%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP069^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:08:12 AM UTC 2026
% Result : Theorem 0.30s 0.43s
% Output : Refutation 0.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP069^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n001.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 19:52:21 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.21/0.30 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
% 0.30/0.43 % (1732401)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.43 % (1732409)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=1348895616: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)
% 0.30/0.43 % (1732408)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=592385617:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.43 % (1732406)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1670474096:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.43 % (1732407)lrs+10_16_si=on:nwc=1.5:random_seed=3299556726:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.43 % (1732408)Instruction limit reached!
% 0.30/0.43 % (1732408)------------------------------
% 0.30/0.43 % (1732408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732408)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732408)Termination reason: Instruction limit
% 0.30/0.43 % (1732408)Termination phase: shuffling
% 0.30/0.43 % (1732408)Time elapsed: 0.002 s
% 0.30/0.43 % (1732408)Peak memory usage: 10 MB
% 0.30/0.43 % (1732408)Instructions burned: 3 (million)
% 0.30/0.43 % (1732407)Instruction limit reached!
% 0.30/0.43 % (1732407)------------------------------
% 0.30/0.43 % (1732407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732407)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732407)Termination reason: Instruction limit
% 0.30/0.43 % (1732407)Termination phase: shuffling
% 0.30/0.43 % (1732407)Time elapsed: 0.009 s
% 0.30/0.43 % (1732407)Peak memory usage: 10 MB
% 0.30/0.43 % (1732407)Instructions burned: 19 (million)
% 0.30/0.43 % (1732412)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.43 % (1732412)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
% 0.30/0.43 % (1732411)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2237049385:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.43 % (1732410)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1960269070:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.43 % (1732412)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=1345021223:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.43 % (1732417)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1736156635:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.43 % (1732417)Instruction limit reached!
% 0.30/0.43 % (1732417)------------------------------
% 0.30/0.43 % (1732417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732417)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732417)Termination reason: Instruction limit
% 0.30/0.43 % (1732417)Termination phase: shuffling
% 0.30/0.43 % (1732417)Time elapsed: 0.003 s
% 0.30/0.43 % (1732417)Peak memory usage: 10 MB
% 0.30/0.43 % (1732417)Instructions burned: 5 (million)
% 0.30/0.43 % (1732410)Instruction limit reached!
% 0.30/0.43 % (1732410)------------------------------
% 0.30/0.43 % (1732410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732410)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732410)Termination reason: Instruction limit
% 0.30/0.43 % (1732410)Termination phase: shuffling
% 0.30/0.43 % (1732410)Time elapsed: 0.012 s
% 0.30/0.43 % (1732410)Peak memory usage: 11 MB
% 0.30/0.43 % (1732410)Instructions burned: 25 (million)
% 0.30/0.43 % (1732418)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2731256709:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.30/0.43 % (1732418)Instruction limit reached!
% 0.30/0.43 % (1732418)------------------------------
% 0.30/0.43 % (1732418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732418)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732418)Termination reason: Instruction limit
% 0.30/0.43 % (1732418)Termination phase: shuffling
% 0.30/0.43 % (1732418)Time elapsed: 0.003 s
% 0.30/0.43 % (1732418)Peak memory usage: 10 MB
% 0.30/0.43 % (1732418)Instructions burned: 5 (million)
% 0.30/0.43 % (1732423)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.43 % (1732406)Instruction limit reached!
% 0.30/0.43 % (1732406)------------------------------
% 0.30/0.43 % (1732406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732406)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732406)Termination reason: Instruction limit
% 0.30/0.43 % (1732406)Termination phase: Clausification
% 0.30/0.43 % (1732406)Time elapsed: 0.042 s
% 0.30/0.43 % (1732406)Peak memory usage: 12 MB
% 0.30/0.43 % (1732406)Instructions burned: 87 (million)
% 0.30/0.43 % (1732423)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2578103926:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.30/0.43 % (1732424)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2474718379:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.30/0.43 % (1732426)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
% 0.30/0.43 % (1732426)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.30/0.43 % (1732423)Instruction limit reached!
% 0.30/0.43 % (1732423)------------------------------
% 0.30/0.43 % (1732423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732423)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732423)Termination reason: Instruction limit
% 0.30/0.43 % (1732423)Termination phase: shuffling
% 0.30/0.43 % (1732423)Time elapsed: 0.004 s
% 0.30/0.43 % (1732423)Peak memory usage: 10 MB
% 0.30/0.43 % (1732423)Instructions burned: 8 (million)
% 0.30/0.43 % (1732411)Instruction limit reached!
