%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT121^1 : 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 07:48:22 AM UTC 2026
% Result : Theorem 0.58s 0.42s
% Output : Refutation 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT121^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:56:26 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.22/0.27 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
% 0.58/0.42 % (3722509)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.58/0.42 % (3722516)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=668718960:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.58/0.42 % (3722516)Instruction limit reached!
% 0.58/0.42 % (3722516)------------------------------
% 0.58/0.42 % (3722516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722516)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722516)Termination reason: Instruction limit
% 0.58/0.42 % (3722516)Termination phase: shuffling
% 0.58/0.42 % (3722516)Time elapsed: 0.001 s
% 0.58/0.42 % (3722516)Peak memory usage: 10 MB
% 0.58/0.42 % (3722516)Instructions burned: 4 (million)
% 0.58/0.42 % (3722514)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1316065918:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.58/0.42 % (3722515)lrs+10_16_si=on:nwc=1.5:random_seed=397595441:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.58/0.42 % (3722522)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4263226188:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.58/0.42 % (3722522)Instruction limit reached!
% 0.58/0.42 % (3722522)------------------------------
% 0.58/0.42 % (3722522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722522)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722522)Termination reason: Instruction limit
% 0.58/0.42 % (3722522)Termination phase: shuffling
% 0.58/0.42 % (3722522)Time elapsed: 0.001 s
% 0.58/0.42 % (3722522)Peak memory usage: 10 MB
% 0.58/0.42 % (3722522)Instructions burned: 2 (million)
% 0.58/0.42 % (3722517)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=1571150246: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)
% 0.58/0.42 % (3722515)Instruction limit reached!
% 0.58/0.42 % (3722515)------------------------------
% 0.58/0.42 % (3722515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722515)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722515)Termination reason: Instruction limit
% 0.58/0.42 % (3722515)Termination phase: Property scanning
% 0.58/0.42 % (3722515)Time elapsed: 0.014 s
% 0.58/0.42 % (3722515)Peak memory usage: 10 MB
% 0.58/0.42 % (3722515)Instructions burned: 20 (million)
% 0.58/0.42 % (3722526)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3659110548:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.58/0.42 % (3722526)Instruction limit reached!
% 0.58/0.42 % (3722526)------------------------------
% 0.58/0.42 % (3722526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722526)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722526)Termination reason: Instruction limit
% 0.58/0.42 % (3722526)Termination phase: shuffling
% 0.58/0.42 % (3722526)Time elapsed: 0.002 s
% 0.58/0.42 % (3722526)Peak memory usage: 10 MB
% 0.58/0.42 % (3722526)Instructions burned: 8 (million)
% 0.58/0.42 % (3722520)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.58/0.42 % (3722520)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
% 0.58/0.42 % (3722530)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4005845872:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.58/0.42 % (3722530)Instruction limit reached!
% 0.58/0.42 % (3722530)------------------------------
% 0.58/0.42 % (3722530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722530)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722530)Termination reason: Instruction limit
% 0.58/0.42 % (3722530)Termination phase: shuffling
% 0.58/0.42 % (3722530)Time elapsed: 0.003 s
% 0.58/0.42 % (3722530)Peak memory usage: 10 MB
% 0.58/0.42 % (3722530)Instructions burned: 13 (million)
% 0.58/0.42 % (3722520)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=9377456:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.58/0.42 % (3722518)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4071386961:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.58/0.42 % (3722514)Instruction limit reached!
% 0.58/0.42 % (3722514)------------------------------
% 0.58/0.42 % (3722514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722514)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722514)Termination reason: Instruction limit
% 0.58/0.42 % (3722514)Termination phase: Saturation
% 0.58/0.42 % (3722514)Time elapsed: 0.043 s
% 0.58/0.42 % (3722514)Peak memory usage: 13 MB
% 0.58/0.42 % (3722514)Instructions burned: 88 (million)
% 0.58/0.42 % (3722519)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1458070838:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.58/0.42 % (3722532)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
% 0.58/0.42 % (3722532)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.42 % (3722528)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.58/0.42 % (3722532)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2127416853:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.58/0.42 % (3722532)Instruction limit reached!
