit
% 0.21/0.38 % (3722993)Termination phase: shuffling
% 0.21/0.38 % (3722993)Time elapsed: 0.011 s
% 0.21/0.38 % (3722993)Peak memory usage: 11 MB
% 0.21/0.38 % (3722993)Instructions burned: 24 (million)
% 0.21/0.38 % (3722999)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4176240688:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (3722999)Instruction limit reached!
% 0.21/0.38 % (3722999)------------------------------
% 0.21/0.38 % (3722999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (3722999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (3722999)CaDiCaL version: 2.1.3
% 0.21/0.38 % (3722999)Termination reason: Instruction limit
% 0.21/0.38 % (3722999)Termination phase: shuffling
% 0.21/0.38 % (3722999)Time elapsed: 0.003 s
% 0.21/0.38 % (3722999)Peak memory usage: 10 MB
% 0.21/0.38 % (3722999)Instructions burned: 5 (million)
% 0.21/0.38 % (3723004)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3186039945:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.38 % (3722990)Instruction limit reached!
% 0.21/0.38 % (3722990)------------------------------
% 0.21/0.38 % (3722990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (3722990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (3722990)CaDiCaL version: 2.1.3
% 0.21/0.38 % (3722990)Termination reason: Instruction limit
% 0.21/0.38 % (3722990)Termination phase: Property scanning
% 0.21/0.38 % (3722990)Time elapsed: 0.020 s
% 0.21/0.38 % (3722990)Peak memory usage: 10 MB
% 0.21/0.38 % (3722990)Instructions burned: 19 (million)
% 0.21/0.38 % (3722992) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3722984-3722992"...
% 0.21/0.38 % (3723004)Instruction limit reached!
% 0.21/0.38 % (3723004)------------------------------
% 0.21/0.38 % (3723004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (3723004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (3723004)CaDiCaL version: 2.1.3
% 0.21/0.38 % (3723004)Termination reason: Instruction limit
% 0.21/0.38 % (3723004)Termination phase: shuffling
% 0.21/0.38 % (3723004)Time elapsed: 0.003 s
% 0.21/0.38 % (3723004)Peak memory usage: 10 MB
% 0.21/0.38 % (3723004)Instructions burned: 5 (million)
% 0.21/0.38 % (3722992)...printing done.
% 0.21/0.38 % (3722992)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.21/0.38 thf(type_def_6, type, extended_enat: $tType).
% 0.21/0.38 thf(type_def_7, type, nat: $tType).
% 0.21/0.38 thf(type_def_8, type, itself: $tType > $tType).
% 0.21/0.38 thf(type_def_9, type, a: $tType).
% 0.21/0.39 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.39 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_2, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_3, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_5, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_6, type, monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_7, type, ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_8, type, comm_monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_9, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_10, type, comm_monoid_diff: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_11, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_12, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_13, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_14, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_17, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_19, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_20, type, ordere223160158up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_21, type, strict2144017051up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_22, type, ordere516151231imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.21/0.39 thf(func_def_23, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.21/0.39 thf(func_def_24, type, coindu191418589_ldrop: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.21/0.39 thf(func_def_25, type, coindu531130065ldropn: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.21/0.39 thf(func_def_26, type, coindu2000965700_llast: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.21/0.39 thf(func_def_27, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 0.21/0.39 thf(func_def_28, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.21/0.39 thf(func_def_29, type, coindu749330388e_lnth: !>[X0: $tType]:((coindu1593790203_llist @ X0 > nat > X0))).
% 0.21/0.39 thf(func_def_30, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.21/0.39 thf(func_def_31, type, extended_enat2: (nat > extended_enat)).
% 0.21/0.39 thf(func_def_32, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.21/0.39 thf(func_def_33, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.21/0.39 thf(func_def_34, type, extended_size_enat: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_35, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(func_def_36, type, extended_the_enat: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_37, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.39 thf(func_def_38, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.39 thf(func_def_39, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(func_def_40, type, suc: (nat > nat)).
