%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM179^1 : 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 : n019.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 07:46:24 AM UTC 2026
% Result : Theorem 0.49s 0.40s
% Output : Refutation 0.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM179^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:49:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.21/0.28 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
% 0.49/0.40 % (1144524)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.49/0.40 % (1144534)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3850477146:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.49/0.40 % (1144535)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.49/0.40 % (1144535)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
% 0.49/0.40 % (1144531)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3733312258:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.49/0.40 % (1144530)lrs+10_16_si=on:nwc=1.5:random_seed=714355600:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.49/0.40 % (1144532)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=1279697629: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)
% 0.49/0.40 % (1144533)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2079820645:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.49/0.40 % (1144535)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=1911362113:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.49/0.40 % (1144531)Instruction limit reached!
% 0.49/0.40 % (1144531)------------------------------
% 0.49/0.40 % (1144531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144531)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144531)Termination reason: Instruction limit
% 0.49/0.40 % (1144531)Termination phase: shuffling
% 0.49/0.40 % (1144531)Time elapsed: 0.003 s
% 0.49/0.40 % (1144531)Peak memory usage: 10 MB
% 0.49/0.40 % (1144531)Instructions burned: 5 (million)
% 0.49/0.40 % (1144529)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1180171154:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.49/0.40 % (1144530)Instruction limit reached!
% 0.49/0.40 % (1144530)------------------------------
% 0.49/0.40 % (1144530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144530)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144530)Termination reason: Instruction limit
% 0.49/0.40 % (1144530)Termination phase: Property scanning
% 0.49/0.40 % (1144530)Time elapsed: 0.010 s
% 0.49/0.40 % (1144530)Peak memory usage: 10 MB
% 0.49/0.40 % (1144530)Instructions burned: 19 (million)
% 0.49/0.40 % (1144533)Instruction limit reached!
% 0.49/0.40 % (1144533)------------------------------
% 0.49/0.40 % (1144533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144533)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144533)Termination reason: Instruction limit
% 0.49/0.40 % (1144533)Termination phase: Property scanning
% 0.49/0.40 % (1144533)Time elapsed: 0.012 s
% 0.49/0.40 % (1144533)Peak memory usage: 10 MB
% 0.49/0.40 % (1144533)Instructions burned: 24 (million)
% 0.49/0.40 % (1144534)Instruction limit reached!
% 0.49/0.40 % (1144534)------------------------------
% 0.49/0.40 % (1144534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144534)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144534)Termination reason: Instruction limit
% 0.49/0.40 % (1144534)Termination phase: Property scanning
% 0.49/0.40 % (1144534)Time elapsed: 0.020 s
% 0.49/0.40 % (1144534)Peak memory usage: 12 MB
% 0.49/0.40 % (1144534)Instructions burned: 79 (million)
% 0.49/0.40 % (1144546)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2936848304:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.49/0.40 % (1144545)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.40 % (1144546)Instruction limit reached!
% 0.49/0.40 % (1144546)------------------------------
% 0.49/0.40 % (1144546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144546)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144546)Termination reason: Instruction limit
% 0.49/0.40 % (1144546)Termination phase: shuffling
% 0.49/0.40 % (1144546)Time elapsed: 0.004 s
% 0.49/0.40 % (1144546)Peak memory usage: 10 MB
% 0.49/0.40 % (1144546)Instructions burned: 14 (million)
% 0.49/0.40 % (1144544)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3562573074:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.49/0.40 % (1144545)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2725740062:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.49/0.40 % (1144544)Instruction limit reached!
% 0.49/0.40 % (1144544)------------------------------
% 0.49/0.40 % (1144544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144544)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144544)Termination reason: Instruction limit
% 0.49/0.40 % (1144544)Termination phase: shuffling
% 0.49/0.40 % (1144544)Time elapsed: 0.003 s
% 0.49/0.40 % (1144544)Peak memory usage: 10 MB
% 0.49/0.40 % (1144544)Instructions burned: 6 (million)
% 0.49/0.40 % (1144545)Instruction limit reached!
