%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT172^1 : 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 : n020.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 07:48:28 AM UTC 2026
% Result : Theorem 0.67s 0.39s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT172^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n020.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 18:06:05 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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
% 0.67/0.39 % (1405447)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.67/0.39 % (1405457)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2052414756:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.67/0.39 % (1405458)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.67/0.39 % (1405458)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
% 0.67/0.39 % (1405452)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2368942084:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.67/0.39 % (1405453)lrs+10_16_si=on:nwc=1.5:random_seed=3184987470:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.67/0.39 % (1405454)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1068526317:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.67/0.39 % (1405455)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=2501832704: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)
% 0.67/0.39 % (1405456)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3746602909:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.67/0.39 % (1405458)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=3268173489:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.67/0.39 % (1405454)Instruction limit reached!
% 0.67/0.39 % (1405454)------------------------------
% 0.67/0.39 % (1405454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405454)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405454)Termination reason: Instruction limit
% 0.67/0.39 % (1405454)Termination phase: shuffling
% 0.67/0.39 % (1405454)Time elapsed: 0.003 s
% 0.67/0.39 % (1405454)Peak memory usage: 10 MB
% 0.67/0.39 % (1405454)Instructions burned: 6 (million)
% 0.67/0.39 % (1405453)Instruction limit reached!
% 0.67/0.39 % (1405453)------------------------------
% 0.67/0.39 % (1405453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405453)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405453)Termination reason: Instruction limit
% 0.67/0.39 % (1405453)Termination phase: shuffling
% 0.67/0.39 % (1405453)Time elapsed: 0.009 s
% 0.67/0.39 % (1405453)Peak memory usage: 10 MB
% 0.67/0.39 % (1405453)Instructions burned: 19 (million)
% 0.67/0.39 % (1405456)Instruction limit reached!
% 0.67/0.39 % (1405456)------------------------------
% 0.67/0.39 % (1405456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405456)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405456)Termination reason: Instruction limit
% 0.67/0.39 % (1405456)Termination phase: Property scanning
% 0.67/0.39 % (1405456)Time elapsed: 0.012 s
% 0.67/0.39 % (1405456)Peak memory usage: 10 MB
% 0.67/0.39 % (1405456)Instructions burned: 26 (million)
% 0.67/0.39 % (1405457)Instruction limit reached!
% 0.67/0.39 % (1405457)------------------------------
% 0.67/0.39 % (1405457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405457)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405457)Termination reason: Instruction limit
% 0.67/0.39 % (1405457)Termination phase: Property scanning
% 0.67/0.39 % (1405457)Time elapsed: 0.021 s
% 0.67/0.39 % (1405457)Peak memory usage: 12 MB
% 0.67/0.39 % (1405457)Instructions burned: 85 (million)
% 0.67/0.39 % (1405469)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2275726484:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.67/0.39 % (1405466)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2830800200:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.39 % (1405466)Instruction limit reached!
% 0.67/0.39 % (1405466)------------------------------
% 0.67/0.39 % (1405466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405466)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405466)Termination reason: Instruction limit
% 0.67/0.39 % (1405466)Termination phase: shuffling
% 0.67/0.39 % (1405466)Time elapsed: 0.002 s
% 0.67/0.39 % (1405466)Peak memory usage: 10 MB
% 0.67/0.39 % (1405466)Instructions burned: 3 (million)
% 0.67/0.39 % (1405469)Instruction limit reached!
% 0.67/0.39 % (1405469)------------------------------
% 0.67/0.39 % (1405469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405469)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405469)Termination reason: Instruction limit
% 0.67/0.39 % (1405469)Termination phase: shuffling
% 0.67/0.39 % (1405469)Time elapsed: 0.004 s
% 0.67/0.39 % (1405468)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.39 % (1405469)Peak memory usage: 10 MB
% 0.67/0.39 % (1405469)Instructions burned: 15 (million)
% 0.67/0.39 % (1405467)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2980760556:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.67/0.39 % (1405468)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4187861892:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.67/0.39 % (1405467)Instruction limit reached!
