%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP113^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:08:24 AM UTC 2026
% Result : Theorem 0.22s 0.38s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP113^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n015.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 19:58:49 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.37 % (4035539)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.37 % (4035547)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=1936597751: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)
% 0.22/0.37 % (4035550)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.37 % (4035550)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
% 0.22/0.37 % (4035549)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3431670598:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.37 % (4035546)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3006190019:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.37 % (4035545)lrs+10_16_si=on:nwc=1.5:random_seed=31846809:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.37 % (4035544)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3072991745:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.37 % (4035548)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=594374025:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.37 % (4035550)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=1005148560:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.37 % (4035546)Instruction limit reached!
% 0.22/0.37 % (4035546)------------------------------
% 0.22/0.37 % (4035546)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (4035546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (4035546)CaDiCaL version: 2.1.3
% 0.22/0.37 % (4035546)Termination reason: Instruction limit
% 0.22/0.37 % (4035546)Termination phase: shuffling
% 0.22/0.37 % (4035546)Time elapsed: 0.003 s
% 0.22/0.37 % (4035546)Peak memory usage: 10 MB
% 0.22/0.37 % (4035546)Instructions burned: 5 (million)
% 0.22/0.37 % (4035548)Instruction limit reached!
% 0.22/0.37 % (4035548)------------------------------
% 0.22/0.37 % (4035548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (4035548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (4035548)CaDiCaL version: 2.1.3
% 0.22/0.37 % (4035548)Termination reason: Instruction limit
% 0.22/0.37 % (4035548)Termination phase: Property scanning
% 0.22/0.37 % (4035548)Time elapsed: 0.012 s
% 0.22/0.37 % (4035548)Peak memory usage: 10 MB
% 0.22/0.37 % (4035548)Instructions burned: 24 (million)
% 0.22/0.37 % (4035545)Instruction limit reached!
% 0.22/0.37 % (4035545)------------------------------
% 0.22/0.37 % (4035545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (4035545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (4035545)CaDiCaL version: 2.1.3
% 0.22/0.37 % (4035545)Termination reason: Instruction limit
% 0.22/0.37 % (4035545)Termination phase: Property scanning
% 0.22/0.37 % (4035545)Time elapsed: 0.016 s
% 0.22/0.37 % (4035545)Peak memory usage: 10 MB
% 0.22/0.37 % (4035545)Instructions burned: 19 (million)
% 0.22/0.37 % (4035558)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2815870131:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.37 % (4035558)Instruction limit reached!
% 0.22/0.37 % (4035558)------------------------------
% 0.22/0.37 % (4035558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (4035558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (4035558)CaDiCaL version: 2.1.3
% 0.22/0.37 % (4035558)Termination reason: Instruction limit
% 0.22/0.37 % (4035558)Termination phase: shuffling
% 0.22/0.37 % (4035558)Time elapsed: 0.002 s
% 0.22/0.37 % (4035558)Peak memory usage: 10 MB
% 0.22/0.37 % (4035558)Instructions burned: 3 (million)
% 0.22/0.37 % (4035547) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4035539-4035547"...
% 0.22/0.37 % (4035549)Instruction limit reached!
% 0.22/0.37 % (4035549)------------------------------
% 0.22/0.37 % (4035549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (4035549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (4035549)CaDiCaL version: 2.1.3
% 0.22/0.37 % (4035549)Termination reason: Instruction limit
% 0.22/0.37 % (4035549)Termination phase: Equality resolution with deletion
% 0.22/0.37 % (4035549)Time elapsed: 0.038 s
% 0.22/0.37 % (4035549)Peak memory usage: 12 MB
% 0.22/0.37 % (4035549)Instructions burned: 78 (million)
% 0.22/0.37 % (4035547)...printing done.
% 0.22/0.37 % (4035559)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1947752428:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.37 % (4035544)Instruction limit reached!
% 0.22/0.37 % (4035544)------------------------------
% 0.22/0.37 % (4035544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.37 % (4035544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.37 % (4035544)CaDiCaL version: 2.1.3
% 0.22/0.37 % (4035544)Termination reason: Instruction limit
% 0.22/0.38 % (4035544)Termination phase: Property scanning
% 0.22/0.38 % (4035544)Time elapsed: 0.043 s
% 0.22/0.38 % (4035544)Peak memory usage: 12 MB
% 0.22/0.38 % (4035544)Instructions burned: 88 (million)
% 0.22/0.38 % (4035547)Refutation found. Thanks to Tanya!