% 0.30/0.43 % (1732411)------------------------------
% 0.30/0.43 % (1732411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732411)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732411)Termination reason: Instruction limit
% 0.30/0.43 % (1732411)Termination phase: Preprocessing 3
% 0.30/0.43 % (1732411)Time elapsed: 0.038 s
% 0.30/0.43 % (1732411)Peak memory usage: 11 MB
% 0.30/0.43 % (1732411)Instructions burned: 75 (million)
% 0.30/0.43 % (1732426)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3245096395:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.30/0.43 % (1732424)Instruction limit reached!
% 0.30/0.43 % (1732424)------------------------------
% 0.30/0.43 % (1732424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732424)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732424)Termination reason: Instruction limit
% 0.30/0.43 % (1732424)Termination phase: shuffling
% 0.30/0.43 % (1732424)Time elapsed: 0.006 s
% 0.30/0.43 % (1732424)Peak memory usage: 10 MB
% 0.30/0.43 % (1732424)Instructions burned: 12 (million)
% 0.30/0.43 % (1732409) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1732401-1732409"...
% 0.30/0.43 % (1732409)...printing done.
% 0.30/0.43 % (1732427)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=1621245896:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.30/0.43 % (1732409)Refutation found. Thanks to Tanya!
% 0.30/0.43 % SZS status Theorem for theBenchmark
% 0.30/0.43 % SZS output start Proof for theBenchmark
% 0.30/0.43 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.30/0.43 thf(type_def_6, type, multiset: $tType > $tType).
% 0.30/0.43 thf(type_def_7, type, list: $tType > $tType).
% 0.30/0.43 thf(type_def_8, type, tree: $tType > $tType).
% 0.30/0.43 thf(type_def_9, type, set: $tType > $tType).
% 0.30/0.43 thf(type_def_10, type, a: $tType).
% 0.30/0.43 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.30/0.43 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_2, type, order: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_3, type, linorder: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_4, type, preorder: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_5, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_6, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_7, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_8, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_9, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_10, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_11, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_12, type, ordere623563068d_diff: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_13, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_14, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 0.30/0.43 thf(func_def_15, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.30/0.43 thf(func_def_16, type, unique455577585es_aux: !>[X0: $tType]:((product_prod @ X0 @ X0 > $o))).
% 0.30/0.43 thf(func_def_17, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.30/0.43 thf(func_def_18, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.30/0.43 thf(func_def_19, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_20, type, nO_MATCH: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o))).
% 0.30/0.43 thf(func_def_21, type, heapIm818251801eapify: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_22, type, heapIm1271749598e_left: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_23, type, heapIm1434396069_right: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_24, type, heapIm748920189ftDown: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_25, type, heap: !>[X0: $tType, X1: $tType]:((X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > tree @ X1) > (X0 > product_prod @ X1 @ X0) > $o))).
% 0.30/0.43 thf(func_def_26, type, heap_axioms: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > tree @ X1) > (X0 > product_prod @ X1 @ X0) > $o))).
% 0.30/0.43 thf(func_def_27, type, e: !>[X0: $tType]:(tree @ X0)).
% 0.30/0.43 thf(func_def_28, type, t: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_29, type, case_Tree: !>[X0: $tType, X1: $tType]:((X0 > (X1 > tree @ X1 > tree @ X1 > X0) > tree @ X1 > X0))).
% 0.30/0.43 thf(func_def_30, type, rec_Tree: !>[X0: $tType, X1: $tType]:((X0 > (X1 > tree @ X1 > tree @ X1 > X0 > X0 > X0) > tree @ X1 > X0))).
% 0.30/0.43 thf(func_def_31, type, in_tree: !>[X0: $tType]:((X0 > tree @ X0 > $o))).
% 0.30/0.43 thf(func_def_32, type, is_heap: !>[X0: $tType]:((tree @ X0 > $o))).
% 0.30/0.43 thf(func_def_33, type, multiset2: !>[X0: $tType]:((tree @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_34, type, val: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_35, type, lattic929149872er_Max: !>[X0: $tType]:((set @ X0 > X0))).
% 0.30/0.43 thf(func_def_36, type, add_mset: !>[X0: $tType]:((X0 > multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_37, type, comm_monoid_sum_mset: !>[X0: $tType]:(((X0 > X0 > X0) > X0 > multiset @ X0 > X0))).
% 0.30/0.43 thf(func_def_38, type, fold_mset: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > X1 > multiset @ X0 > X1))).
% 0.30/0.43 thf(func_def_39, type, is_empty: !>[X0: $tType]:((multiset @ X0 > $o))).
% 0.30/0.43 thf(func_def_40, type, mult: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0))).
% 0.30/0.43 thf(func_def_41, type, mult1: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ multiset @ X0 @ multiset @ X0))).
% 0.30/0.43 thf(func_def_42, type, multp: !>[X0: $tType]:(((X0 > X0 > $o) > multiset @ X0 > multiset @ X0 > $o))).