% 0.49/0.40 % (1144545)------------------------------
% 0.49/0.40 % (1144545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144545)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144545)Termination reason: Instruction limit
% 0.49/0.40 % (1144545)Termination phase: shuffling
% 0.49/0.40 % (1144545)Time elapsed: 0.004 s
% 0.49/0.40 % (1144545)Peak memory usage: 10 MB
% 0.49/0.40 % (1144545)Instructions burned: 8 (million)
% 0.49/0.40 % (1144543)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=485640597:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.40 % (1144543)Instruction limit reached!
% 0.49/0.40 % (1144543)------------------------------
% 0.49/0.40 % (1144543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144543)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144543)Termination reason: Instruction limit
% 0.49/0.40 % (1144543)Termination phase: shuffling
% 0.49/0.40 % (1144543)Time elapsed: 0.002 s
% 0.49/0.40 % (1144543)Peak memory usage: 10 MB
% 0.49/0.40 % (1144543)Instructions burned: 2 (million)
% 0.49/0.40 % (1144551)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=1755469897:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.49/0.40 % (1144550)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
% 0.49/0.40 % (1144550)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.40 % (1144554)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.49/0.40 % (1144554)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=2973208211:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.40 % (1144550)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2519886692:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.49/0.40 % (1144552)lrs+10_1_si=on:cs=on:random_seed=2694915316:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.49/0.40 % (1144554)Instruction limit reached!
% 0.49/0.40 % (1144554)------------------------------
% 0.49/0.40 % (1144554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144554)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144554)Termination reason: Instruction limit
% 0.49/0.40 % (1144554)Termination phase: shuffling
% 0.49/0.40 % (1144554)Time elapsed: 0.001 s
% 0.49/0.40 % (1144554)Peak memory usage: 10 MB
% 0.49/0.40 % (1144554)Instructions burned: 4 (million)
% 0.49/0.40 % (1144532) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1144524-1144532"...
% 0.49/0.40 % (1144532)...printing done.
% 0.49/0.40 % (1144552)Instruction limit reached!
% 0.49/0.40 % (1144552)------------------------------
% 0.49/0.40 % (1144552)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144552)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144552)Termination reason: Instruction limit
% 0.49/0.40 % (1144552)Termination phase: shuffling
% 0.49/0.40 % (1144552)Time elapsed: 0.005 s
% 0.49/0.40 % (1144552)Peak memory usage: 10 MB
% 0.49/0.40 % (1144552)Instructions burned: 9 (million)
% 0.49/0.40 % (1144532)Refutation found. Thanks to Tanya!
% 0.49/0.40 % SZS status Theorem for theBenchmark
% 0.49/0.40 % SZS output start Proof for theBenchmark
% 0.49/0.40 thf(type_def_5, type, coinductive_llist: $tType > $tType).
% 0.49/0.40 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.49/0.40 thf(type_def_7, type, sum_sum: ($tType * $tType) > $tType).
% 0.49/0.40 thf(type_def_8, type, option: $tType > $tType).
% 0.49/0.40 thf(type_def_9, type, set: $tType > $tType).
% 0.49/0.40 thf(type_def_10, type, itself: $tType > $tType).
% 0.49/0.40 thf(type_def_11, type, node: $tType).
% 0.49/0.40 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.49/0.40 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_1, type, minus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_2, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_3, type, bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_4, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_5, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_6, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_7, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_8, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_9, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_10, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_12, type, order_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_13, type, order_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_16, type, cancel146912293up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_17, type, topolo890362671_space: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.49/0.40 thf(func_def_18, type, basic_fsts: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > set @ X0))).
% 0.49/0.40 thf(func_def_19, type, basic_snds: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > set @ X1))).
% 0.49/0.40 thf(func_def_20, type, coinductive_gen_lset: !>[X0: $tType]:((set @ X0 > coinductive_llist @ X0 > set @ X0))).
