%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT213^1 : 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 : n012.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 07:48:33 AM UTC 2026
% Result : Theorem 0.33s 0.25s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT213^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.11 % Computer : n012.cluster.edu
% 0.06/0.11 % Model : x86_64 x86_64
% 0.06/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.11 % Memory : 8046.5625MB
% 0.06/0.11 % OS : Linux 6.8.0-71-generic
% 0.06/0.11 % CPULimit : 300
% 0.06/0.11 % WCLimit : 300
% 0.06/0.11 % DateTime : Tue Sep 29 18:09:04 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.16 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
% 0.33/0.25 % (486047)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.25 % (486058)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.25 % (486058)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
% 0.33/0.25 % (486052)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2018175919:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.25 % (486057)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=720304875:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.25 % (486053)lrs+10_16_si=on:nwc=1.5:random_seed=2484628543:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.25 % (486054)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1294470008:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.25 % (486056)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=689794345:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.25 % (486055)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=10579667: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)
% 0.33/0.25 % (486058)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=2272787104:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.25 % (486054)Instruction limit reached!
% 0.33/0.25 % (486054)------------------------------
% 0.33/0.25 % (486054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486054)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486054)Termination reason: Instruction limit
% 0.33/0.25 % (486054)Termination phase: shuffling
% 0.33/0.25 % (486054)Time elapsed: 0.002 s
% 0.33/0.25 % (486054)Peak memory usage: 10 MB
% 0.33/0.25 % (486054)Instructions burned: 7 (million)
% 0.33/0.25 % (486053)Instruction limit reached!
% 0.33/0.25 % (486053)------------------------------
% 0.33/0.25 % (486053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486053)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486053)Termination reason: Instruction limit
% 0.33/0.25 % (486053)Termination phase: shuffling
% 0.33/0.25 % (486053)Time elapsed: 0.005 s
% 0.33/0.25 % (486053)Peak memory usage: 10 MB
% 0.33/0.25 % (486053)Instructions burned: 20 (million)
% 0.33/0.25 % (486056)Instruction limit reached!
% 0.33/0.25 % (486056)------------------------------
% 0.33/0.25 % (486056)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486056)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486056)Termination reason: Instruction limit
% 0.33/0.25 % (486056)Termination phase: Property scanning
% 0.33/0.25 % (486056)Time elapsed: 0.006 s
% 0.33/0.25 % (486056)Peak memory usage: 10 MB
% 0.33/0.25 % (486056)Instructions burned: 24 (million)
% 0.33/0.25 % (486066)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4176432430:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.33/0.25 % (486068)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.33/0.25 % (486066)Instruction limit reached!
% 0.33/0.25 % (486066)------------------------------
% 0.33/0.25 % (486066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486066)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486066)Termination reason: Instruction limit
% 0.33/0.25 % (486066)Termination phase: shuffling
% 0.33/0.25 % (486066)Time elapsed: 0.003 s
% 0.33/0.25 % (486066)Peak memory usage: 10 MB
% 0.33/0.25 % (486066)Instructions burned: 12 (million)
% 0.33/0.25 % (486068)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3872032504:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.33/0.25 % (486067)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=94452699:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.33/0.25 % (486067)Instruction limit reached!
% 0.33/0.25 % (486067)------------------------------
% 0.33/0.25 % (486067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486067)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486067)Termination reason: Instruction limit
% 0.33/0.25 % (486067)Termination phase: shuffling
% 0.33/0.25 % (486067)Time elapsed: 0.001 s
% 0.33/0.25 % (486067)Peak memory usage: 10 MB
% 0.33/0.25 % (486067)Instructions burned: 5 (million)
% 0.33/0.25 % (486068)Instruction limit reached!