% 0.30/0.43 thf(func_def_43, type, set_mset: !>[X0: $tType]:((multiset @ X0 > set @ X0))).
% 0.30/0.43 thf(func_def_44, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.30/0.43 thf(func_def_45, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_46, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.30/0.43 thf(func_def_47, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.30/0.43 thf(func_def_48, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.30/0.43 thf(func_def_49, type, irrefl: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.43 thf(func_def_50, type, trans: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 0.30/0.43 thf(func_def_51, type, collection: !>[X0: $tType, X1: $tType]:((X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > $o))).
% 0.30/0.43 thf(func_def_52, type, set2: !>[X0: $tType, X1: $tType]:(((X0 > multiset @ X1) > X0 > set @ X1))).
% 0.30/0.43 thf(func_def_53, type, removeMax: !>[X0: $tType, X1: $tType]:((X0 > (X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > product_prod @ X1 @ X0) > (X0 > $o) > $o))).
% 0.30/0.43 thf(func_def_54, type, removeMax_axioms: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (list @ X1 > X0) > (X0 > multiset @ X1) > (X0 > product_prod @ X1 @ X0) > (X0 > $o) > $o))).
% 0.30/0.43 thf(func_def_55, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.30/0.43 thf(func_def_56, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.30/0.43 thf(func_def_57, type, l: tree @ a).
% 0.30/0.43 thf(func_def_58, type, r: tree @ a).
% 0.30/0.43 thf(func_def_59, type, v: a).
% 0.30/0.43 thf(func_def_63, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.30/0.43 thf(func_def_64, type, vNOT: ($o > $o)).
% 0.30/0.43 thf(func_def_65, type, db0: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_66, type, db1: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_67, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.30/0.43 thf(func_def_68, type, vAND: ($o > $o > $o)).
% 0.30/0.43 thf(func_def_69, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.30/0.43 thf(func_def_70, type, vIMP: ($o > $o > $o)).
% 0.30/0.43 thf(func_def_71, type, db7: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_72, type, db3: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_73, type, db4: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_74, type, db2: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_75, type, db5: !>[X0: $tType]:(X0)).
% 0.30/0.43 thf(func_def_76, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.30/0.43 thf(func_def_77, type, sP0: !>[X0: $tType, X1: $tType]:(((X0 > product_prod @ X1 @ X0) > (X0 > $o) > (X0 > $o) > $o))).
% 0.30/0.43 thf(func_def_78, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.30/0.43 thf(func_def_79, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.30/0.43 thf(func_def_80, type, sP3: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > $o))).
% 0.30/0.43 thf(func_def_81, type, sP4: !>[X0: $tType, X1: $tType]:(((X0 > tree @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > $o))).
% 0.30/0.43 thf(func_def_82, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X2))).
% 0.30/0.43 thf(func_def_83, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X4))).
% 0.30/0.43 thf(func_def_84, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X0))).
% 0.30/0.43 thf(func_def_85, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X3))).
% 0.30/0.43 thf(func_def_86, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > $o) > X1))).
% 0.30/0.43 thf(func_def_87, type, sK10: !>[X0: $tType]:((multiset @ X0 > X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_88, type, sK11: !>[X0: $tType]:((X0 > X0 > multiset @ X0 > multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_89, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > product_prod @ X1 @ X0) > (X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_90, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > product_prod @ X1 @ X0) > (X0 > $o) > (X0 > $o) > X1))).
% 0.30/0.43 thf(func_def_91, type, sK14: !>[X0: $tType, X1: $tType]:(((X0 > product_prod @ X1 @ X0) > (X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_92, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > multiset @ X0) > (X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_93, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > multiset @ X0) > (X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_94, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > multiset @ X0) > (X1 > $o) > X0))).
% 0.30/0.43 thf(func_def_95, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > multiset @ X0) > (X1 > $o) > X0))).
% 0.30/0.43 thf(func_def_96, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > multiset @ X0) > (X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_97, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > multiset @ X0) > (X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_98, type, sK21: !>[X0: $tType, X1: $tType]:(((list @ X0 > X1) > (X1 > $o) > list @ X0))).
% 0.30/0.43 thf(func_def_99, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.30/0.43 thf(func_def_100, type, sK23: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X1))).
% 0.30/0.43 thf(func_def_101, type, sK24: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X0))).
% 0.30/0.43 thf(func_def_102, type, sK25: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_103, type, sK26: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X1))).
% 0.30/0.43 thf(func_def_104, type, sK27: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > multiset @ X0))).
% 0.30/0.43 thf(func_def_105, type, sK28: !>[X0: $tType, X1: $tType]:(((multiset @ X0 > multiset @ X1 > $o) > X0))).
% 0.30/0.43 thf(func_def_106, type, sK29: !>[X0: $tType]:((multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_107, type, sK30: !>[X0: $tType]:((multiset @ X0 > X0))).