% 0.22/0.38 % SZS status Theorem for theBenchmark
% 0.22/0.38 % SZS output start Proof for theBenchmark
% 0.22/0.38 thf(type_def_5, type, extended_ereal: $tType).
% 0.22/0.38 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.22/0.38 thf(type_def_7, type, real: $tType).
% 0.22/0.38 thf(type_def_8, type, set: $tType > $tType).
% 0.22/0.38 thf(type_def_9, type, nat: $tType).
% 0.22/0.38 thf(type_def_10, type, a: $tType).
% 0.22/0.38 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.38 thf(func_def_0, type, euclid925273238_space: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_4, type, top: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_6, type, no_bot: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_7, type, no_top: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_8, type, linorder: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_9, type, preorder: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_10, type, order_top: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_12, type, dense_order: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_13, type, linordered_field: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_14, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_15, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_16, type, topolo890362671_space: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_17, type, real_V1759440057_space: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_18, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_19, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_20, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_21, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_22, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_23, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.22/0.38 thf(func_def_24, type, elementary_closure: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.22/0.38 thf(func_def_25, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_26, type, lower_261390618igraph: !>[X0: $tType]:((set @ X0 > (X0 > extended_ereal) > set @ product_prod @ X0 @ real))).
% 0.22/0.38 thf(func_def_27, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.38 thf(func_def_28, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.38 thf(func_def_29, type, top_top: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_30, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.22/0.38 thf(func_def_31, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.22/0.38 thf(func_def_32, type, real_V2000881966t_dist: !>[X0: $tType]:((X0 > X0 > real))).
% 0.22/0.38 thf(func_def_33, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.22/0.38 thf(func_def_34, type, unifor760693226chy_on: !>[X0: $tType, X1: $tType]:((set @ X0 > (nat > X0 > X1) > $o))).
% 0.22/0.38 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.22/0.38 thf(func_def_36, type, e: real).
% 0.22/0.38 thf(func_def_37, type, f: (a > extended_ereal)).
% 0.22/0.38 thf(func_def_38, type, thesis: $o).
% 0.22/0.38 thf(func_def_39, type, x: a).
% 0.22/0.38 thf(func_def_40, type, y: real).
% 0.22/0.38 thf(func_def_41, type, z: real).
% 0.22/0.38 thf(func_def_45, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_46, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.38 thf(func_def_47, type, vAND: ($o > $o > $o)).
% 0.22/0.38 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_49, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.38 thf(func_def_50, type, vNOT: ($o > $o)).
% 0.22/0.38 thf(func_def_51, type, vOR: ($o > $o > $o)).
% 0.22/0.38 thf(func_def_52, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.38 thf(func_def_53, type, vIMP: ($o > $o > $o)).
% 0.22/0.38 thf(func_def_54, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.38 thf(func_def_56, type, db4: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_57, type, db3: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_58, type, db5: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_59, type, sP0: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (nat > X1 > X0) > $o))).
% 0.22/0.38 thf(func_def_60, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.38 thf(func_def_61, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.22/0.38 thf(func_def_62, type, sK3: (nat > (nat > $o) > nat)).
% 0.22/0.38 thf(func_def_63, type, sK4: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_64, type, sK5: !>[X0: $tType]:((X0 > set @ X0 > real))).
% 0.22/0.38 thf(func_def_65, type, sK6: !>[X0: $tType]:((real > X0 > set @ X0 > X0))).
% 0.22/0.38 thf(func_def_66, type, sK7: !>[X0: $tType]:(X0)).
% 0.22/0.38 thf(func_def_67, type, sK8: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.22/0.38 thf(func_def_68, type, sK9: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.22/0.38 thf(func_def_69, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_70, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_71, type, sK12: (real > set @ real > real)).
% 0.22/0.38 thf(func_def_72, type, sK13: (set @ real > real)).
% 0.22/0.38 thf(func_def_73, type, sK14: (real > set @ real > real)).
% 0.22/0.38 thf(func_def_74, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_75, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_76, type, sK17: ((nat > $o) > nat > nat)).
% 0.22/0.38 thf(func_def_77, type, sK18: ((nat > $o) > nat > nat)).
% 0.22/0.38 thf(func_def_78, type, sK19: ((nat > $o) > nat)).
% 0.22/0.38 thf(func_def_79, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_80, type, sK21: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_81, type, sK22: !>[X0: $tType]:((set @ X0 > X0 > real > X0))).