% 0.49/0.40 thf(func_def_21, type, coinductive_lfinite: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.49/0.40 thf(func_def_22, type, coinductive_lnull: !>[X0: $tType]:((coinductive_llist @ X0 > $o))).
% 0.49/0.40 thf(func_def_23, type, coinductive_lset: !>[X0: $tType]:((coinductive_llist @ X0 > set @ X0))).
% 0.49/0.40 thf(func_def_24, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.49/0.40 thf(func_def_25, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.49/0.40 thf(func_def_26, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.49/0.40 thf(func_def_27, type, koenig793108494nected: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.49/0.40 thf(func_def_28, type, koenig317145564le_via: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0 > set @ X0))).
% 0.49/0.40 thf(func_def_29, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.49/0.40 thf(func_def_30, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.49/0.40 thf(func_def_31, type, top_top: !>[X0: $tType]:(X0)).
% 0.49/0.40 thf(func_def_32, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.49/0.40 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.40 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.49/0.40 thf(func_def_35, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.49/0.40 thf(func_def_36, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_37, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.49/0.40 thf(func_def_38, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.49/0.40 thf(func_def_39, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.49/0.40 thf(func_def_40, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.49/0.40 thf(func_def_42, type, f: (product_prod @ node @ set @ node > coinductive_llist @ node)).
% 0.49/0.40 thf(func_def_43, type, graph: (node > node > $o)).
% 0.49/0.40 thf(func_def_44, type, n: node).
% 0.49/0.40 thf(func_def_45, type, ns: set @ node).
% 0.49/0.40 thf(func_def_49, type, vOR: ($o > $o > $o)).
% 0.49/0.40 thf(func_def_50, type, db0: !>[X0: $tType]:(X0)).
% 0.49/0.40 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.49/0.40 thf(func_def_52, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.49/0.40 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.49/0.40 thf(func_def_54, type, db1: !>[X0: $tType]:(X0)).
% 0.49/0.40 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.49/0.40 thf(func_def_56, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.49/0.40 thf(func_def_57, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.49/0.40 thf(func_def_58, type, vIMP: ($o > $o > $o)).
% 0.49/0.40 thf(func_def_59, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.49/0.40 thf(func_def_60, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.49/0.40 thf(func_def_61, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > $o) > X0))).
% 0.49/0.40 thf(func_def_62, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > $o) > X2))).
% 0.49/0.40 thf(func_def_63, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > $o) > X3))).
% 0.49/0.40 thf(func_def_64, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > $o) > X1))).
% 0.49/0.40 thf(func_def_65, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X4 > $o) > X4))).
% 0.49/0.40 thf(func_def_66, type, sK7: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_67, type, sK8: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_68, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X2))).
% 0.49/0.40 thf(func_def_69, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X3))).
% 0.49/0.40 thf(func_def_70, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X1))).
% 0.49/0.40 thf(func_def_71, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X0))).
% 0.49/0.40 thf(func_def_72, type, sK13: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_73, type, sK14: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_74, type, sK15: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.49/0.40 thf(func_def_75, type, sK16: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.49/0.40 thf(func_def_76, type, sK17: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_77, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X5))).
% 0.49/0.40 thf(func_def_78, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X1))).
% 0.49/0.40 thf(func_def_79, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X4))).
% 0.49/0.40 thf(func_def_80, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X6))).
% 0.49/0.40 thf(func_def_81, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X2))).
% 0.49/0.40 thf(func_def_82, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X3))).
% 0.49/0.40 thf(func_def_83, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ product_prod @ X4 @ X6 > X0))).
% 0.49/0.40 thf(func_def_84, type, sK25: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_85, type, sK26: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.49/0.40 thf(func_def_86, type, sK27: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_87, type, sK28: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.49/0.40 thf(func_def_88, type, sK29: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_89, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ X2 > X4))).
% 0.49/0.40 thf(func_def_90, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ X2 > X2))).
% 0.49/0.40 thf(func_def_91, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ X2 > X5))).