% 0.30/0.43 thf(func_def_108, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.30/0.43 thf(func_def_109, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.30/0.43 thf(func_def_110, type, sK33: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_111, type, sK34: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_112, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X2))).
% 0.30/0.43 thf(func_def_113, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X3))).
% 0.30/0.43 thf(func_def_114, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X0))).
% 0.30/0.43 thf(func_def_115, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ X2 > X1))).
% 0.30/0.43 thf(func_def_116, type, sK39: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.30/0.43 thf(func_def_117, type, sK40: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.30/0.43 thf(func_def_118, type, sK41: !>[X0: $tType]:(((multiset @ X0 > $o) > multiset @ X0))).
% 0.30/0.43 thf(func_def_119, type, sK42: !>[X0: $tType]:(((multiset @ X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_120, type, sK43: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.43 thf(func_def_121, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_122, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_123, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_124, type, sK47: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_125, type, sK48: !>[X0: $tType]:((X0 > multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_126, type, sK49: !>[X0: $tType]:((X0 > tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_127, type, sK50: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_128, type, sK51: !>[X0: $tType]:((X0 > tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_129, type, sK52: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_130, type, sK53: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_131, type, sK54: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_132, type, sK55: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_133, type, sK56: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_134, type, sK57: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_135, type, sK58: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_136, type, sK59: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_137, type, sK60: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_138, type, sK61: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_139, type, sK62: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_140, type, sK63: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_141, type, sK64: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_142, type, sK65: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_143, type, sK66: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_144, type, sK67: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_145, type, sK68: !>[X0: $tType]:((multiset @ multiset @ X0 > X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_146, type, sK69: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_147, type, sK70: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.30/0.43 thf(func_def_148, type, sK71: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_149, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_150, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_151, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.30/0.43 thf(func_def_152, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.30/0.43 thf(func_def_153, type, sK76: !>[X0: $tType]:((multiset @ X0 > X0))).
% 0.30/0.43 thf(func_def_154, type, sK77: !>[X0: $tType]:((multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_155, type, sK78: !>[X0: $tType]:((multiset @ X0 > X0))).
% 0.30/0.43 thf(func_def_156, type, sK79: !>[X0: $tType]:((multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0 > X0))).
% 0.30/0.43 thf(func_def_157, type, sK80: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_158, type, sK81: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_159, type, sK82: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_160, type, sK83: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.30/0.43 thf(func_def_161, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 0.30/0.43 thf(func_def_162, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 0.30/0.43 thf(func_def_163, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 0.30/0.43 thf(func_def_164, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X4))).
% 0.30/0.43 thf(func_def_165, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X3))).
% 0.30/0.43 thf(func_def_166, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ X0 > X5))).
% 0.30/0.43 thf(func_def_167, type, sK90: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_168, type, sK91: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_169, type, sK92: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_170, type, sK93: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_171, type, sK94: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_172, type, sK95: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_173, type, sK96: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_174, type, sK97: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_175, type, sK98: !>[X0: $tType]:((X0 > multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.43 thf(func_def_176, type, sK99: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.30/0.43 thf(func_def_177, type, sK100: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.30/0.43 thf(func_def_178, type, sK101: !>[X0: $tType]:((multiset @ multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_179, type, sK102: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.30/0.43 thf(func_def_180, type, sK103: !>[X0: $tType]:(((multiset @ X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_181, type, sK104: !>[X0: $tType]:(((multiset @ X0 > $o) > multiset @ X0))).
% 0.30/0.43 thf(func_def_182, type, sK105: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_183, type, sK106: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.30/0.43 thf(func_def_184, type, sK107: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.43 thf(func_def_185, type, sK108: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_186, type, sK109: !>[X0: $tType]:((multiset @ X0 > multiset @ X0 > set @ product_prod @ X0 @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_187, type, sK110: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > multiset @ X0 > multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_188, type, sK111: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0 > multiset @ X0 > multiset @ X0 > multiset @ X0))).
% 0.30/0.43 thf(func_def_189, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X5 > $o) > X4))).
% 0.30/0.43 thf(func_def_190, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X5 > $o) > X5))).
% 0.30/0.43 thf(func_def_191, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X5 > $o) > X3))).
% 0.30/0.43 thf(func_def_192, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X5 > $o) > X0))).
% 0.30/0.43 thf(func_def_193, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X5 > $o) > X1))).
% 0.30/0.43 thf(func_def_194, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ X5 > $o) > X2))).
% 0.30/0.43 thf(func_def_195, type, sK118: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.30/0.43 thf(func_def_196, type, sK119: !>[X0: $tType]:(((tree @ X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_197, type, sK120: !>[X0: $tType]:(((tree @ X0 > $o) > tree @ X0))).