% 0.58/0.42 % (3722532)------------------------------
% 0.58/0.42 % (3722532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722532)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722532)Termination reason: Instruction limit
% 0.58/0.42 % (3722532)Termination phase: Property scanning
% 0.58/0.42 % (3722532)Time elapsed: 0.008 s
% 0.58/0.42 % (3722532)Peak memory usage: 10 MB
% 0.58/0.42 % (3722532)Instructions burned: 32 (million)
% 0.58/0.42 % (3722528)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2539368548:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.58/0.42 % (3722536)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=73484442:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.58/0.42 % (3722528)Instruction limit reached!
% 0.58/0.42 % (3722528)------------------------------
% 0.58/0.42 % (3722528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722528)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722528)Termination reason: Instruction limit
% 0.58/0.42 % (3722528)Termination phase: shuffling
% 0.58/0.42 % (3722528)Time elapsed: 0.008 s
% 0.58/0.42 % (3722528)Peak memory usage: 10 MB
% 0.58/0.42 % (3722528)Instructions burned: 7 (million)
% 0.58/0.42 % (3722538)lrs+10_1_si=on:cs=on:random_seed=3312455493:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.58/0.42 % (3722538)Instruction limit reached!
% 0.58/0.42 % (3722538)------------------------------
% 0.58/0.42 % (3722538)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722538)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722538)Termination reason: Instruction limit
% 0.58/0.42 % (3722538)Termination phase: shuffling
% 0.58/0.42 % (3722538)Time elapsed: 0.002 s
% 0.58/0.42 % (3722538)Peak memory usage: 10 MB
% 0.58/0.42 % (3722538)Instructions burned: 9 (million)
% 0.58/0.42 % (3722518)Instruction limit reached!
% 0.58/0.42 % (3722518)------------------------------
% 0.58/0.42 % (3722518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722518)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722518)Termination reason: Instruction limit
% 0.58/0.42 % (3722518)Termination phase: Preprocessing 1
% 0.58/0.42 % (3722518)Time elapsed: 0.030 s
% 0.58/0.42 % (3722518)Peak memory usage: 10 MB
% 0.58/0.42 % (3722518)Instructions burned: 24 (million)
% 0.58/0.42 % (3722543)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1587908418:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.58/0.42 % (3722542)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.58/0.42 % (3722542)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=951650281:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.58/0.42 % (3722517) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3722509-3722517"...
% 0.58/0.42 % (3722543)Instruction limit reached!
% 0.58/0.42 % (3722543)------------------------------
% 0.58/0.42 % (3722543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722543)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722543)Termination reason: Instruction limit
% 0.58/0.42 % (3722543)Termination phase: Saturation
% 0.58/0.42 % (3722543)Time elapsed: 0.010 s
% 0.58/0.42 % (3722543)Peak memory usage: 12 MB
% 0.58/0.42 % (3722543)Instructions burned: 41 (million)
% 0.58/0.42 % (3722542)Instruction limit reached!
% 0.58/0.42 % (3722542)------------------------------
% 0.58/0.42 % (3722542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722542)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722542)Termination reason: Instruction limit
% 0.58/0.42 % (3722542)Termination phase: shuffling
% 0.58/0.42 % (3722542)Time elapsed: 0.003 s
% 0.58/0.42 % (3722542)Peak memory usage: 10 MB
% 0.58/0.42 % (3722542)Instructions burned: 6 (million)
% 0.58/0.42 % (3722517)...printing done.
% 0.58/0.42 % (3722517)Refutation found. Thanks to Tanya!
% 0.58/0.42 % SZS status Theorem for theBenchmark
% 0.58/0.42 % SZS output start Proof for theBenchmark
% 0.58/0.42 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.58/0.42 thf(type_def_6, type, code_natural: $tType).
% 0.58/0.42 thf(type_def_7, type, extended_enat: $tType).
% 0.58/0.42 thf(type_def_8, type, real: $tType).
% 0.58/0.42 thf(type_def_9, type, num: $tType).
% 0.58/0.42 thf(type_def_10, type, nat: $tType).
% 0.58/0.42 thf(type_def_11, type, int: $tType).
% 0.58/0.42 thf(type_def_12, type, itself: $tType > $tType).
% 0.58/0.42 thf(type_def_13, type, a: $tType).