% 0.21/0.39 thf(func_def_41, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.21/0.39 thf(func_def_42, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.39 thf(func_def_43, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.21/0.39 thf(func_def_44, type, n: extended_enat).
% 0.21/0.39 thf(func_def_45, type, n2: nat).
% 0.21/0.39 thf(func_def_46, type, n_a: nat).
% 0.21/0.39 thf(func_def_47, type, xs: coindu1593790203_llist @ a).
% 0.21/0.39 thf(func_def_48, type, xsa: coindu1593790203_llist @ a).
% 0.21/0.39 thf(func_def_52, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.39 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(func_def_54, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(func_def_55, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.39 thf(func_def_56, type, vOR: ($o > $o > $o)).
% 0.21/0.39 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(func_def_58, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.39 thf(func_def_59, type, sP0: (extended_enat > extended_enat > extended_enat > $o)).
% 0.21/0.39 thf(func_def_60, type, sP1: (extended_enat > extended_enat > extended_enat > $o)).
% 0.21/0.39 thf(func_def_61, type, sP2: (extended_enat > extended_enat > extended_enat > $o)).
% 0.21/0.39 thf(func_def_62, type, sP3: (extended_enat > extended_enat > extended_enat > $o)).
% 0.21/0.39 thf(func_def_63, type, sP4: (extended_enat > extended_enat > extended_enat > $o)).
% 0.21/0.39 thf(func_def_64, type, sP5: (extended_enat > extended_enat > extended_enat > $o)).
% 0.21/0.39 thf(func_def_65, type, sK6: ((nat > $o) > nat)).
% 0.21/0.39 thf(func_def_66, type, sK7: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_67, type, sK8: (extended_enat > nat > nat)).
% 0.21/0.39 thf(func_def_68, type, sK9: (nat > nat)).
% 0.21/0.39 thf(func_def_69, type, sK10: (nat > nat)).
% 0.21/0.39 thf(func_def_70, type, sK11: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.21/0.39 thf(func_def_71, type, sK12: ((nat > $o) > nat)).
% 0.21/0.39 thf(func_def_72, type, sK13: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.39 thf(func_def_73, type, sK14: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.21/0.39 thf(func_def_74, type, sK15: !>[X0: $tType]:(((nat > X0) > nat))).
% 0.21/0.39 thf(func_def_75, type, sK16: (nat > nat > nat)).
% 0.21/0.39 thf(func_def_76, type, sK17: ((nat > $o) > nat)).
% 0.21/0.39 thf(func_def_77, type, sK18: ((nat > $o) > nat)).
% 0.21/0.39 thf(func_def_78, type, sK19: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_79, type, sK20: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_80, type, sK21: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_81, type, sK22: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_82, type, sK23: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_83, type, sK24: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_84, type, sK25: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_85, type, sK26: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_86, type, sK27: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_87, type, sK28: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_88, type, sK29: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_89, type, sK30: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_90, type, sK31: ((nat > $o) > nat)).
% 0.21/0.39 thf(func_def_91, type, sK32: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.21/0.39 thf(func_def_92, type, sK33: (nat > nat > nat)).
% 0.21/0.39 thf(func_def_93, type, sK34: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.39 thf(func_def_94, type, sK35: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.39 thf(func_def_95, type, sK36: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.39 thf(func_def_96, type, sK37: (nat > nat)).
% 0.21/0.39 thf(func_def_97, type, sK38: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_98, type, sK39: ((extended_enat > $o) > extended_enat)).
% 0.21/0.39 thf(func_def_99, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.21/0.39 thf(func_def_100, type, sK41: (extended_enat > nat)).
% 0.21/0.39 thf(func_def_101, type, sK42: !>[X0: $tType]:((nat > (X0 > extended_enat) > X0))).
% 0.21/0.39 thf(func_def_102, type, sK43: !>[X0: $tType]:(((X0 > extended_enat) > X0))).