% 0.67/0.39 % (1405467)------------------------------
% 0.67/0.39 % (1405467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405467)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405467)Termination reason: Instruction limit
% 0.67/0.39 % (1405467)Termination phase: shuffling
% 0.67/0.39 % (1405467)Time elapsed: 0.003 s
% 0.67/0.39 % (1405467)Peak memory usage: 10 MB
% 0.67/0.39 % (1405467)Instructions burned: 6 (million)
% 0.67/0.39 % (1405468)Instruction limit reached!
% 0.67/0.39 % (1405468)------------------------------
% 0.67/0.39 % (1405468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405468)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405468)Termination reason: Instruction limit
% 0.67/0.39 % (1405468)Termination phase: shuffling
% 0.67/0.39 % (1405468)Time elapsed: 0.004 s
% 0.67/0.39 % (1405468)Peak memory usage: 10 MB
% 0.67/0.39 % (1405468)Instructions burned: 7 (million)
% 0.67/0.39 % (1405473)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=3514601271:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.67/0.39 % (1405472)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
% 0.67/0.39 % (1405472)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.39 % (1405472)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=896488550:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.67/0.39 % (1405476)lrs+10_1_si=on:cs=on:random_seed=2519994232:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.67/0.39 % (1405477)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.67/0.39 % (1405477)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=407043866:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.39 % (1405476)Instruction limit reached!
% 0.67/0.39 % (1405476)------------------------------
% 0.67/0.39 % (1405476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405476)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405476)Termination reason: Instruction limit
% 0.67/0.39 % (1405476)Termination phase: shuffling
% 0.67/0.39 % (1405476)Time elapsed: 0.005 s
% 0.67/0.39 % (1405476)Peak memory usage: 10 MB
% 0.67/0.39 % (1405476)Instructions burned: 10 (million)
% 0.67/0.39 % (1405477)Instruction limit reached!
% 0.67/0.39 % (1405477)------------------------------
% 0.67/0.39 % (1405477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405477)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405477)Termination reason: Instruction limit
% 0.67/0.39 % (1405477)Termination phase: shuffling
% 0.67/0.39 % (1405477)Time elapsed: 0.001 s
% 0.67/0.39 % (1405477)Peak memory usage: 10 MB
% 0.67/0.39 % (1405477)Instructions burned: 2 (million)
% 0.67/0.39 % (1405473)Instruction limit reached!
% 0.67/0.39 % (1405473)------------------------------
% 0.67/0.39 % (1405473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405473)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405473)Termination reason: Instruction limit
% 0.67/0.39 % (1405473)Termination phase: Property scanning
% 0.67/0.39 % (1405473)Time elapsed: 0.020 s
% 0.67/0.39 % (1405473)Peak memory usage: 11 MB
% 0.67/0.39 % (1405473)Instructions burned: 89 (million)
% 0.67/0.39 % (1405472)Instruction limit reached!
% 0.67/0.39 % (1405472)------------------------------
% 0.67/0.39 % (1405472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.39 % (1405472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.39 % (1405472)CaDiCaL version: 2.1.3
% 0.67/0.39 % (1405472)Termination reason: Instruction limit
% 0.67/0.39 % (1405472)Termination phase: shuffling
% 0.67/0.39 % (1405472)Time elapsed: 0.013 s
% 0.67/0.39 % (1405472)Peak memory usage: 10 MB
% 0.67/0.39 % (1405472)Instructions burned: 29 (million)
% 0.67/0.39 % (1405455) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1405447-1405455"...
% 0.67/0.39 % (1405455)...printing done.
% 0.67/0.39 % (1405455)Refutation found. Thanks to Tanya!
% 0.67/0.39 % SZS status Theorem for theBenchmark
% 0.67/0.39 % SZS output start Proof for theBenchmark
% 0.67/0.39 thf(type_def_5, type, huffma16452318e_tree: $tType > $tType).
% 0.67/0.39 thf(type_def_6, type, set: $tType > $tType).