% 0.33/0.25 % (486068)------------------------------
% 0.33/0.25 % (486068)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486068)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486068)Termination reason: Instruction limit
% 0.33/0.25 % (486068)Termination phase: shuffling
% 0.33/0.25 % (486068)Time elapsed: 0.002 s
% 0.33/0.25 % (486068)Peak memory usage: 10 MB
% 0.33/0.25 % (486068)Instructions burned: 8 (million)
% 0.33/0.25 % (486057)Instruction limit reached!
% 0.33/0.25 % (486057)------------------------------
% 0.33/0.25 % (486057)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486057)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486057)Termination reason: Instruction limit
% 0.33/0.25 % (486057)Termination phase: Property scanning
% 0.33/0.25 % (486057)Time elapsed: 0.020 s
% 0.33/0.25 % (486057)Peak memory usage: 12 MB
% 0.33/0.25 % (486057)Instructions burned: 77 (million)
% 0.33/0.25 % (486052)Instruction limit reached!
% 0.33/0.25 % (486052)------------------------------
% 0.33/0.25 % (486052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486052)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486052)Termination reason: Instruction limit
% 0.33/0.25 % (486052)Termination phase: Property scanning
% 0.33/0.25 % (486052)Time elapsed: 0.022 s
% 0.33/0.25 % (486052)Peak memory usage: 12 MB
% 0.33/0.25 % (486052)Instructions burned: 88 (million)
% 0.33/0.25 % (486072)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3845142963:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.33/0.25 % (486073)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
% 0.33/0.25 % (486073)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.33/0.25 % (486073)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=42275752:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.33/0.25 % (486074)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=2630707129:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.33/0.25 % (486075)lrs+10_1_si=on:cs=on:random_seed=3260145711:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.33/0.25 % (486072)Instruction limit reached!
% 0.33/0.25 % (486072)------------------------------
% 0.33/0.25 % (486072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486072)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486072)Termination reason: Instruction limit
% 0.33/0.25 % (486072)Termination phase: shuffling
% 0.33/0.25 % (486072)Time elapsed: 0.003 s
% 0.33/0.25 % (486072)Peak memory usage: 10 MB
% 0.33/0.25 % (486072)Instructions burned: 12 (million)
% 0.33/0.25 % (486076)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.33/0.25 % (486076)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=748554149:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.33/0.25 % (486075)Instruction limit reached!
% 0.33/0.25 % (486075)------------------------------
% 0.33/0.25 % (486075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486075)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486075)Termination reason: Instruction limit
% 0.33/0.25 % (486075)Termination phase: shuffling
% 0.33/0.25 % (486075)Time elapsed: 0.003 s
% 0.33/0.25 % (486075)Peak memory usage: 10 MB
% 0.33/0.25 % (486075)Instructions burned: 12 (million)
% 0.33/0.25 % (486076)Instruction limit reached!
% 0.33/0.25 % (486076)------------------------------
% 0.33/0.25 % (486076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486076)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486076)Termination reason: Instruction limit
% 0.33/0.25 % (486076)Termination phase: shuffling
% 0.33/0.25 % (486076)Time elapsed: 0.001 s
% 0.33/0.25 % (486076)Peak memory usage: 10 MB
% 0.33/0.25 % (486076)Instructions burned: 3 (million)
% 0.33/0.25 % (486073)Instruction limit reached!
% 0.33/0.25 % (486073)------------------------------
% 0.33/0.25 % (486073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486073)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486073)Termination reason: Instruction limit
% 0.33/0.25 % (486073)Termination phase: shuffling
% 0.33/0.25 % (486073)Time elapsed: 0.007 s
% 0.33/0.25 % (486073)Peak memory usage: 11 MB
% 0.33/0.25 % (486073)Instructions burned: 30 (million)
% 0.33/0.25 % (486058)Instruction limit reached!
% 0.33/0.25 % (486058)------------------------------
% 0.33/0.25 % (486058)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486058)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486058)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486058)Termination reason: Instruction limit
% 0.33/0.25 % (486058)Termination phase: Saturation
% 0.33/0.25 % (486058)Time elapsed: 0.040 s
% 0.33/0.25 % (486058)Peak memory usage: 14 MB
% 0.33/0.25 % (486058)Instructions burned: 158 (million)
% 0.33/0.25 % (486081)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3091793338:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.33/0.25 % (486055) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-486047-486055"...