% 0.22/0.38 thf(func_def_82, type, sK23: ((nat > $o) > nat)).
% 0.22/0.38 thf(func_def_83, type, sK24: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.22/0.38 thf(func_def_84, type, sK25: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.22/0.38 thf(func_def_85, type, sK26: (nat > (nat > real) > nat)).
% 0.22/0.38 thf(func_def_86, type, sK27: (nat > (nat > real) > (nat > real) > nat)).
% 0.22/0.38 thf(func_def_87, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_88, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_89, type, sK30: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_90, type, sK31: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_91, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_92, type, sK33: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_93, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_94, type, sK35: !>[X0: $tType]:((set @ X0 > X0 > real))).
% 0.22/0.38 thf(func_def_95, type, sK36: !>[X0: $tType]:((real > set @ X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_96, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_97, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_98, type, sK39: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.22/0.38 thf(func_def_99, type, sK40: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_100, type, sK41: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.22/0.38 thf(func_def_101, type, sK42: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.22/0.38 thf(func_def_102, type, sK43: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_103, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (nat > X1 > X0) > real))).
% 0.22/0.38 thf(func_def_104, type, sK45: !>[X0: $tType, X1: $tType]:((nat > (X1 > $o) > (nat > X1 > X0) > nat))).
% 0.22/0.38 thf(func_def_105, type, sK46: !>[X0: $tType, X1: $tType]:((nat > (X1 > $o) > (nat > X1 > X0) > nat))).
% 0.22/0.38 thf(func_def_106, type, sK47: !>[X0: $tType, X1: $tType]:((nat > (X1 > $o) > (nat > X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_107, type, sK48: !>[X0: $tType, X1: $tType]:((real > (nat > X0 > X1) > (X0 > $o) > (X0 > X1) > nat))).
% 0.22/0.38 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType]:(((nat > X0 > X1) > (X0 > $o) > (X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_109, type, sK50: !>[X0: $tType, X1: $tType]:(((nat > X0 > X1) > (X0 > $o) > (X0 > X1) > real))).
% 0.22/0.38 thf(func_def_110, type, sK51: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > (X0 > $o) > (X0 > X1) > nat))).
% 0.22/0.38 thf(func_def_111, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.22/0.38 thf(func_def_112, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.22/0.38 thf(func_def_113, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.22/0.38 thf(func_def_114, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.22/0.38 thf(func_def_115, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_116, type, sK57: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_117, type, sK58: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_118, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_119, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.22/0.38 thf(func_def_120, type, sK61: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_121, type, sK62: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_122, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X3))).
% 0.22/0.38 thf(func_def_123, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X1))).
% 0.22/0.38 thf(func_def_124, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X4))).
% 0.22/0.38 thf(func_def_125, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X0))).
% 0.22/0.38 thf(func_def_126, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ X2 > X2))).
% 0.22/0.38 thf(func_def_127, type, sK68: !>[X0: $tType]:((set @ X0 > X0))).
% 0.22/0.38 thf(func_def_128, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_129, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_130, type, sK71: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 0.22/0.38 thf(func_def_131, type, sK72: !>[X0: $tType]:(((X0 > $o) > nat > (X0 > nat) > X0))).
% 0.22/0.38 thf(func_def_132, type, sK73: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_133, type, sK74: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_134, type, sK75: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_135, type, sK76: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_136, type, sK77: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_137, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X2))).
% 0.22/0.38 thf(func_def_138, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X5))).
% 0.22/0.38 thf(func_def_139, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X6))).
% 0.22/0.38 thf(func_def_140, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X4))).
% 0.22/0.38 thf(func_def_141, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X3))).
% 0.22/0.38 thf(func_def_142, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X0))).
% 0.22/0.38 thf(func_def_143, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ X6 > $o) > X1))).
% 0.22/0.38 thf(func_def_144, type, sK85: !>[X0: $tType]:(((X0 > real) > (X0 > $o) > (X0 > $o) > real))).
% 0.22/0.38 thf(func_def_145, type, sK86: !>[X0: $tType]:((real > (X0 > real) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_146, type, sK87: !>[X0: $tType]:(((X0 > real) > (X0 > $o) > (X0 > $o) > real))).
% 0.22/0.38 thf(func_def_147, type, sK88: !>[X0: $tType]:((real > (X0 > real) > (X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_148, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X5 > X3))).
% 0.22/0.38 thf(func_def_149, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X5 > X4))).