% 0.30/0.43 thf(func_def_198, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X5))).
% 0.30/0.43 thf(func_def_199, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X6))).
% 0.30/0.43 thf(func_def_200, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X2))).
% 0.30/0.43 thf(func_def_201, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X0))).
% 0.30/0.43 thf(func_def_202, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X1))).
% 0.30/0.43 thf(func_def_203, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X3))).
% 0.30/0.43 thf(func_def_204, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X1 @ X5 > $o) > X4))).
% 0.30/0.43 thf(func_def_205, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > X2))).
% 0.30/0.43 thf(func_def_206, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > X4))).
% 0.30/0.43 thf(func_def_207, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > X1))).
% 0.30/0.43 thf(func_def_208, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > X3))).
% 0.30/0.43 thf(func_def_209, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X2 @ X1 > X0))).
% 0.30/0.43 thf(func_def_210, type, sK133: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.43 thf(func_def_211, type, sK134: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.43 thf(func_def_212, type, sK135: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 0.30/0.43 thf(func_def_213, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.30/0.43 thf(func_def_214, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.30/0.43 thf(func_def_215, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.30/0.43 thf(func_def_216, type, sK139: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_217, type, sK140: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_218, type, sK141: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_219, type, sK142: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_220, type, sK143: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_221, type, sK144: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_222, type, sK145: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_223, type, sK146: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_224, type, sK147: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_225, type, sK148: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_226, type, sK149: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_227, type, sK150: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_228, type, sK151: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_229, type, sK152: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_230, type, sK153: !>[X0: $tType]:((tree @ X0 > tree @ X0))).
% 0.30/0.43 thf(func_def_231, type, sK154: !>[X0: $tType]:((tree @ X0 > X0))).
% 0.30/0.43 thf(func_def_232, type, sK155: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X4))).
% 0.30/0.43 thf(func_def_233, type, sK156: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X1))).
% 0.30/0.43 thf(func_def_234, type, sK157: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X5))).
% 0.30/0.43 thf(func_def_235, type, sK158: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X0))).
% 0.30/0.43 thf(func_def_236, type, sK159: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X6))).
% 0.30/0.43 thf(func_def_237, type, sK160: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X2))).
% 0.30/0.43 thf(func_def_238, type, sK161: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X6 @ X2 > X3))).
% 0.30/0.43 thf(func_def_239, type, sK162: !>[X0: $tType, X1: $tType]:(((X0 > tree @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > X0))).
% 0.30/0.43 thf(func_def_240, type, sK163: !>[X0: $tType, X1: $tType]:(((X0 > tree @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > X1))).
% 0.30/0.43 thf(func_def_241, type, sK164: !>[X0: $tType, X1: $tType]:(((X0 > tree @ X1) > (X0 > $o) > (X0 > product_prod @ X1 @ X0) > X0))).
% 0.30/0.43 thf(func_def_242, type, sK165: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > X0))).
% 0.30/0.43 thf(func_def_243, type, sK166: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > X1))).
% 0.30/0.43 thf(func_def_244, type, sK167: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > product_prod @ X0 @ X1) > (X1 > tree @ X0) > X1))).
% 0.30/0.43 thf(func_def_245, type, sK168: !>[X0: $tType, X1: $tType]:(((list @ X0 > X1) > (X1 > tree @ X0) > list @ X0))).
% 0.30/0.43 thf(func_def_246, type, sK169: !>[X0: $tType, X1: $tType]:(((X1 > multiset @ X0) > (X1 > product_prod @ X0 @ X1) > (X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_247, type, sK170: !>[X0: $tType, X1: $tType]:(((X1 > multiset @ X0) > (X1 > product_prod @ X0 @ X1) > (X1 > $o) > X0))).
% 0.30/0.43 thf(func_def_248, type, sK171: !>[X0: $tType, X1: $tType]:(((X1 > multiset @ X0) > (X1 > product_prod @ X0 @ X1) > (X1 > $o) > X1))).
% 0.30/0.43 thf(func_def_249, type, sK172: !>[X0: $tType, X1: $tType]:(((X1 > multiset @ X0) > (X1 > tree @ X0) > X1))).
% 0.30/0.43 thf(func_def_250, type, sK173: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > tree @ X0) > X1))).
% 0.30/0.43 thf(func_def_251, type, sK174: !>[X0: $tType]:(((multiset @ X0 > $o) > multiset @ X0))).
% 0.30/0.43 thf(func_def_252, type, sK175: !>[X0: $tType]:(((multiset @ X0 > $o) > X0))).
% 0.30/0.43 thf(func_def_253, type, sK176: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_254, type, sK177: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X3))).