% 0.33/0.25 % (486083)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3578410657:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.33/0.25 % (486055)...printing done.
% 0.33/0.25 % (486084)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=257034399:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.33/0.25 % (486055)Refutation found. Thanks to Tanya!
% 0.33/0.25 % SZS status Theorem for theBenchmark
% 0.33/0.25 % SZS output start Proof for theBenchmark
% 0.33/0.25 thf(type_def_5, type, tree: $tType > $tType).
% 0.33/0.25 thf(type_def_6, type, real: $tType).
% 0.33/0.25 thf(type_def_7, type, set: $tType > $tType).
% 0.33/0.25 thf(type_def_8, type, nat: $tType).
% 0.33/0.25 thf(type_def_9, type, itself: $tType > $tType).
% 0.33/0.25 thf(type_def_10, type, a: $tType).
% 0.33/0.25 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.25 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_1, type, one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_3, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_4, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_5, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_6, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_7, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_8, type, ln: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_9, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_10, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_11, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_12, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_13, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_14, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_15, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_16, type, linordered_semidom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_17, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_18, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_20, type, ordere236663937imp_le: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_21, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.33/0.25 thf(func_def_22, type, one_one: !>[X0: $tType]:(X0)).
% 0.33/0.25 thf(func_def_23, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_24, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_25, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.25 thf(func_def_26, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.25 thf(func_def_27, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.33/0.25 thf(func_def_28, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.33/0.25 thf(func_def_29, type, splay_is_root: !>[X0: $tType]:((X0 > tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_30, type, splay_splay: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_31, type, splay_splay_max: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_32, type, splay_914434265_splay: !>[X0: $tType]:((X0 > tree @ X0 > nat))).
% 0.33/0.25 thf(func_def_33, type, splay_266122055elle_A: !>[X0: $tType]:((X0 > tree @ X0 > real))).
% 0.33/0.25 thf(func_def_34, type, powr: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_35, type, linorder_bst: !>[X0: $tType]:((tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_36, type, linorder_bst_eq: !>[X0: $tType]:((tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_37, type, mirror: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_38, type, subtrees: !>[X0: $tType]:((tree @ X0 > set @ tree @ X0))).
% 0.33/0.25 thf(func_def_39, type, leaf: !>[X0: $tType]:(tree @ X0)).
% 0.33/0.25 thf(func_def_40, type, node: !>[X0: $tType]:((tree @ X0 > X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_41, type, case_tree: !>[X0: $tType, X1: $tType]:((X0 > (tree @ X1 > X1 > tree @ X1 > X0) > tree @ X1 > X0))).
% 0.33/0.25 thf(func_def_42, type, is_Leaf: !>[X0: $tType]:((tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_43, type, left: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_44, type, pred_tree: !>[X0: $tType]:(((X0 > $o) > tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_45, type, rec_tree: !>[X0: $tType, X1: $tType]:((X0 > (tree @ X1 > X1 > tree @ X1 > X0 > X0 > X0) > tree @ X1 > X0))).
% 0.33/0.25 thf(func_def_46, type, rel_tree: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > tree @ X0 > tree @ X1 > $o))).
% 0.33/0.25 thf(func_def_47, type, right: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_48, type, set_tree: !>[X0: $tType]:((tree @ X0 > set @ X0))).
% 0.33/0.25 thf(func_def_49, type, val: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_50, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.33/0.25 thf(func_def_51, type, a2: a).
% 0.33/0.25 thf(func_def_52, type, t: tree @ a).
% 0.33/0.25 thf(func_def_53, type, thesis: $o).
% 0.33/0.25 thf(func_def_57, type, vOR: ($o > $o > $o)).
% 0.33/0.25 thf(func_def_58, type, db1: !>[X0: $tType]:(X0)).