% 0.49/0.40 thf(func_def_92, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ X2 > X1))).
% 0.49/0.40 thf(func_def_93, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ X2 > X0))).
% 0.49/0.40 thf(func_def_94, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ X2 > X3))).
% 0.49/0.40 thf(func_def_95, type, sK36: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.49/0.40 thf(func_def_96, type, sK37: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.49/0.40 thf(func_def_97, type, sK38: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_98, type, sK39: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_99, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_100, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_101, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_102, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_103, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.49/0.40 thf(func_def_104, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.49/0.40 thf(func_def_105, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X3))).
% 0.49/0.40 thf(func_def_106, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.49/0.40 thf(func_def_107, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.49/0.40 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.49/0.40 thf(func_def_109, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X4))).
% 0.49/0.40 thf(func_def_110, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X3))).
% 0.49/0.40 thf(func_def_111, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X1))).
% 0.49/0.40 thf(func_def_112, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X2))).
% 0.49/0.40 thf(func_def_113, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X1 > X0))).
% 0.49/0.40 thf(func_def_114, type, sK55: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.49/0.40 thf(func_def_115, type, sK56: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_116, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.49/0.40 thf(func_def_117, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.49/0.40 thf(func_def_118, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.49/0.40 thf(func_def_119, type, sK60: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.40 thf(func_def_120, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.40 thf(func_def_121, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X0))).
% 0.49/0.40 thf(func_def_122, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X2))).
% 0.49/0.40 thf(func_def_123, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > X1))).
% 0.49/0.40 thf(func_def_124, type, sK65: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.49/0.40 thf(func_def_125, type, sK66: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.49/0.40 thf(func_def_126, type, sK67: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.49/0.40 thf(func_def_127, type, sK68: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_128, type, sK69: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_129, type, sK70: !>[X0: $tType]:(X0)).
% 0.49/0.40 thf(func_def_130, type, sK71: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_131, type, sK72: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_132, type, sK73: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_133, type, sK74: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_134, type, sK75: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_135, type, sK76: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.49/0.40 thf(func_def_136, type, sK77: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_137, type, sK78: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_138, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X5 > $o) > X2))).
% 0.49/0.40 thf(func_def_139, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X5 > $o) > X0))).
% 0.49/0.40 thf(func_def_140, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X5 > $o) > X1))).
% 0.49/0.40 thf(func_def_141, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X5 > $o) > X5))).
% 0.49/0.40 thf(func_def_142, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X5 > $o) > X3))).
% 0.49/0.40 thf(func_def_143, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ X5 > $o) > X4))).
% 0.49/0.40 thf(func_def_144, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X5))).
% 0.49/0.40 thf(func_def_145, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.49/0.40 thf(func_def_146, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.49/0.40 thf(func_def_147, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.49/0.40 thf(func_def_148, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X6))).
% 0.49/0.40 thf(func_def_149, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X3))).
% 0.49/0.40 thf(func_def_150, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X4 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X0 @ X2 > $o) > X4))).
% 0.49/0.40 thf(func_def_151, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_152, type, sK93: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_153, type, sK94: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_154, type, sK95: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.40 thf(func_def_155, type, sK96: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.49/0.40 thf(func_def_156, type, sK97: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_157, type, sK98: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.49/0.40 thf(func_def_158, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.49/0.40 thf(func_def_159, type, sK100: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_160, type, sK101: !>[X0: $tType]:((set @ X0 > X0))).
% 0.49/0.40 thf(func_def_161, type, sK102: !>[X0: $tType]:((X0 > set @ X0 > set @ X0 > X0 > set @ X0))).
% 0.49/0.40 thf(func_def_162, type, sK103: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.49/0.40 thf(func_def_163, type, sK104: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.49/0.40 thf(func_def_164, type, sK105: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ X0 > X0 > X1))).
% 0.49/0.40 thf(func_def_165, type, sK106: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > set @ X0 > X0))).
% 0.49/0.40 thf(func_def_166, type, sK107: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0 > set @ X0))).