% 0.67/0.39 thf(type_def_7, type, nat: $tType).
% 0.67/0.39 thf(type_def_8, type, itself: $tType > $tType).
% 0.67/0.39 thf(type_def_9, type, a: $tType).
% 0.67/0.39 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.67/0.39 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_1, type, zero: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_3, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_4, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_5, type, monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_6, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_7, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_8, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_9, type, comm_monoid_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_10, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_11, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_12, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_13, type, cancel1352612707id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_14, type, linord219039673up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_15, type, ordere216010020id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_16, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_17, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_18, type, ordere1818651114id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_19, type, strict797366125id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_20, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.39 thf(func_def_21, type, ordere223160158up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.40 thf(func_def_22, type, strict2144017051up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.40 thf(func_def_23, type, ordere516151231imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.67/0.40 thf(func_def_24, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.67/0.40 thf(func_def_25, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.67/0.40 thf(func_def_26, type, huffma505251170phabet: !>[X0: $tType]:((huffma16452318e_tree @ X0 > set @ X0))).
% 0.67/0.40 thf(func_def_27, type, huffma1050891809istent: !>[X0: $tType]:((huffma16452318e_tree @ X0 > $o))).
% 0.67/0.40 thf(func_def_28, type, huffma636208924e_cost: !>[X0: $tType]:((huffma16452318e_tree @ X0 > nat))).
% 0.67/0.40 thf(func_def_29, type, huffma223349076_depth: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > nat))).
% 0.67/0.40 thf(func_def_30, type, huffma854352999e_freq: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > nat))).
% 0.67/0.40 thf(func_def_31, type, huffma1554076246height: !>[X0: $tType]:((huffma16452318e_tree @ X0 > nat))).
% 0.67/0.40 thf(func_def_32, type, huffma1954420889ibling: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > huffma16452318e_tree @ X0))).
% 0.67/0.40 thf(func_def_33, type, huffma1154738298minima: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > X0 > $o))).
% 0.67/0.40 thf(func_def_34, type, huffma936049440ptimum: !>[X0: $tType]:((huffma16452318e_tree @ X0 > $o))).
% 0.67/0.40 thf(func_def_35, type, huffma943100115ibling: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > X0))).
% 0.67/0.40 thf(func_def_36, type, huffma454997449itLeaf: !>[X0: $tType]:((huffma16452318e_tree @ X0 > nat > X0 > nat > X0 > huffma16452318e_tree @ X0))).
% 0.67/0.40 thf(func_def_37, type, huffma304375860urSyms: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > X0 > X0 > X0 > huffma16452318e_tree @ X0))).
% 0.67/0.40 thf(func_def_38, type, huffma2094459102Leaves: !>[X0: $tType]:((huffma16452318e_tree @ X0 > nat > X0 > nat > X0 > huffma16452318e_tree @ X0))).
% 0.67/0.40 thf(func_def_39, type, huffma469337550apSyms: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0 > X0 > huffma16452318e_tree @ X0))).
% 0.67/0.40 thf(func_def_40, type, huffma691733767weight: !>[X0: $tType]:((huffma16452318e_tree @ X0 > nat))).
% 0.67/0.40 thf(func_def_41, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.67/0.40 thf(func_def_42, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.67/0.40 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.67/0.40 thf(func_def_44, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.67/0.40 thf(func_def_45, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.67/0.40 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.67/0.40 thf(func_def_47, type, a2: a).
% 0.67/0.40 thf(func_def_48, type, b: a).
% 0.67/0.40 thf(func_def_49, type, c: a).
% 0.67/0.40 thf(func_def_50, type, t: huffma16452318e_tree @ a).
% 0.67/0.40 thf(func_def_51, type, u: huffma16452318e_tree @ a).
% 0.67/0.40 thf(func_def_52, type, w_a: nat).
% 0.67/0.40 thf(func_def_53, type, w_b: nat).