% 0.33/0.25 thf(func_def_59, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.25 thf(func_def_60, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.25 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.25 thf(func_def_62, type, vAND: ($o > $o > $o)).
% 0.33/0.25 thf(func_def_63, type, vNOT: ($o > $o)).
% 0.33/0.25 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.25 thf(func_def_65, type, vIMP: ($o > $o > $o)).
% 0.33/0.25 thf(func_def_66, type, db2: !>[X0: $tType]:(X0)).
% 0.33/0.25 thf(func_def_67, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.25 thf(func_def_68, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.33/0.25 thf(func_def_69, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.33/0.25 thf(func_def_70, type, sP2: !>[X0: $tType]:(($o > tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_71, type, sP3: !>[X0: $tType]:(($o > tree @ X0 > $o))).
% 0.33/0.25 thf(func_def_72, type, sK4: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_73, type, sK5: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_74, type, sK6: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_75, type, sK7: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_76, type, sK8: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_77, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_78, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_79, type, sK11: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_80, type, sK12: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_81, type, sK13: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_82, type, sK14: !>[X0: $tType]:((tree @ X0 > (X0 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_83, type, sK15: !>[X0: $tType]:((tree @ X0 > X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_84, type, sK16: !>[X0: $tType]:((tree @ X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_85, type, sK17: !>[X0: $tType]:((tree @ X0 > X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_86, type, sK18: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_87, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_88, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_89, type, sK21: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_90, type, sK22: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_91, type, sK23: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_92, type, sK24: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_93, type, sK25: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_94, type, sK26: !>[X0: $tType]:((X0 > X0))).
% 0.33/0.25 thf(func_def_95, type, sK27: !>[X0: $tType]:((tree @ X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_96, type, sK28: !>[X0: $tType]:(((X0 > $o) > tree @ X0 > (X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_97, type, sK29: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_98, type, sK30: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_99, type, sK31: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_100, type, sK32: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_101, type, sK33: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_102, type, sK34: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_103, type, sK35: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_104, type, sK36: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_105, type, sK37: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_106, type, sK38: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_107, type, sK39: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_108, type, sK40: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_109, type, sK41: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_110, type, sK42: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_111, type, sK43: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_112, type, sK44: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_113, type, sK45: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_114, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_115, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_116, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (tree @ X1 > tree @ X0 > $o) > X1))).
% 0.33/0.25 thf(func_def_117, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (tree @ X1 > tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_118, type, sK50: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (tree @ X1 > tree @ X0 > $o) > tree @ X1))).
% 0.33/0.25 thf(func_def_119, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (tree @ X1 > tree @ X0 > $o) > tree @ X1))).
% 0.33/0.25 thf(func_def_120, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (tree @ X1 > tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_121, type, sK53: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (tree @ X1 > tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_122, type, sK54: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_123, type, sK55: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_124, type, sK56: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_125, type, sK57: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_126, type, sK58: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_127, type, sK59: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_128, type, sK60: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_129, type, sK61: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_130, type, sK62: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_131, type, sK63: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_132, type, sK64: !>[X0: $tType, X1: $tType]:((tree @ X0 > tree @ X1 > (X0 > X1 > $o) > X0))).
% 0.33/0.25 thf(func_def_133, type, sK65: !>[X0: $tType, X1: $tType]:((tree @ X0 > tree @ X1 > (X0 > X1 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_134, type, sK66: !>[X0: $tType, X1: $tType]:((tree @ X0 > tree @ X1 > (X0 > X1 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_135, type, sK67: !>[X0: $tType, X1: $tType]:((tree @ X0 > tree @ X1 > (X0 > X1 > $o) > tree @ X1))).
% 0.33/0.25 thf(func_def_136, type, sK68: !>[X0: $tType, X1: $tType]:((tree @ X0 > tree @ X1 > (X0 > X1 > $o) > tree @ X1))).