% 0.49/0.40 thf(func_def_167, type, sK108: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_168, type, sK109: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_169, type, sK110: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_170, type, sK111: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.49/0.40 thf(func_def_171, type, sK112: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.49/0.40 thf(func_def_172, type, sK113: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.49/0.40 thf(func_def_173, type, sK114: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.49/0.40 thf(func_def_174, type, vNOT: ($o > $o)).
% 0.49/0.40 thf(f3,axiom,(
% 0.49/0.40 ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))),
% 0.49/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062infinite_A_Ireachable__via_Agraph_A_I_N_A_123n_125_J_An_J_092_060close_062)).
% 0.49/0.40 thf(f104,axiom,(
% 0.49/0.40 ! [X0 : $tType] : (finite_finite2 @ X0 @ bot_bot @ set @ X0)),
% 0.49/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_finite_OemptyI)).
% 0.49/0.40 thf(f292,conjecture,(
% 0.49/0.40 ? [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))) = ((f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) & ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0)) & (finite_finite2 @ node @ X1))),
% 0.49/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.49/0.40 thf(f293,negated_conjecture,(
% 0.49/0.40 ~ ? [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))) = ((f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) & ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0)) & (finite_finite2 @ node @ X1))),
% 0.49/0.40 inference(negated_conjecture,[status(cth)],[f292])).
% 0.49/0.40 thf(f588,plain,(
% 0.49/0.40 ~ ? [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node))) = ((f @ (product_Pair @ node @ set @ node @ X0 @ X1)))) & ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0)) & (finite_finite2 @ node @ X1))),
% 0.49/0.40 inference(rectify,[],[f293])).
% 0.49/0.40 thf(f589,plain,(
% 0.49/0.40 ~ ? [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) = ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))) & ~ (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) = $true) & (((finite_finite2 @ node @ X1)) = $true))),
% 0.49/0.40 inference(fool_elimination,[],[f588])).
% 0.49/0.40 thf(f692,plain,(
% 0.49/0.40 ~(finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))),
% 0.49/0.40 inference(rectify,[],[f3])).
% 0.49/0.40 thf(f693,plain,(
% 0.49/0.40 ~ (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) = $true)),
% 0.49/0.40 inference(fool_elimination,[],[f692])).
% 0.49/0.40 thf(f744,plain,(
% 0.49/0.40 ! [X0 : $tType] : (finite_finite2 @ X0 @ bot_bot @ set @ X0)),
% 0.49/0.40 inference(rectify,[],[f104])).
% 0.49/0.40 thf(f745,plain,(
% 0.49/0.40 ! [X0 : $tType] : (((finite_finite2 @ X0 @ bot_bot @ set @ X0)) = $true)),
% 0.49/0.40 inference(fool_elimination,[],[f744])).
% 0.49/0.40 thf(f829,plain,(
% 0.49/0.40 ~ ? [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) = ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))) & (((finite_finite2 @ node @ X1)) = $true) & (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) != $true))),
% 0.49/0.40 inference(flattening,[],[f589])).
% 0.49/0.40 thf(f836,plain,(
% 0.49/0.40 (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) != $true)),
% 0.49/0.40 inference(flattening,[],[f693])).
% 0.49/0.40 thf(f935,plain,(
% 0.49/0.40 ! [X0 : node,X1 : set @ node] : ((((finite_finite2 @ node @ X1)) != $true) | (((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) != ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))) | (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) = $true))),
% 0.49/0.40 inference(ennf_transformation,[],[f829])).
% 0.49/0.40 thf(f1455,plain,(
% 0.49/0.40 ( ! [X0 : node,X1 : set @ node] : ((((f @ (product_Pair @ node @ set @ node @ X0 @ X1))) != ((f @ (product_Pair @ node @ set @ node @ n @ bot_bot @ set @ node)))) | (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ X0 @ X1)) @ X0))) = $true) | (((finite_finite2 @ node @ X1)) != $true)) )),
% 0.49/0.40 inference(cnf_transformation,[],[f935])).