% 0.67/0.40 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 0.67/0.40 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 0.67/0.40 thf(func_def_59, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.67/0.40 thf(func_def_60, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.67/0.40 thf(func_def_61, type, vAND: ($o > $o > $o)).
% 0.67/0.40 thf(func_def_62, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.67/0.40 thf(func_def_63, type, vIMP: ($o > $o > $o)).
% 0.67/0.40 thf(func_def_64, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.67/0.40 thf(func_def_65, type, db2: !>[X0: $tType]:(X0)).
% 0.67/0.40 thf(func_def_66, type, vNOT: ($o > $o)).
% 0.67/0.40 thf(func_def_67, type, db3: !>[X0: $tType]:(X0)).
% 0.67/0.40 thf(func_def_68, type, db4: !>[X0: $tType]:(X0)).
% 0.67/0.40 thf(func_def_69, type, vOR: ($o > $o > $o)).
% 0.67/0.40 thf(func_def_70, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.67/0.40 thf(func_def_71, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.67/0.40 thf(func_def_72, type, sK2: (nat > nat > nat)).
% 0.67/0.40 thf(func_def_73, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.67/0.40 thf(func_def_74, type, sK4: !>[X0: $tType]:((X0 > X0))).
% 0.67/0.40 thf(func_def_75, type, sK5: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0))).
% 0.67/0.40 thf(func_def_76, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.67/0.40 thf(func_def_77, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.67/0.40 thf(func_def_78, type, sK8: !>[X0: $tType]:((nat > X0 > (X0 > $o) > (X0 > nat) > X0))).
% 0.67/0.40 thf(func_def_79, type, sK9: a).
% 0.67/0.40 thf(func_def_80, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.67/0.40 thf(func_def_81, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.67/0.40 thf(func_def_82, type, sK12: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.67/0.40 thf(func_def_83, type, sK13: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.67/0.40 thf(func_def_84, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.67/0.40 thf(func_def_85, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.67/0.40 thf(func_def_86, type, sK16: ((nat > $o) > nat)).
% 0.67/0.40 thf(func_def_87, type, sK17: a).
% 0.67/0.40 thf(func_def_88, type, sK18: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.67/0.40 thf(func_def_89, type, sK19: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.67/0.40 thf(func_def_90, type, sK20: ((nat > nat) > nat)).
% 0.67/0.40 thf(func_def_91, type, sK21: ((nat > nat) > nat)).
% 0.67/0.40 thf(func_def_92, type, sK22: ((nat > $o) > nat)).
% 0.67/0.40 thf(func_def_93, type, sK23: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.67/0.40 thf(func_def_94, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.67/0.40 thf(func_def_95, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.67/0.40 thf(func_def_96, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.67/0.40 thf(func_def_97, type, sK27: ((nat > nat) > nat)).
% 0.67/0.40 thf(func_def_98, type, sK28: ((nat > nat) > nat)).
% 0.67/0.40 thf(func_def_99, type, sK29: !>[X0: $tType]:((huffma16452318e_tree @ X0 > X0))).
% 0.67/0.40 thf(func_def_100, type, sK30: ((nat > $o) > nat > nat)).
% 0.67/0.40 thf(func_def_101, type, sK31: ((nat > $o) > nat)).
% 0.67/0.40 thf(func_def_102, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.67/0.40 thf(func_def_103, type, sK33: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.67/0.40 thf(func_def_104, type, sK34: !>[X0: $tType]:((X0 > X0))).
% 0.67/0.40 thf(func_def_105, type, sK35: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.67/0.40 thf(func_def_106, type, sK36: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.67/0.40 thf(func_def_107, type, sK37: (nat > nat > nat)).
% 0.67/0.40 thf(func_def_108, type, sK38: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.67/0.40 thf(func_def_109, type, sK39: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > nat > X0))).
% 0.67/0.40 thf(f1,axiom,(
% 0.67/0.40 (huffma1050891809istent @ a @ u)),
% 0.67/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_c_092_060_094sub_062u)).