% 0.33/0.25 thf(func_def_137, type, sK69: !>[X0: $tType, X1: $tType]:((tree @ X0 > tree @ X1 > (X0 > X1 > $o) > X1))).
% 0.33/0.25 thf(func_def_138, type, sK70: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_139, type, sK71: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_140, type, sK72: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_141, type, sK73: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_142, type, sK74: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_143, type, sK75: !>[X0: $tType]:((X0 > X0))).
% 0.33/0.25 thf(func_def_144, type, sK76: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_145, type, sK77: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_146, type, sK78: !>[X0: $tType]:((X0 > X0))).
% 0.33/0.25 thf(func_def_147, type, sK79: !>[X0: $tType]:((X0 > X0))).
% 0.33/0.25 thf(func_def_148, type, sK80: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_149, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_150, type, sK82: !>[X0: $tType]:(($o > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_151, type, sK83: !>[X0: $tType]:(($o > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_152, type, sK84: !>[X0: $tType]:(($o > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_153, type, sK85: !>[X0: $tType]:(($o > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_154, type, sK86: !>[X0: $tType]:(($o > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_155, type, sK87: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_156, type, sK88: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_157, type, sK89: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_158, type, sK90: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_159, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_160, type, sK92: !>[X0: $tType]:(((X0 > $o) > tree @ X0 > (X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_161, type, sK93: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_162, type, sK94: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_163, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_164, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_165, type, sK97: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_166, type, sK98: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_167, type, sK99: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_168, type, sK100: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_169, type, sK101: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_170, type, sK102: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_171, type, sK103: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_172, type, sK104: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_173, type, sK105: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_174, type, sK106: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_175, type, sK107: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_176, type, sK108: !>[X0: $tType]:((X0 > X0))).
% 0.33/0.25 thf(func_def_177, type, sK109: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_178, type, sK110: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_179, type, sK111: !>[X0: $tType, X1: $tType]:((tree @ X1 > (X1 > X0 > $o) > tree @ X0 > (X1 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_180, type, sK112: !>[X0: $tType, X1: $tType]:((tree @ X1 > (X1 > X0 > $o) > tree @ X0 > (X1 > X0 > $o) > X1))).
% 0.33/0.25 thf(func_def_181, type, sK113: !>[X0: $tType]:((tree @ X0 > X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_182, type, sK114: !>[X0: $tType]:((tree @ X0 > X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_183, type, sK115: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_184, type, sK116: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_185, type, sK117: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_186, type, sK118: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_187, type, sK119: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.33/0.25 thf(func_def_188, type, sK120: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_189, type, sK121: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_190, type, sK122: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_191, type, sK123: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_192, type, sK124: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_193, type, sK125: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_194, type, sK126: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_195, type, sK127: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.33/0.25 thf(func_def_196, type, sK128: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_197, type, sK129: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_198, type, sK130: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_199, type, sK131: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_200, type, sK132: !>[X0: $tType]:(($o > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_201, type, sK133: !>[X0: $tType]:(($o > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_202, type, sK134: !>[X0: $tType]:(($o > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_203, type, sK135: !>[X0: $tType]:(($o > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_204, type, sK136: !>[X0: $tType]:(($o > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_205, type, sK137: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_206, type, sK138: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_207, type, sK139: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_208, type, sK140: !>[X0: $tType]:((X0 > X0))).
% 0.33/0.25 thf(func_def_209, type, sK141: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_210, type, sK142: !>[X0: $tType]:((tree @ X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_211, type, sK143: !>[X0: $tType]:((tree @ X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_212, type, sK144: !>[X0: $tType]:((tree @ X0 > tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_213, type, sK145: !>[X0: $tType, X1: $tType]:((tree @ X1 > (X0 > X1 > $o) > (X0 > X1 > $o) > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_214, type, sK146: !>[X0: $tType, X1: $tType]:((tree @ X1 > (X0 > X1 > $o) > (X0 > X1 > $o) > tree @ X0 > X1))).