% 0.58/0.42 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.58/0.42 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_2, type, numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_3, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_4, type, ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_5, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_6, type, ring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_7, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_8, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_9, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_10, type, semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_11, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_12, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_13, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_14, type, linordered_idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_15, type, comm_monoid_diff: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_16, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_17, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_18, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_19, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_20, type, archim1727834104eiling: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_21, type, ordere142940540dd_abs: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_22, type, comple187826305attice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_23, type, archim1804426504_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_24, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.58/0.42 thf(func_def_25, type, archimedean_ceiling: !>[X0: $tType]:((X0 > int))).
% 0.58/0.42 thf(func_def_26, type, archimedean_round: !>[X0: $tType]:((X0 > int))).
% 0.58/0.42 thf(func_def_27, type, code_Suc: (code_natural > code_natural)).
% 0.58/0.42 thf(func_def_28, type, code_case_natural: !>[X0: $tType]:((X0 > (code_natural > X0) > code_natural > X0))).
% 0.58/0.42 thf(func_def_29, type, code_rec_natural: !>[X0: $tType]:((X0 > (code_natural > X0 > X0) > code_natural > X0))).
% 0.58/0.42 thf(func_def_30, type, code_size_natural: (code_natural > nat)).
% 0.58/0.42 thf(func_def_31, type, coindu493225792length: !>[X0: $tType]:((nat > coindu1593790203_llist @ X0 > extended_enat))).
% 0.58/0.42 thf(func_def_32, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.58/0.42 thf(func_def_33, type, coindu191418589_ldrop: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.58/0.42 thf(func_def_34, type, coindu1018505716length: !>[X0: $tType]:((coindu1593790203_llist @ X0 > extended_enat))).
% 0.58/0.42 thf(func_def_35, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 0.58/0.42 thf(func_def_36, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.58/0.42 thf(func_def_37, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.58/0.42 thf(func_def_38, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 0.58/0.42 thf(func_def_39, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.58/0.42 thf(func_def_40, type, coindu574146665prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.58/0.42 thf(func_def_41, type, coindu1802687541_ltake: !>[X0: $tType]:((extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.58/0.42 thf(func_def_42, type, coindu721411036eWhile: !>[X0: $tType]:(((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.58/0.42 thf(func_def_43, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.58/0.42 thf(func_def_44, type, extended_the_enat: (extended_enat > nat)).
% 0.58/0.42 thf(func_def_45, type, abs_abs: !>[X0: $tType]:((X0 > X0))).
% 0.58/0.42 thf(func_def_46, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.58/0.42 thf(func_def_47, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.58/0.42 thf(func_def_48, type, hilbert_LeastM: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_49, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.58/0.42 thf(func_def_50, type, nat2: (int > nat)).
% 0.58/0.42 thf(func_def_51, type, ring_1_of_int: !>[X0: $tType]:((int > X0))).
% 0.58/0.42 thf(func_def_52, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.58/0.42 thf(func_def_53, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.58/0.42 thf(func_def_54, type, nat_tsub: (int > int > int)).
% 0.58/0.42 thf(func_def_55, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 0.58/0.42 thf(func_def_56, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 0.58/0.42 thf(func_def_57, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.58/0.42 thf(func_def_58, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.58/0.42 thf(func_def_59, type, m: extended_enat).
% 0.58/0.42 thf(func_def_60, type, xs: coindu1593790203_llist @ a).
% 0.58/0.42 thf(func_def_64, type, db0: !>[X0: $tType]:(X0)).
% 0.58/0.42 thf(func_def_65, type, db1: !>[X0: $tType]:(X0)).
% 0.58/0.42 thf(func_def_66, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.58/0.42 thf(func_def_67, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.58/0.42 thf(func_def_68, type, db2: !>[X0: $tType]:(X0)).
% 0.58/0.42 thf(func_def_69, type, vAND: ($o > $o > $o)).
% 0.58/0.42 thf(func_def_70, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.58/0.42 thf(func_def_71, type, vNOT: ($o > $o)).
% 0.58/0.42 thf(func_def_72, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.58/0.42 thf(func_def_73, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.58/0.42 thf(func_def_74, type, sK2: (int > nat)).