% 0.22/0.38 thf(func_def_150, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X5 > X2))).
% 0.22/0.38 thf(func_def_151, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X5 > X0))).
% 0.22/0.38 thf(func_def_152, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X5 > X1))).
% 0.22/0.38 thf(func_def_153, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X1 @ X5 > X5))).
% 0.22/0.38 thf(func_def_154, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_155, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_156, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.22/0.38 thf(func_def_157, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.22/0.38 thf(func_def_158, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X4))).
% 0.22/0.38 thf(func_def_159, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.22/0.38 thf(func_def_160, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X3))).
% 0.22/0.38 thf(func_def_161, type, sK102: product_prod @ a @ real).
% 0.22/0.38 thf(func_def_162, type, sK103: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.22/0.38 thf(func_def_163, type, sK104: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.22/0.38 thf(func_def_164, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X1))).
% 0.22/0.38 thf(func_def_165, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X2))).
% 0.22/0.38 thf(func_def_166, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X3))).
% 0.22/0.38 thf(func_def_167, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X0))).
% 0.22/0.38 thf(func_def_168, type, sK109: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_169, type, sK110: !>[X0: $tType]:((X0 > X0 > set @ X0 > X0))).
% 0.22/0.38 thf(func_def_170, type, sK111: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_171, type, sK112: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.22/0.38 thf(func_def_172, type, sK113: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_173, type, sK114: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_174, type, sK115: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.38 thf(func_def_175, type, sK116: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_176, type, sK117: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.38 thf(func_def_177, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X1))).
% 0.22/0.38 thf(func_def_178, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X5))).
% 0.22/0.38 thf(func_def_179, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X4))).
% 0.22/0.38 thf(func_def_180, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X0))).
% 0.22/0.38 thf(func_def_181, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X2))).
% 0.22/0.38 thf(func_def_182, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X3))).
% 0.22/0.38 thf(func_def_183, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X6 @ product_prod @ X3 @ X5 > X6))).
% 0.22/0.38 thf(func_def_184, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ X1 > $o) > X2))).
% 0.22/0.38 thf(func_def_185, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ X1 > $o) > X0))).
% 0.22/0.38 thf(func_def_186, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ X1 > $o) > X5))).
% 0.22/0.38 thf(func_def_187, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ X1 > $o) > X4))).
% 0.22/0.38 thf(func_def_188, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ X1 > $o) > X3))).
% 0.22/0.38 thf(func_def_189, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ X1 > $o) > X1))).
% 0.22/0.38 thf(func_def_190, type, sK131: ((nat > nat) > nat)).
% 0.22/0.38 thf(func_def_191, type, sK132: ((nat > nat) > nat)).
% 0.22/0.38 thf(func_def_192, type, sK133: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.38 thf(func_def_193, type, sK134: !>[X0: $tType]:((X0 > X0))).
% 0.22/0.38 thf(func_def_194, type, sK135: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 0.22/0.38 thf(func_def_195, type, sK136: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 0.22/0.38 thf(func_def_196, type, sK137: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 0.22/0.38 thf(func_def_197, type, sK138: ((nat > $o) > nat)).
% 0.22/0.38 thf(func_def_198, type, sK139: (nat > (nat > $o) > nat)).
% 0.22/0.38 thf(func_def_199, type, sK140: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_200, type, sK141: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.22/0.38 thf(func_def_201, type, sK142: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.22/0.38 thf(func_def_202, type, sK143: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.22/0.38 thf(func_def_203, type, sK144: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_204, type, sK145: !>[X0: $tType, X1: $tType]:(((nat > X1 > X0) > set @ X1 > real))).
% 0.22/0.38 thf(func_def_205, type, sK146: !>[X0: $tType, X1: $tType]:((nat > (nat > X1 > X0) > set @ X1 > X1))).
% 0.22/0.38 thf(func_def_206, type, sK147: !>[X0: $tType, X1: $tType]:((nat > (nat > X1 > X0) > set @ X1 > nat))).
% 0.22/0.38 thf(func_def_207, type, sK148: !>[X0: $tType, X1: $tType]:((nat > (nat > X1 > X0) > set @ X1 > nat))).
% 0.22/0.38 thf(func_def_208, type, sK149: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_209, type, sK150: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_210, type, sK151: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_211, type, sK152: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_212, type, sK153: !>[X0: $tType]:((X0 > real > X0))).