% 0.49/0.40 thf(f1516,plain,(
% 0.49/0.40 (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) != $true)),
% 0.49/0.40 inference(cnf_transformation,[],[f836])).
% 0.49/0.40 thf(f1638,plain,(
% 0.49/0.40 ( ! [X0 : $tType] : ((((finite_finite2 @ X0 @ bot_bot @ set @ X0)) = $true)) )),
% 0.49/0.40 inference(cnf_transformation,[],[f745])).
% 0.49/0.40 thf(f1905,definition,(
% 0.49/0.40 spl115_10 <=> (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) = $true)),
% 0.49/0.40 introduced(definition,[new_symbols(definition,[spl115_10])],[avatar_definition])).
% 0.49/0.40 thf(f1908,plain,(
% 0.49/0.40 ~spl115_10),
% 0.49/0.40 inference(avatar_split_clause,[],[f1516,f1905])).
% 0.49/0.40 thf(f1954,plain,(
% 0.49/0.40 (((finite_finite2 @ node @ bot_bot @ set @ node)) != $true) | (((finite_finite2 @ node @ (koenig317145564le_via @ node @ graph @ (uminus_uminus @ set @ node @ (insert @ node @ n @ bot_bot @ set @ node)) @ n))) = $true)),
% 0.49/0.40 inference(equality_resolution,[],[f1455])).
% 0.49/0.40 thf(f1956,definition,(
% 0.49/0.40 spl115_20 <=> (((finite_finite2 @ node @ bot_bot @ set @ node)) = $true)),
% 0.49/0.40 introduced(definition,[new_symbols(definition,[spl115_20])],[avatar_definition])).
% 0.49/0.40 thf(f1958,plain,(
% 0.49/0.40 (((finite_finite2 @ node @ bot_bot @ set @ node)) != $true) | spl115_20),
% 0.49/0.40 inference(avatar_component_clause,[],[f1956])).
% 0.49/0.40 thf(f1959,plain,(
% 0.49/0.40 ~spl115_20 | spl115_10),
% 0.49/0.40 inference(avatar_split_clause,[],[f1954,f1905,f1956])).
% 0.49/0.40 thf(f1960,plain,(
% 0.49/0.40 $false | spl115_20),
% 0.49/0.40 inference(forward_subsumption_resolution,[],[f1958,f1638])).
% 0.49/0.40 thf(f1961,plain,(
% 0.49/0.40 spl115_20),
% 0.49/0.40 inference(avatar_contradiction_clause,[],[f1960])).
% 0.49/0.40 cnf(s10, plain, ~spl115_10, inference(sat_conversion,[],[f1908])).
% 0.49/0.40 cnf(s20, plain, spl115_10 | ~spl115_20, inference(sat_conversion,[],[f1959])).
% 0.49/0.40 cnf(s21, plain, spl115_20, inference(sat_conversion,[],[f1961])).
% 0.49/0.40 cnf(s22, plain, spl115_10, inference(rat,[],[s20,s21])).
% 0.49/0.40 cnf(s23, plain, $false, inference(rat,[],[s10,s22])).
% 0.49/0.40 thf(f1962,plain,(
% 0.49/0.40 $false),
% 0.49/0.40 inference(avatar_sat_refutation,[],[s23])).
% 0.49/0.40 % SZS output end Proof for theBenchmark
% 0.49/0.40 % (1144532)------------------------------
% 0.49/0.40 % (1144532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.40 % (1144532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.40 % (1144532)CaDiCaL version: 2.1.3
% 0.49/0.40 % (1144532)Termination reason: Refutation
% 0.49/0.40 % (1144532)Time elapsed: 0.058 s
% 0.49/0.40 % (1144532)Peak memory usage: 14 MB
% 0.49/0.40 % (1144532)Instructions burned: 116 (million)
% 0.49/0.40 % (1144524)Success in time 0.105 s
% 0.49/0.40 % Vampire exiting
%------------------------------------------------------------------------------