% 0.67/0.40 thf(f9,axiom,(
% 0.67/0.40 ! [X0 : $tType,X2 : X0,X4 : X0,X1 : huffma16452318e_tree @ X0,X5 : X0,X3 : X0] : ((huffma1050891809istent @ X0 @ X1) => (huffma1050891809istent @ X0 @ (huffma304375860urSyms @ X0 @ X1 @ X2 @ X3 @ X4 @ X5)))),
% 0.67/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_consistent__swapFourSyms)).
% 0.67/0.40 thf(f288,conjecture,(
% 0.67/0.40 (huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))),
% 0.67/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.67/0.40 thf(f289,negated_conjecture,(
% 0.67/0.40 ~(huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))),
% 0.67/0.40 inference(negated_conjecture,[status(cth)],[f288])).
% 0.67/0.40 thf(f511,plain,(
% 0.67/0.40 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : huffma16452318e_tree @ X0,X4 : X0,X5 : X0] : ((huffma1050891809istent @ X0 @ X3) => (huffma1050891809istent @ X0 @ (huffma304375860urSyms @ X0 @ X3 @ X1 @ X5 @ X2 @ X4)))),
% 0.67/0.40 inference(rectify,[],[f9])).
% 0.67/0.40 thf(f512,plain,(
% 0.67/0.40 ! [X0 : $tType,X3 : huffma16452318e_tree @ X0,X2 : X0,X4 : X0,X5 : X0,X1 : X0] : (($true = ((huffma1050891809istent @ X0 @ X3))) => ($true = ((huffma1050891809istent @ X0 @ (huffma304375860urSyms @ X0 @ X3 @ X1 @ X5 @ X2 @ X4)))))),
% 0.67/0.40 inference(fool_elimination,[],[f511])).
% 0.67/0.40 thf(f712,plain,(
% 0.67/0.40 (huffma1050891809istent @ a @ u)),
% 0.67/0.40 inference(rectify,[],[f1])).
% 0.67/0.40 thf(f713,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ u)) = $true)),
% 0.67/0.40 inference(fool_elimination,[],[f712])).
% 0.67/0.40 thf(f777,plain,(
% 0.67/0.40 ~(huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))),
% 0.67/0.40 inference(rectify,[],[f289])).
% 0.67/0.40 thf(f778,plain,(
% 0.67/0.40 ~ (((huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))) = $true)),
% 0.67/0.40 inference(fool_elimination,[],[f777])).
% 0.67/0.40 thf(f853,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))) != $true)),
% 0.67/0.40 inference(flattening,[],[f778])).
% 0.67/0.40 thf(f981,plain,(
% 0.67/0.40 ! [X0 : $tType,X1 : X0,X4 : X0,X5 : X0,X3 : huffma16452318e_tree @ X0,X2 : X0] : (($true = ((huffma1050891809istent @ X0 @ (huffma304375860urSyms @ X0 @ X3 @ X1 @ X5 @ X2 @ X4)))) | ($true != ((huffma1050891809istent @ X0 @ X3))))),
% 0.67/0.40 inference(ennf_transformation,[],[f512])).
% 0.67/0.40 thf(f1182,plain,(
% 0.67/0.40 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0,X4 : huffma16452318e_tree @ X0,X5 : X0] : ((((huffma1050891809istent @ X0 @ (huffma304375860urSyms @ X0 @ X4 @ X1 @ X3 @ X5 @ X2))) = $true) | (((huffma1050891809istent @ X0 @ X4)) != $true))),
% 0.67/0.40 inference(rectify,[],[f981])).
% 0.67/0.40 thf(f1344,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ u)) = $true)),
% 0.67/0.40 inference(cnf_transformation,[],[f713])).
% 0.67/0.40 thf(f1427,plain,(
% 0.67/0.40 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : huffma16452318e_tree @ X0,X5 : X0] : ((((huffma1050891809istent @ X0 @ (huffma304375860urSyms @ X0 @ X4 @ X1 @ X3 @ X5 @ X2))) = $true) | (((huffma1050891809istent @ X0 @ X4)) != $true)) )),
% 0.67/0.40 inference(cnf_transformation,[],[f1182])).