% 0.21/0.39 thf(func_def_103, type, sK44: ((nat > $o) > nat)).
% 0.65/0.39 thf(func_def_104, type, sK45: ((extended_enat > $o) > nat)).
% 0.65/0.39 thf(func_def_105, type, sK46: (extended_enat > nat)).
% 0.65/0.39 thf(func_def_106, type, sK47: (extended_enat > nat)).
% 0.65/0.39 thf(func_def_107, type, sK48: (extended_enat > nat)).
% 0.65/0.39 thf(func_def_108, type, sK49: (extended_enat > nat)).
% 0.65/0.39 thf(func_def_109, type, sK50: (nat > nat)).
% 0.65/0.39 thf(func_def_110, type, sK51: (nat > nat > nat)).
% 0.65/0.39 thf(func_def_111, type, sK52: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_112, type, sK53: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_113, type, sK54: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_114, type, sK55: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_115, type, sK56: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_116, type, sK57: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_117, type, sK58: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_118, type, sK59: ((nat > nat > $o) > nat)).
% 0.65/0.39 thf(func_def_119, type, sK60: (nat > nat > nat)).
% 0.65/0.39 thf(func_def_120, type, sK61: nat).
% 0.65/0.39 thf(func_def_121, type, sK62: ((nat > $o) > nat)).
% 0.65/0.39 thf(func_def_122, type, sK63: (nat > (nat > $o) > nat)).
% 0.65/0.39 thf(func_def_123, type, sK64: (nat > (nat > $o) > nat)).
% 0.65/0.39 thf(func_def_124, type, sK65: ((nat > $o) > nat)).
% 0.65/0.39 thf(func_def_125, type, sK66: (extended_enat > nat)).
% 0.65/0.39 thf(func_def_126, type, sK67: (extended_enat > nat)).
% 0.65/0.39 thf(func_def_127, type, vNOT: ($o > $o)).
% 0.65/0.39 thf(func_def_129, type, inv_suc_69: (nat > nat)).
% 0.65/0.39 thf(func_def_130, type, inv_extended_enat2_70: (extended_enat > nat)).
% 0.65/0.39 thf(f3,axiom,(
% 0.65/0.39 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))),
% 0.65/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Suc_Oprems)).
% 0.65/0.39 thf(f11,axiom,(
% 0.65/0.39 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : nat] : (((coindu191418589_ldrop @ X0 @ (extended_enat2 @ X1) @ X2)) = ((coindu531130065ldropn @ X0 @ X1 @ X2)))),
% 0.65/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_ldrop__enat)).
% 0.65/0.39 thf(f21,axiom,(
% 0.65/0.39 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2)) => (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))))),
% 0.65/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_llast__ldropn)).
% 0.65/0.39 thf(f283,conjecture,(
% 0.65/0.39 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) = ((coindu2000965700_llast @ a @ xsa)))),
% 0.65/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.65/0.39 thf(f284,negated_conjecture,(
% 0.65/0.39 ~ (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) = ((coindu2000965700_llast @ a @ xsa)))),
% 0.65/0.39 inference(negated_conjecture,[status(cth)],[f283])).
% 0.65/0.39 thf(f403,plain,(
% 0.65/0.39 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2)) => (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))))),
% 0.65/0.39 inference(rectify,[],[f21])).
% 0.65/0.39 thf(f404,plain,(
% 0.65/0.39 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : nat] : ((((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2))) = $true) => (((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))))),
% 0.65/0.39 inference(fool_elimination,[],[f403])).
% 0.65/0.39 thf(f624,plain,(
% 0.65/0.39 (ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))),
% 0.65/0.39 inference(rectify,[],[f3])).
% 0.65/0.39 thf(f625,plain,(
% 0.65/0.39 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) = $true)),
% 0.65/0.39 inference(fool_elimination,[],[f624])).