% 0.58/0.42 thf(func_def_75, type, sK3: ((int > $o) > nat)).
% 0.58/0.42 thf(func_def_76, type, sK4: ((int > $o) > int)).
% 0.58/0.42 thf(func_def_77, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_78, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_79, type, sK7: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_80, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_81, type, sK9: (int > nat)).
% 0.58/0.42 thf(func_def_82, type, sK10: (int > nat)).
% 0.58/0.42 thf(func_def_83, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.58/0.42 thf(func_def_84, type, sK12: (int > nat)).
% 0.58/0.42 thf(func_def_85, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_86, type, sK14: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_87, type, sK15: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_88, type, sK16: (code_natural > code_natural)).
% 0.58/0.42 thf(func_def_89, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_90, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_91, type, sK19: (int > nat)).
% 0.58/0.42 thf(func_def_92, type, sK20: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_93, type, sK21: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_94, type, sK22: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_95, type, sK23: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_96, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.58/0.42 thf(func_def_97, type, sK25: !>[X0: $tType]:((X0 > nat))).
% 0.58/0.42 thf(func_def_98, type, sK26: ((code_natural > $o) > code_natural)).
% 0.58/0.42 thf(func_def_99, type, sK27: ((int > $o) > int)).
% 0.58/0.42 thf(func_def_100, type, sK28: ((int > $o) > nat)).
% 0.58/0.42 thf(func_def_101, type, sK29: !>[X0: $tType]:((X0 > int))).
% 0.58/0.42 thf(func_def_102, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_103, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.58/0.42 thf(func_def_104, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1) > (X0 > $o) > X0))).
% 0.58/0.42 thf(func_def_105, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > X0))).
% 0.58/0.42 thf(f2,axiom,(
% 0.58/0.42 ! [X0 : $tType,X1 : extended_enat,X2 : coindu1593790203_llist @ X0] : ((((coindu191418589_ldrop @ X0 @ X1 @ X2)) = coindu1598213697e_LNil @ X0) = ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)))),
% 0.58/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_ldrop__eq__LNil)).
% 0.58/0.42 thf(f345,axiom,(
% 0.58/0.42 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)),
% 0.58/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.58/0.42 thf(f346,conjecture,(
% 0.58/0.42 (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.58/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.58/0.42 thf(f347,negated_conjecture,(
% 0.58/0.42 ~ (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.58/0.42 inference(negated_conjecture,[status(cth)],[f346])).
% 0.58/0.42 thf(f513,plain,(
% 0.58/0.42 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)),
% 0.58/0.42 inference(rectify,[],[f345])).
% 0.58/0.42 thf(f514,plain,(
% 0.58/0.42 (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 0.58/0.42 inference(fool_elimination,[],[f513])).
% 0.58/0.42 thf(f639,plain,(
% 0.58/0.42 ! [X0 : $tType,X1 : extended_enat,X2 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 = ((coindu191418589_ldrop @ X0 @ X1 @ X2))) <=> (((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) = $true))),
% 0.58/0.42 inference(fool_elimination,[],[f2])).
% 0.58/0.42 thf(f963,plain,(
% 0.58/0.42 (((coindu191418589_ldrop @ a @ m @ xs)) != coindu1598213697e_LNil @ a)),
% 0.58/0.42 inference(flattening,[],[f347])).
% 0.58/0.42 thf(f1231,plain,(
% 0.58/0.42 ! [X0 : $tType,X1 : extended_enat,X2 : coindu1593790203_llist @ X0] : (((coindu1598213697e_LNil @ X0 = ((coindu191418589_ldrop @ X0 @ X1 @ X2))) | (((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) != $true)) & ((((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) = $true) | (coindu1598213697e_LNil @ X0 != ((coindu191418589_ldrop @ X0 @ X1 @ X2)))))),
% 0.58/0.42 inference(nnf_transformation,[],[f639])).
% 0.58/0.42 thf(f1442,plain,(
% 0.58/0.42 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : ((coindu1598213697e_LNil @ X0 = ((coindu191418589_ldrop @ X0 @ X1 @ X2))) | (((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) != $true)) )),
% 0.58/0.42 inference(cnf_transformation,[],[f1231])).