% 0.67/0.40 thf(f1614,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))) != $true)),
% 0.67/0.40 inference(cnf_transformation,[],[f853])).
% 0.67/0.40 thf(f1900,definition,(
% 0.67/0.40 spl40_19 <=> (((huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))) = $true)),
% 0.67/0.40 introduced(definition,[new_symbols(definition,[spl40_19])],[avatar_definition])).
% 0.67/0.40 thf(f1902,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ (huffma304375860urSyms @ a @ u @ a2 @ b @ c @ (huffma943100115ibling @ a @ u @ c)))) != $true) | spl40_19),
% 0.67/0.40 inference(avatar_component_clause,[],[f1900])).
% 0.67/0.40 thf(f1903,plain,(
% 0.67/0.40 ~spl40_19),
% 0.67/0.40 inference(avatar_split_clause,[],[f1614,f1900])).
% 0.67/0.40 thf(f2040,definition,(
% 0.67/0.40 spl40_47 <=> (((huffma1050891809istent @ a @ u)) = $true)),
% 0.67/0.40 introduced(definition,[new_symbols(definition,[spl40_47])],[avatar_definition])).
% 0.67/0.40 thf(f2042,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ u)) = $true) | ~spl40_47),
% 0.67/0.40 inference(avatar_component_clause,[],[f2040])).
% 0.67/0.40 thf(f2043,plain,(
% 0.67/0.40 spl40_47),
% 0.67/0.40 inference(avatar_split_clause,[],[f1344,f2040])).
% 0.67/0.40 thf(f2210,plain,(
% 0.67/0.40 ($true != $true) | (((huffma1050891809istent @ a @ u)) != $true) | spl40_19),
% 0.67/0.40 inference(superposition,[],[f1902,f1427])).
% 0.67/0.40 thf(f2211,plain,(
% 0.67/0.40 (((huffma1050891809istent @ a @ u)) != $true) | spl40_19),
% 0.67/0.40 inference(trivial_inequality_removal,[],[f2210])).
% 0.67/0.40 thf(f2212,plain,(
% 0.67/0.40 $false | (spl40_19 | ~spl40_47)),
% 0.67/0.40 inference(forward_subsumption_resolution,[],[f2211,f2042])).
% 0.67/0.40 thf(f2213,plain,(
% 0.67/0.40 spl40_19 | ~spl40_47),
% 0.67/0.40 inference(avatar_contradiction_clause,[],[f2212])).
% 0.67/0.40 cnf(s19, plain, ~spl40_19, inference(sat_conversion,[],[f1903])).
% 0.67/0.40 cnf(s47, plain, spl40_47, inference(sat_conversion,[],[f2043])).
% 0.67/0.40 cnf(s65, plain, spl40_19 | ~spl40_47, inference(sat_conversion,[],[f2213])).
% 0.67/0.40 cnf(s66, plain, spl40_19, inference(rat,[],[s65,s47])).
% 0.67/0.40 cnf(s68, plain, $false, inference(rat,[],[s19,s66])).
% 0.67/0.40 thf(f2214,plain,(
% 0.67/0.40 $false),
% 0.67/0.40 inference(avatar_sat_refutation,[],[s68])).
% 0.67/0.40 % SZS output end Proof for theBenchmark
% 0.67/0.40 % (1405455)------------------------------
% 0.67/0.40 % (1405455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.40 % (1405455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.40 % (1405455)CaDiCaL version: 2.1.3
% 0.67/0.40 % (1405455)Termination reason: Refutation
% 0.67/0.40 % (1405455)Time elapsed: 0.067 s
% 0.67/0.40 % (1405455)Peak memory usage: 14 MB
% 0.67/0.40 % (1405455)Instructions burned: 132 (million)
% 0.67/0.40 % (1405447)Success in time 0.125 s
% 0.67/0.40 % Vampire exiting
%------------------------------------------------------------------------------