% 0.30/0.43 thf(func_def_255, type, sK178: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.30/0.43 thf(func_def_256, type, sK179: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.30/0.43 thf(func_def_257, type, sK180: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.30/0.43 thf(func_def_258, type, sK181: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.30/0.43 thf(func_def_259, type, sK182: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.30/0.43 thf(func_def_260, type, sK183: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_261, type, sK184: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.30/0.43 thf(func_def_262, type, sK185: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > multiset @ X0 > X0 > X0))).
% 0.30/0.43 thf(f1,axiom,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ r))),
% 0.30/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_T_Ohyps_I2_J)).
% 0.30/0.43 thf(f2,axiom,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ l))),
% 0.30/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_T_Ohyps_I1_J)).
% 0.30/0.43 thf(f3,axiom,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ l)) => ((is_heap @ a @ (heapIm818251801eapify @ a @ r)) => ((((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))) = ((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r)))) => (is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))))),
% 0.30/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062)).
% 0.30/0.43 thf(f4,axiom,(
% 0.30/0.43 ! [X0 : $tType] : (linorder @ X0 => ! [X3 : tree @ X0,X1 : X0,X2 : tree @ X0] : (((heapIm818251801eapify @ X0 @ (t @ X0 @ X1 @ X2 @ X3))) = ((heapIm748920189ftDown @ X0 @ (t @ X0 @ X1 @ (heapIm818251801eapify @ X0 @ X2) @ (heapIm818251801eapify @ X0 @ X3))))))),
% 0.30/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_heapify_Osimps_I2_J)).
% 0.30/0.43 thf(f275,axiom,(
% 0.30/0.43 linorder @ a),
% 0.30/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0)).
% 0.30/0.43 thf(f276,conjecture,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))),
% 0.30/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.30/0.43 thf(f277,negated_conjecture,(
% 0.30/0.43 ~(is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))),
% 0.30/0.43 inference(negated_conjecture,[status(cth)],[f276])).
% 0.30/0.43 thf(f366,plain,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ r))),
% 0.30/0.43 inference(rectify,[],[f1])).
% 0.30/0.43 thf(f367,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) = $true)),
% 0.30/0.43 inference(fool_elimination,[],[f366])).
% 0.30/0.43 thf(f453,plain,(
% 0.30/0.43 ! [X0 : $tType] : (linorder @ X0 => ! [X1 : tree @ X0,X2 : X0,X3 : tree @ X0] : (((heapIm748920189ftDown @ X0 @ (t @ X0 @ X2 @ (heapIm818251801eapify @ X0 @ X3) @ (heapIm818251801eapify @ X0 @ X1)))) = ((heapIm818251801eapify @ X0 @ (t @ X0 @ X2 @ X3 @ X1)))))),
% 0.30/0.43 inference(rectify,[],[f4])).
% 0.30/0.43 thf(f454,plain,(
% 0.30/0.43 ! [X0 : $tType] : ((linorder @ X0 = $true) => ! [X3 : tree @ X0,X1 : tree @ X0,X2 : X0] : (((heapIm748920189ftDown @ X0 @ (t @ X0 @ X2 @ (heapIm818251801eapify @ X0 @ X3) @ (heapIm818251801eapify @ X0 @ X1)))) = ((heapIm818251801eapify @ X0 @ (t @ X0 @ X2 @ X3 @ X1)))))),
% 0.30/0.43 inference(fool_elimination,[],[f453])).
% 0.30/0.43 thf(f616,plain,(
% 0.30/0.43 linorder @ a),
% 0.30/0.43 inference(rectify,[],[f275])).
% 0.30/0.43 thf(f617,plain,(
% 0.30/0.43 (linorder @ a = $true)),
% 0.30/0.43 inference(fool_elimination,[],[f616])).
% 0.30/0.43 thf(f695,plain,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ l)) => ((is_heap @ a @ (heapIm818251801eapify @ a @ r)) => ((((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))) = ((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r)))) => (is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))))),
% 0.30/0.43 inference(rectify,[],[f3])).
% 0.30/0.43 thf(f696,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) = $true) => ((((is_heap @ a @ (heapIm818251801eapify @ a @ r))) = $true) => ((((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))) = ((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r)))) => (((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true)))),
% 0.30/0.43 inference(fool_elimination,[],[f695])).
% 0.30/0.43 thf(f708,plain,(
% 0.30/0.43 ~(is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))),
% 0.30/0.43 inference(rectify,[],[f277])).
% 0.30/0.43 thf(f709,plain,(
% 0.30/0.43 ~ (((is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))) = $true)),
% 0.30/0.43 inference(fool_elimination,[],[f708])).
% 0.30/0.43 thf(f714,plain,(
% 0.30/0.43 (is_heap @ a @ (heapIm818251801eapify @ a @ l))),
% 0.30/0.43 inference(rectify,[],[f2])).