% 0.65/0.39 thf(f730,plain,(
% 0.65/0.39 ! [X0 : $tType,X2 : nat,X1 : coindu1593790203_llist @ X0] : (((coindu531130065ldropn @ X0 @ X2 @ X1)) = ((coindu191418589_ldrop @ X0 @ (extended_enat2 @ X2) @ X1)))),
% 0.65/0.39 inference(rectify,[],[f11])).
% 0.65/0.39 thf(f740,plain,(
% 0.65/0.39 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) != ((coindu2000965700_llast @ a @ xsa)))),
% 0.65/0.39 inference(flattening,[],[f284])).
% 0.65/0.39 thf(f897,plain,(
% 0.65/0.39 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : ((((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))) | (((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2))) != $true))),
% 0.65/0.39 inference(ennf_transformation,[],[f404])).
% 0.65/0.39 thf(f1142,plain,(
% 0.65/0.39 ! [X0 : $tType,X1 : nat,X2 : coindu1593790203_llist @ X0] : (((coindu191418589_ldrop @ X0 @ (extended_enat2 @ X1) @ X2)) = ((coindu531130065ldropn @ X0 @ X1 @ X2)))),
% 0.65/0.39 inference(rectify,[],[f730])).
% 0.65/0.39 thf(f1402,plain,(
% 0.65/0.39 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) != ((coindu2000965700_llast @ a @ xsa)))),
% 0.65/0.39 inference(cnf_transformation,[],[f740])).
% 0.65/0.39 thf(f1428,plain,(
% 0.65/0.39 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : nat] : ((((coindu2000965700_llast @ X0 @ (coindu531130065ldropn @ X0 @ X1 @ X2))) = ((coindu2000965700_llast @ X0 @ X2))) | (((ord_less @ extended_enat @ (extended_enat2 @ X1) @ (coindu1018505716length @ X0 @ X2))) != $true)) )),
% 0.65/0.39 inference(cnf_transformation,[],[f897])).
% 0.65/0.39 thf(f1476,plain,(
% 0.65/0.39 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) = $true)),
% 0.65/0.39 inference(cnf_transformation,[],[f625])).
% 0.65/0.39 thf(f1546,plain,(
% 0.65/0.39 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : nat] : ((((coindu191418589_ldrop @ X0 @ (extended_enat2 @ X1) @ X2)) = ((coindu531130065ldropn @ X0 @ X1 @ X2)))) )),
% 0.65/0.39 inference(cnf_transformation,[],[f1142])).
% 0.65/0.39 thf(f1789,definition,(
% 0.65/0.39 spl68_27 <=> (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) = $true)),
% 0.65/0.39 introduced(definition,[new_symbols(definition,[spl68_27])],[avatar_definition])).
% 0.65/0.39 thf(f1791,plain,(
% 0.65/0.39 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) = $true) | ~spl68_27),
% 0.65/0.39 inference(avatar_component_clause,[],[f1789])).
% 0.65/0.39 thf(f1792,plain,(
% 0.65/0.39 spl68_27),
% 0.65/0.39 inference(avatar_split_clause,[],[f1476,f1789])).
% 0.65/0.39 thf(f1810,definition,(
% 0.65/0.39 spl68_31 <=> (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) = ((coindu2000965700_llast @ a @ xsa)))),
% 0.65/0.39 introduced(definition,[new_symbols(definition,[spl68_31])],[avatar_definition])).
% 0.65/0.39 thf(f1812,plain,(
% 0.65/0.39 (((coindu2000965700_llast @ a @ (coindu191418589_ldrop @ a @ (extended_enat2 @ (suc @ n_a)) @ xsa))) != ((coindu2000965700_llast @ a @ xsa))) | spl68_31),
% 0.65/0.39 inference(avatar_component_clause,[],[f1810])).
% 0.65/0.39 thf(f1813,plain,(
% 0.65/0.39 ~spl68_31),
% 0.65/0.39 inference(avatar_split_clause,[],[f1402,f1810])).