% 0.33/0.25 thf(func_def_215, type, sK147: !>[X0: $tType]:((tree @ X0 > X0 > X0))).
% 0.33/0.25 thf(func_def_216, type, sK148: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_217, type, sK149: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_218, type, sK150: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_219, type, sK151: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.33/0.25 thf(func_def_220, type, sK152: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_221, type, sK153: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.33/0.25 thf(func_def_222, type, sK154: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.33/0.25 thf(func_def_223, type, sK155: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_224, type, sK156: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.33/0.25 thf(func_def_225, type, sK157: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.33/0.25 thf(func_def_226, type, sK158: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.33/0.25 thf(func_def_227, type, sK159: !>[X0: $tType]:((X0 > X0 > (X0 > $o) > X0))).
% 0.33/0.25 thf(f1,axiom,(
% 0.33/0.25 (member @ a @ a2 @ (set_tree @ a @ t))),
% 0.33/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I2_J)).
% 0.33/0.25 thf(f4,axiom,(
% 0.33/0.25 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : ((member @ X0 @ X1 @ (set_tree @ X0 @ X2)) => ? [X3 : tree @ X0,X4 : tree @ X0] : (member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2)))),
% 0.33/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_set__treeE)).
% 0.33/0.25 thf(f307,axiom,(
% 0.33/0.25 ! [X1 : tree @ a,X0 : tree @ a] : ((member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t)) => thesis)),
% 0.33/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.33/0.25 thf(f308,conjecture,(
% 0.33/0.25 thesis),
% 0.33/0.25 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.33/0.25 thf(f309,negated_conjecture,(
% 0.33/0.25 ~thesis),
% 0.33/0.25 inference(negated_conjecture,[status(cth)],[f308])).
% 0.33/0.25 thf(f353,plain,(
% 0.33/0.25 ~thesis),
% 0.33/0.25 inference(rectify,[],[f309])).
% 0.33/0.25 thf(f354,plain,(
% 0.33/0.25 ~ (thesis = $true)),
% 0.33/0.25 inference(fool_elimination,[],[f353])).
% 0.33/0.25 thf(f395,plain,(
% 0.33/0.25 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : ((member @ X0 @ X1 @ (set_tree @ X0 @ X2)) => ? [X3 : tree @ X0,X4 : tree @ X0] : (member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2)))),
% 0.33/0.25 inference(rectify,[],[f4])).
% 0.33/0.25 thf(f396,plain,(
% 0.33/0.25 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : ((((member @ X0 @ X1 @ (set_tree @ X0 @ X2))) = $true) => ? [X3 : tree @ X0,X4 : tree @ X0] : (((member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2))) = $true))),
% 0.33/0.25 inference(fool_elimination,[],[f395])).
% 0.33/0.25 thf(f859,plain,(
% 0.33/0.25 ! [X0 : tree @ a,X1 : tree @ a] : ((member @ tree @ a @ (node @ a @ X1 @ a2 @ X0) @ (subtrees @ a @ t)) => thesis)),
% 0.33/0.25 inference(rectify,[],[f307])).
% 0.33/0.25 thf(f860,plain,(
% 0.33/0.25 ! [X0 : tree @ a,X1 : tree @ a] : ((((member @ tree @ a @ (node @ a @ X1 @ a2 @ X0) @ (subtrees @ a @ t))) = $true) => (thesis = $true))),
% 0.33/0.25 inference(fool_elimination,[],[f859])).
% 0.33/0.25 thf(f873,plain,(
% 0.33/0.25 (member @ a @ a2 @ (set_tree @ a @ t))),
% 0.33/0.25 inference(rectify,[],[f1])).
% 0.33/0.25 thf(f874,plain,(
% 0.33/0.25 (((member @ a @ a2 @ (set_tree @ a @ t))) = $true)),
% 0.33/0.25 inference(fool_elimination,[],[f873])).