% 0.22/0.38 thf(func_def_213, type, sK154: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_214, type, sK155: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_215, type, sK156: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.22/0.38 thf(func_def_216, type, sK157: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.22/0.38 thf(func_def_217, type, sK158: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.22/0.38 thf(func_def_218, type, sK159: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.22/0.38 thf(func_def_219, type, sK160: ((nat > $o) > nat)).
% 0.22/0.38 thf(func_def_220, type, sK161: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.22/0.38 thf(func_def_221, type, sK162: !>[X0: $tType, X1: $tType]:((real > (nat > X0 > X1) > (X0 > $o) > nat))).
% 0.22/0.38 thf(func_def_222, type, sK163: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (nat > X0 > X1) > (X0 > $o) > real))).
% 0.22/0.38 thf(func_def_223, type, sK164: !>[X0: $tType, X1: $tType]:((nat > (X0 > X1) > (nat > X0 > X1) > (X0 > $o) > nat))).
% 0.22/0.38 thf(func_def_224, type, sK165: !>[X0: $tType, X1: $tType]:((nat > (X0 > X1) > (nat > X0 > X1) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_225, type, sK166: !>[X0: $tType, X1: $tType]:(((nat > X0 > X1) > (X0 > $o) > X0 > X1))).
% 0.22/0.38 thf(func_def_226, type, sK167: !>[X0: $tType, X1: $tType]:((real > (nat > X0 > X1) > (X0 > $o) > nat))).
% 0.22/0.38 thf(func_def_227, type, sK168: !>[X0: $tType, X1: $tType]:(((nat > X0 > X1) > (X0 > $o) > real))).
% 0.22/0.38 thf(func_def_228, type, sK169: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_229, type, sK170: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > (X0 > $o) > nat))).
% 0.22/0.38 thf(func_def_230, type, sK171: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > (X0 > $o) > nat))).
% 0.22/0.38 thf(func_def_231, type, sK172: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_232, type, sK173: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.22/0.38 thf(func_def_233, type, sK174: !>[X0: $tType]:((X0 > real > X0))).
% 0.22/0.38 thf(func_def_234, type, sK175: !>[X0: $tType, X1: $tType]:(((nat > X0 > X1) > set @ X0 > real))).
% 0.22/0.38 thf(func_def_235, type, sK176: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > set @ X0 > X0))).
% 0.22/0.38 thf(func_def_236, type, sK177: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > set @ X0 > nat))).
% 0.22/0.38 thf(func_def_237, type, sK178: !>[X0: $tType, X1: $tType]:((nat > (nat > X0 > X1) > set @ X0 > nat))).
% 0.22/0.38 thf(f1,axiom,(
% 0.22/0.38 ? [X3 : product_prod @ a @ real] : ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ X3 @ (product_Pair @ a @ real @ x @ y)) @ e) & (member @ product_prod @ a @ real @ X3 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))),
% 0.22/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062)).
% 0.22/0.38 thf(f130,axiom,(
% 0.22/0.38 ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : ~ ! [X4 : X1,X3 : X0] : (X2 != ((product_Pair @ X0 @ X1 @ X3 @ X4)))),
% 0.22/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_old_Oprod_Oexhaust)).
% 0.22/0.38 thf(f319,axiom,(
% 0.22/0.38 ! [X1 : real,X0 : a] : (((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (product_Pair @ a @ real @ x @ y)) @ e) & (member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) => thesis)),
% 0.22/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.22/0.38 thf(f320,conjecture,(
% 0.22/0.38 thesis),
% 0.22/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.22/0.38 thf(f321,negated_conjecture,(
% 0.22/0.38 ~thesis),
% 0.22/0.38 inference(negated_conjecture,[status(cth)],[f320])).
% 0.22/0.38 thf(f350,plain,(
% 0.22/0.38 ! [X0 : real,X1 : a] : (((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (product_Pair @ a @ real @ x @ y)) @ e) & (member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) => thesis)),
% 0.22/0.38 inference(rectify,[],[f319])).
% 0.22/0.38 thf(f351,plain,(
% 0.22/0.38 ! [X0 : real,X1 : a] : (((((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (product_Pair @ a @ real @ x @ y)) @ e)) = $true) & (((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) = $true)) => (thesis = $true))),
% 0.22/0.38 inference(fool_elimination,[],[f350])).