% 0.65/0.39 thf(f2264,plain,(
% 0.65/0.39 (((coindu2000965700_llast @ a @ xsa)) != ((coindu2000965700_llast @ a @ (coindu531130065ldropn @ a @ (suc @ n_a) @ xsa)))) | spl68_31),
% 0.65/0.39 inference(superposition,[],[f1812,f1546])).
% 0.65/0.39 thf(f2268,definition,(
% 0.65/0.39 spl68_68 <=> (((coindu2000965700_llast @ a @ xsa)) = ((coindu2000965700_llast @ a @ (coindu531130065ldropn @ a @ (suc @ n_a) @ xsa))))),
% 0.65/0.39 introduced(definition,[new_symbols(definition,[spl68_68])],[avatar_definition])).
% 0.65/0.39 thf(f2270,plain,(
% 0.65/0.39 (((coindu2000965700_llast @ a @ xsa)) != ((coindu2000965700_llast @ a @ (coindu531130065ldropn @ a @ (suc @ n_a) @ xsa)))) | spl68_68),
% 0.65/0.39 inference(avatar_component_clause,[],[f2268])).
% 0.65/0.39 thf(f2271,plain,(
% 0.65/0.39 ~spl68_68 | spl68_31),
% 0.65/0.39 inference(avatar_split_clause,[],[f2264,f1810,f2268])).
% 0.65/0.39 thf(f2543,plain,(
% 0.65/0.39 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) != $true) | (((coindu2000965700_llast @ a @ xsa)) != ((coindu2000965700_llast @ a @ xsa))) | spl68_68),
% 0.65/0.39 inference(superposition,[],[f2270,f1428])).
% 0.65/0.39 thf(f2544,plain,(
% 0.65/0.39 (((ord_less @ extended_enat @ (extended_enat2 @ (suc @ n_a)) @ (coindu1018505716length @ a @ xsa))) != $true) | spl68_68),
% 0.65/0.39 inference(trivial_inequality_removal,[],[f2543])).
% 0.65/0.39 thf(f2545,plain,(
% 0.65/0.39 $false | (~spl68_27 | spl68_68)),
% 0.65/0.39 inference(forward_subsumption_resolution,[],[f2544,f1791])).
% 0.65/0.39 thf(f2546,plain,(
% 0.65/0.39 ~spl68_27 | spl68_68),
% 0.65/0.39 inference(avatar_contradiction_clause,[],[f2545])).
% 0.65/0.39 cnf(s23, plain, spl68_27, inference(sat_conversion,[],[f1792])).
% 0.65/0.39 cnf(s28, plain, ~spl68_31, inference(sat_conversion,[],[f1813])).
% 0.65/0.39 cnf(s75, plain, spl68_31 | ~spl68_68, inference(sat_conversion,[],[f2271])).
% 0.65/0.39 cnf(s77, plain, ~spl68_27 | spl68_68, inference(sat_conversion,[],[f2546])).
% 0.65/0.39 cnf(s78, plain, ~spl68_68, inference(rat,[],[s75,s28])).
% 0.65/0.39 cnf(s80, plain, ~spl68_27, inference(rat,[],[s77,s78])).
% 0.65/0.39 cnf(s87, plain, $false, inference(rat,[],[s23,s80])).
% 0.65/0.39 thf(f2547,plain,(
% 0.65/0.39 $false),
% 0.65/0.39 inference(avatar_sat_refutation,[],[s87])).
% 0.65/0.39 % SZS output end Proof for theBenchmark
% 0.65/0.39 % (3722992)------------------------------
% 0.65/0.39 % (3722992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.39 % (3722992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.39 % (3722992)CaDiCaL version: 2.1.3
% 0.65/0.39 % (3722992)Termination reason: Refutation
% 0.65/0.39 % (3722992)Time elapsed: 0.046 s
% 0.65/0.39 % (3722992)Peak memory usage: 15 MB
% 0.65/0.39 % (3722992)Instructions burned: 160 (million)
% 0.65/0.39 % (3722984)Success in time 0.089 s
% 0.65/0.39 % Vampire exiting
%------------------------------------------------------------------------------