% 0.33/0.25 thf(f884,plain,(
% 0.33/0.25 (thesis != $true)),
% 0.33/0.25 inference(flattening,[],[f354])).
% 0.33/0.25 thf(f946,plain,(
% 0.33/0.25 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : (? [X3 : tree @ X0,X4 : tree @ X0] : (((member @ tree @ X0 @ (node @ X0 @ X3 @ X1 @ X4) @ (subtrees @ X0 @ X2))) = $true) | (((member @ X0 @ X1 @ (set_tree @ X0 @ X2))) != $true))),
% 0.33/0.25 inference(ennf_transformation,[],[f396])).
% 0.33/0.25 thf(f1208,plain,(
% 0.33/0.25 ! [X1 : tree @ a,X0 : tree @ a] : ((thesis = $true) | (((member @ tree @ a @ (node @ a @ X1 @ a2 @ X0) @ (subtrees @ a @ t))) != $true))),
% 0.33/0.25 inference(ennf_transformation,[],[f860])).
% 0.33/0.25 thf(f1302,plain,(
% 0.33/0.25 ! [X0 : tree @ a,X1 : tree @ a] : ((thesis = $true) | (((member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) != $true))),
% 0.33/0.25 inference(rectify,[],[f1208])).
% 0.33/0.25 thf(f1449,plain,(
% 0.33/0.25 ! [X0 : $tType,X1 : X0,X2 : tree @ X0] : ((((member @ tree @ X0 @ (node @ X0 @ (sK113 @ X0 @ X2 @ X1) @ X1 @ (sK114 @ X0 @ X2 @ X1)) @ (subtrees @ X0 @ X2))) = $true) | (((member @ X0 @ X1 @ (set_tree @ X0 @ X2))) != $true))),
% 0.33/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK4 @ X0 @ X2 @ X1),skolemize(X3,sK4 @ X0 @ X2 @ X1)],[f946])).
% 0.33/0.25 thf(f1597,plain,(
% 0.33/0.25 ( ! [X0 : tree @ a,X1 : tree @ a] : ((thesis = $true) | (((member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) != $true)) )),
% 0.33/0.25 inference(cnf_transformation,[],[f1302])).
% 0.33/0.25 thf(f1872,plain,(
% 0.33/0.25 ( ! [X0 : $tType,X2 : tree @ X0,X1 : X0] : ((((member @ tree @ X0 @ (node @ X0 @ (sK113 @ X0 @ X2 @ X1) @ X1 @ (sK114 @ X0 @ X2 @ X1)) @ (subtrees @ X0 @ X2))) = $true) | (((member @ X0 @ X1 @ (set_tree @ X0 @ X2))) != $true)) )),
% 0.33/0.25 inference(cnf_transformation,[],[f1449])).
% 0.33/0.25 thf(f1930,plain,(
% 0.33/0.25 (((member @ a @ a2 @ (set_tree @ a @ t))) = $true)),
% 0.33/0.25 inference(cnf_transformation,[],[f874])).
% 0.33/0.25 thf(f1937,plain,(
% 0.33/0.25 (thesis != $true)),
% 0.33/0.25 inference(cnf_transformation,[],[f884])).
% 0.33/0.25 thf(f2217,definition,(
% 0.33/0.25 spl160_17 <=> (thesis = $true)),
% 0.33/0.25 introduced(definition,[new_symbols(definition,[spl160_17])],[avatar_definition])).
% 0.33/0.25 thf(f2220,plain,(
% 0.33/0.25 ~spl160_17),
% 0.33/0.25 inference(avatar_split_clause,[],[f1937,f2217])).
% 0.33/0.25 thf(f2287,definition,(
% 0.33/0.25 spl160_31 <=> ! [X0 : tree @ a,X1 : tree @ a] : (((member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) != $true)),
% 0.33/0.25 introduced(definition,[new_symbols(definition,[spl160_31])],[avatar_definition])).