% 0.30/0.43 thf(f715,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) = $true)),
% 0.30/0.43 inference(fool_elimination,[],[f714])).
% 0.30/0.43 thf(f779,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))) != $true)),
% 0.30/0.43 inference(flattening,[],[f709])).
% 0.30/0.43 thf(f788,plain,(
% 0.30/0.43 (((((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true) | (((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))) != ((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) | (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) != $true)) | (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) != $true)),
% 0.30/0.43 inference(ennf_transformation,[],[f696])).
% 0.30/0.43 thf(f789,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true) | (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) != $true) | (((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))) != ((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r)))) | (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) != $true)),
% 0.30/0.43 inference(flattening,[],[f788])).
% 0.30/0.43 thf(f1012,plain,(
% 0.30/0.43 ! [X0 : $tType] : ((linorder @ X0 != $true) | ! [X3 : tree @ X0,X1 : tree @ X0,X2 : X0] : (((heapIm748920189ftDown @ X0 @ (t @ X0 @ X2 @ (heapIm818251801eapify @ X0 @ X3) @ (heapIm818251801eapify @ X0 @ X1)))) = ((heapIm818251801eapify @ X0 @ (t @ X0 @ X2 @ X3 @ X1)))))),
% 0.30/0.43 inference(ennf_transformation,[],[f454])).
% 0.30/0.43 thf(f1268,plain,(
% 0.30/0.43 ! [X0 : $tType] : ((linorder @ X0 != $true) | ! [X1 : tree @ X0,X2 : tree @ X0,X3 : X0] : (((heapIm818251801eapify @ X0 @ (t @ X0 @ X3 @ X1 @ X2))) = ((heapIm748920189ftDown @ X0 @ (t @ X0 @ X3 @ (heapIm818251801eapify @ X0 @ X1) @ (heapIm818251801eapify @ X0 @ X2))))))),
% 0.30/0.43 inference(rectify,[],[f1012])).
% 0.30/0.43 thf(f1369,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) != $true) | (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) != $true) | (((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))) != ((t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r)))) | (((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true)),
% 0.30/0.43 inference(cnf_transformation,[],[f789])).
% 0.30/0.43 thf(f1476,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) = $true)),
% 0.30/0.43 inference(cnf_transformation,[],[f367])).
% 0.30/0.43 thf(f1622,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) = $true)),
% 0.30/0.43 inference(cnf_transformation,[],[f715])).
% 0.30/0.43 thf(f1681,plain,(
% 0.30/0.43 (linorder @ a = $true)),
% 0.30/0.43 inference(cnf_transformation,[],[f617])).
% 0.30/0.43 thf(f1686,plain,(
% 0.30/0.43 ( ! [X0 : $tType,X2 : tree @ X0,X3 : X0,X1 : tree @ X0] : ((((heapIm818251801eapify @ X0 @ (t @ X0 @ X3 @ X1 @ X2))) = ((heapIm748920189ftDown @ X0 @ (t @ X0 @ X3 @ (heapIm818251801eapify @ X0 @ X1) @ (heapIm818251801eapify @ X0 @ X2))))) | (linorder @ X0 != $true)) )),
% 0.30/0.43 inference(cnf_transformation,[],[f1268])).
% 0.30/0.43 thf(f1735,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))) != $true)),
% 0.30/0.43 inference(cnf_transformation,[],[f779])).
% 0.30/0.43 thf(f1901,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true) | (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) != $true) | (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) != $true)),
% 0.30/0.43 inference(trivial_inequality_removal,[],[f1369])).
% 0.30/0.43 thf(f1926,definition,(
% 0.30/0.43 spl186_1 <=> (((is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))) = $true)),
% 0.30/0.43 introduced(definition,[new_symbols(definition,[spl186_1])],[avatar_definition])).
% 0.30/0.43 thf(f1928,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))) != $true) | spl186_1),
% 0.30/0.43 inference(avatar_component_clause,[],[f1926])).
% 0.30/0.43 thf(f1929,plain,(
% 0.30/0.43 ~spl186_1),
% 0.30/0.43 inference(avatar_split_clause,[],[f1735,f1926])).
% 0.30/0.43 thf(f1941,definition,(
% 0.30/0.43 spl186_4 <=> (((is_heap @ a @ (heapIm818251801eapify @ a @ l))) = $true)),
% 0.30/0.43 introduced(definition,[new_symbols(definition,[spl186_4])],[avatar_definition])).
% 0.30/0.43 thf(f1944,plain,(
% 0.30/0.43 spl186_4),
% 0.30/0.43 inference(avatar_split_clause,[],[f1622,f1941])).
% 0.30/0.43 thf(f1951,definition,(
% 0.30/0.43 spl186_6 <=> (((is_heap @ a @ (heapIm818251801eapify @ a @ r))) = $true)),
% 0.30/0.43 introduced(definition,[new_symbols(definition,[spl186_6])],[avatar_definition])).