% 0.58/0.42 thf(f1503,plain,(
% 0.58/0.42 (((coindu191418589_ldrop @ a @ m @ xs)) != coindu1598213697e_LNil @ a)),
% 0.58/0.42 inference(cnf_transformation,[],[f963])).
% 0.58/0.42 thf(f1727,plain,(
% 0.58/0.42 (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 0.58/0.42 inference(cnf_transformation,[],[f514])).
% 0.58/0.42 thf(f2108,definition,(
% 0.58/0.42 spl34_30 <=> (((coindu191418589_ldrop @ a @ m @ xs)) = coindu1598213697e_LNil @ a)),
% 0.58/0.42 introduced(definition,[new_symbols(definition,[spl34_30])],[avatar_definition])).
% 0.58/0.42 thf(f2110,plain,(
% 0.58/0.42 (((coindu191418589_ldrop @ a @ m @ xs)) != coindu1598213697e_LNil @ a) | spl34_30),
% 0.58/0.42 inference(avatar_component_clause,[],[f2108])).
% 0.58/0.42 thf(f2111,plain,(
% 0.58/0.42 ~spl34_30),
% 0.58/0.42 inference(avatar_split_clause,[],[f1503,f2108])).
% 0.58/0.42 thf(f2203,definition,(
% 0.58/0.42 spl34_49 <=> (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 0.58/0.42 introduced(definition,[new_symbols(definition,[spl34_49])],[avatar_definition])).
% 0.58/0.42 thf(f2205,plain,(
% 0.58/0.42 (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true) | ~spl34_49),
% 0.58/0.42 inference(avatar_component_clause,[],[f2203])).
% 0.58/0.42 thf(f2206,plain,(
% 0.58/0.42 spl34_49),
% 0.58/0.42 inference(avatar_split_clause,[],[f1727,f2203])).
% 0.58/0.42 thf(f2491,plain,(
% 0.58/0.42 (coindu1598213697e_LNil @ a != coindu1598213697e_LNil @ a) | (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) != $true) | spl34_30),
% 0.58/0.42 inference(superposition,[],[f2110,f1442])).
% 0.58/0.42 thf(f2493,plain,(
% 0.58/0.42 (((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) != $true) | spl34_30),
% 0.58/0.42 inference(trivial_inequality_removal,[],[f2491])).
% 0.58/0.42 thf(f2494,plain,(
% 0.58/0.42 $false | (spl34_30 | ~spl34_49)),
% 0.58/0.42 inference(forward_subsumption_resolution,[],[f2493,f2205])).
% 0.58/0.42 thf(f2495,plain,(
% 0.58/0.42 spl34_30 | ~spl34_49),
% 0.58/0.42 inference(avatar_contradiction_clause,[],[f2494])).
% 0.58/0.42 cnf(s30, plain, ~spl34_30, inference(sat_conversion,[],[f2111])).
% 0.58/0.42 cnf(s49, plain, spl34_49, inference(sat_conversion,[],[f2206])).
% 0.58/0.42 cnf(s101, plain, spl34_30 | ~spl34_49, inference(sat_conversion,[],[f2495])).
% 0.58/0.42 cnf(s102, plain, spl34_30, inference(rat,[],[s101,s49])).
% 0.58/0.42 cnf(s103, plain, $false, inference(rat,[],[s30,s102])).
% 0.58/0.42 thf(f2496,plain,(
% 0.58/0.42 $false),
% 0.58/0.42 inference(avatar_sat_refutation,[],[s103])).
% 0.58/0.42 % SZS output end Proof for theBenchmark
% 0.58/0.42 % (3722517)------------------------------
% 0.58/0.42 % (3722517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.58/0.42 % (3722517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.58/0.42 % (3722517)CaDiCaL version: 2.1.3
% 0.58/0.42 % (3722517)Termination reason: Refutation
% 0.58/0.42 % (3722517)Time elapsed: 0.081 s
% 0.58/0.42 % (3722517)Peak memory usage: 14 MB
% 0.58/0.42 % (3722517)Instructions burned: 108 (million)
% 0.58/0.42 % (3722509)Success in time 0.142 s
% 0.58/0.42 % Vampire exiting
%------------------------------------------------------------------------------