% 0.33/0.25 thf(f2288,plain,(
% 0.33/0.25 ( ! [X0 : tree @ a,X1 : tree @ a] : ((((member @ tree @ a @ (node @ a @ X0 @ a2 @ X1) @ (subtrees @ a @ t))) != $true)) ) | ~spl160_31),
% 0.33/0.25 inference(avatar_component_clause,[],[f2287])).
% 0.33/0.25 thf(f2289,plain,(
% 0.33/0.25 spl160_17 | spl160_31),
% 0.33/0.25 inference(avatar_split_clause,[],[f1597,f2287,f2217])).
% 0.33/0.25 thf(f2339,definition,(
% 0.33/0.25 spl160_42 <=> (((member @ a @ a2 @ (set_tree @ a @ t))) = $true)),
% 0.33/0.25 introduced(definition,[new_symbols(definition,[spl160_42])],[avatar_definition])).
% 0.33/0.25 thf(f2341,plain,(
% 0.33/0.25 (((member @ a @ a2 @ (set_tree @ a @ t))) = $true) | ~spl160_42),
% 0.33/0.25 inference(avatar_component_clause,[],[f2339])).
% 0.33/0.25 thf(f2342,plain,(
% 0.33/0.25 spl160_42),
% 0.33/0.25 inference(avatar_split_clause,[],[f1930,f2339])).
% 0.33/0.25 thf(f2369,plain,(
% 0.33/0.25 ($true != $true) | (((member @ a @ a2 @ (set_tree @ a @ t))) != $true) | ~spl160_31),
% 0.33/0.25 inference(superposition,[],[f2288,f1872])).
% 0.33/0.25 thf(f2371,plain,(
% 0.33/0.25 (((member @ a @ a2 @ (set_tree @ a @ t))) != $true) | ~spl160_31),
% 0.33/0.25 inference(trivial_inequality_removal,[],[f2369])).
% 0.33/0.25 thf(f2372,plain,(
% 0.33/0.25 $false | (~spl160_31 | ~spl160_42)),
% 0.33/0.25 inference(forward_subsumption_resolution,[],[f2371,f2341])).
% 0.33/0.25 thf(f2373,plain,(
% 0.33/0.25 ~spl160_31 | ~spl160_42),
% 0.33/0.25 inference(avatar_contradiction_clause,[],[f2372])).
% 0.33/0.25 cnf(s17, plain, ~spl160_17, inference(sat_conversion,[],[f2220])).
% 0.33/0.25 cnf(s31, plain, spl160_17 | spl160_31, inference(sat_conversion,[],[f2289])).
% 0.33/0.25 cnf(s42, plain, spl160_42, inference(sat_conversion,[],[f2342])).
% 0.33/0.25 cnf(s47, plain, ~spl160_31 | ~spl160_42, inference(sat_conversion,[],[f2373])).
% 0.33/0.25 cnf(s48, plain, ~spl160_31, inference(rat,[],[s47,s42])).
% 0.33/0.25 cnf(s49, plain, spl160_17, inference(rat,[],[s31,s48])).
% 0.33/0.25 cnf(s50, plain, $false, inference(rat,[],[s17,s49])).
% 0.33/0.25 thf(f2374,plain,(
% 0.33/0.25 $false),
% 0.33/0.25 inference(avatar_sat_refutation,[],[s50])).
% 0.33/0.25 % SZS output end Proof for theBenchmark
% 0.33/0.25 % (486055)------------------------------
% 0.33/0.25 % (486055)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.25 % (486055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.25 % (486055)CaDiCaL version: 2.1.3
% 0.33/0.25 % (486055)Termination reason: Refutation
% 0.33/0.25 % (486055)Time elapsed: 0.044 s
% 0.33/0.25 % (486055)Peak memory usage: 15 MB
% 0.33/0.25 % (486055)Instructions burned: 170 (million)
% 0.33/0.25 % (486047)Success in time 0.086 s
% 0.33/0.25 % Vampire exiting
%------------------------------------------------------------------------------