% 0.30/0.43 thf(f1954,plain,(
% 0.30/0.43 spl186_6),
% 0.30/0.43 inference(avatar_split_clause,[],[f1476,f1951])).
% 0.30/0.43 thf(f1956,definition,(
% 0.30/0.43 spl186_7 <=> (((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true)),
% 0.30/0.43 introduced(definition,[new_symbols(definition,[spl186_7])],[avatar_definition])).
% 0.30/0.43 thf(f1958,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm748920189ftDown @ a @ (t @ a @ v @ (heapIm818251801eapify @ a @ l) @ (heapIm818251801eapify @ a @ r))))) = $true) | ~spl186_7),
% 0.30/0.43 inference(avatar_component_clause,[],[f1956])).
% 0.30/0.43 thf(f1959,plain,(
% 0.30/0.43 spl186_7 | ~spl186_6 | ~spl186_4),
% 0.30/0.43 inference(avatar_split_clause,[],[f1901,f1941,f1951,f1956])).
% 0.30/0.43 thf(f1966,definition,(
% 0.30/0.43 spl186_9 <=> (linorder @ a = $true)),
% 0.30/0.43 introduced(definition,[new_symbols(definition,[spl186_9])],[avatar_definition])).
% 0.30/0.43 thf(f1968,plain,(
% 0.30/0.43 (linorder @ a = $true) | ~spl186_9),
% 0.30/0.43 inference(avatar_component_clause,[],[f1966])).
% 0.30/0.43 thf(f1969,plain,(
% 0.30/0.43 spl186_9),
% 0.30/0.43 inference(avatar_split_clause,[],[f1681,f1966])).
% 0.30/0.43 thf(f2136,plain,(
% 0.30/0.43 (((is_heap @ a @ (heapIm818251801eapify @ a @ (t @ a @ v @ l @ r)))) = $true) | (linorder @ a != $true) | ~spl186_7),
% 0.30/0.43 inference(superposition,[],[f1958,f1686])).
% 0.30/0.43 thf(f2141,plain,(
% 0.30/0.43 (linorder @ a != $true) | (spl186_1 | ~spl186_7)),
% 0.30/0.43 inference(forward_subsumption_resolution,[],[f2136,f1928])).
% 0.30/0.43 thf(f2142,plain,(
% 0.30/0.43 $false | (spl186_1 | ~spl186_7 | ~spl186_9)),
% 0.30/0.43 inference(forward_subsumption_resolution,[],[f2141,f1968])).
% 0.30/0.43 thf(f2143,plain,(
% 0.30/0.43 spl186_1 | ~spl186_7 | ~spl186_9),
% 0.30/0.43 inference(avatar_contradiction_clause,[],[f2142])).
% 0.30/0.43 cnf(s1, plain, ~spl186_1, inference(sat_conversion,[],[f1929])).
% 0.30/0.43 cnf(s4, plain, spl186_4, inference(sat_conversion,[],[f1944])).
% 0.30/0.43 cnf(s6, plain, spl186_6, inference(sat_conversion,[],[f1954])).
% 0.30/0.43 cnf(s7, plain, ~spl186_4 | ~spl186_6 | spl186_7, inference(sat_conversion,[],[f1959])).
% 0.30/0.43 cnf(s9, plain, spl186_9, inference(sat_conversion,[],[f1969])).
% 0.30/0.43 cnf(s14, plain, spl186_1 | ~spl186_7 | ~spl186_9, inference(sat_conversion,[],[f2143])).
% 0.30/0.43 cnf(s15, plain, spl186_7, inference(rat,[],[s7,s6,s4])).
% 0.30/0.43 cnf(s16, plain, spl186_1, inference(rat,[],[s14,s9,s15])).
% 0.30/0.43 cnf(s17, plain, $false, inference(rat,[],[s1,s16])).
% 0.30/0.43 thf(f2144,plain,(
% 0.30/0.43 $false),
% 0.30/0.43 inference(avatar_sat_refutation,[],[s17])).
% 0.30/0.43 % SZS output end Proof for theBenchmark
% 0.30/0.43 % (1732409)------------------------------
% 0.30/0.43 % (1732409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.43 % (1732409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.43 % (1732409)CaDiCaL version: 2.1.3
% 0.30/0.43 % (1732409)Termination reason: Refutation
% 0.30/0.43 % (1732409)Time elapsed: 0.063 s
% 0.30/0.43 % (1732409)Peak memory usage: 15 MB
% 0.30/0.43 % (1732409)Instructions burned: 223 (million)
% 0.30/0.43 % (1732401)Success in time 0.12 s
% 0.30/0.43 % Vampire exiting
%------------------------------------------------------------------------------