% 0.22/0.38 thf(f437,plain,(
% 0.22/0.38 ? [X0 : product_prod @ a @ real] : ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ X0 @ (product_Pair @ a @ real @ x @ y)) @ e) & (member @ product_prod @ a @ real @ X0 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))),
% 0.22/0.38 inference(rectify,[],[f1])).
% 0.22/0.38 thf(f438,plain,(
% 0.22/0.38 ? [X0 : product_prod @ a @ real] : (($true = ((member @ product_prod @ a @ real @ X0 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))) & ($true = ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ X0 @ (product_Pair @ a @ real @ x @ y)) @ e))))),
% 0.22/0.38 inference(fool_elimination,[],[f437])).
% 0.22/0.38 thf(f446,plain,(
% 0.22/0.38 ~thesis),
% 0.22/0.38 inference(rectify,[],[f321])).
% 0.22/0.38 thf(f447,plain,(
% 0.22/0.38 ~ (thesis = $true)),
% 0.22/0.38 inference(fool_elimination,[],[f446])).
% 0.22/0.38 thf(f939,plain,(
% 0.22/0.38 (thesis != $true)),
% 0.22/0.38 inference(flattening,[],[f447])).
% 0.22/0.38 thf(f950,plain,(
% 0.22/0.38 ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X1 @ X0] : ~ ! [X3 : X0,X4 : X1] : (((product_Pair @ X1 @ X0 @ X4 @ X3)) != X2)),
% 0.22/0.38 inference(rectify,[],[f130])).
% 0.22/0.38 thf(f1013,plain,(
% 0.22/0.38 ! [X0 : real,X1 : a] : ((thesis = $true) | ((((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (product_Pair @ a @ real @ x @ y)) @ e)) != $true) | (((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) != $true)))),
% 0.22/0.38 inference(ennf_transformation,[],[f351])).
% 0.22/0.38 thf(f1014,plain,(
% 0.22/0.38 ! [X1 : a,X0 : real] : ((((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) != $true) | (thesis = $true) | (((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X1 @ X0) @ (product_Pair @ a @ real @ x @ y)) @ e)) != $true))),
% 0.22/0.38 inference(flattening,[],[f1013])).
% 0.22/0.38 thf(f1252,plain,(
% 0.22/0.38 ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X1 @ X0] : ? [X3 : X0,X4 : X1] : (((product_Pair @ X1 @ X0 @ X4 @ X3)) = X2)),
% 0.22/0.38 inference(ennf_transformation,[],[f950])).
% 0.22/0.38 thf(f1349,plain,(
% 0.22/0.38 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : ? [X3 : X1,X4 : X0] : (((product_Pair @ X0 @ X1 @ X4 @ X3)) = X2)),
% 0.22/0.38 inference(rectify,[],[f1252])).
% 0.22/0.38 thf(f1350,plain,(
% 0.22/0.38 ! [X0 : $tType,X1 : $tType,X2 : product_prod @ X0 @ X1] : (((product_Pair @ X0 @ X1 @ (sK25 @ X0 @ X1 @ X2) @ (sK24 @ X0 @ X1 @ X2))) = X2)),
% 0.22/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK3 @ X1 @ X0),skolemize(X2,sK3 @ X1 @ X0)],[f1349])).
% 0.22/0.38 thf(f1457,plain,(
% 0.22/0.38 ($true = ((member @ product_prod @ a @ real @ sK102 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))) & ($true = ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ sK102 @ (product_Pair @ a @ real @ x @ y)) @ e)))),
% 0.22/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(X0,sK102)],[f438])).
% 0.22/0.38 thf(f1539,plain,(
% 0.22/0.38 ! [X0 : a,X1 : real] : ((((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) != $true) | (thesis = $true) | (((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (product_Pair @ a @ real @ x @ y)) @ e)) != $true))),
% 0.22/0.38 inference(rectify,[],[f1014])).
% 0.22/0.38 thf(f1654,plain,(
% 0.22/0.38 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod @ X0 @ X1] : ((((product_Pair @ X0 @ X1 @ (sK25 @ X0 @ X1 @ X2) @ (sK24 @ X0 @ X1 @ X2))) = X2)) )),
% 0.22/0.38 inference(cnf_transformation,[],[f1350])).
% 0.22/0.38 thf(f1858,plain,(
% 0.22/0.38 ($true = ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ sK102 @ (product_Pair @ a @ real @ x @ y)) @ e)))),
% 0.22/0.38 inference(cnf_transformation,[],[f1457])).
% 0.22/0.38 thf(f1859,plain,(
% 0.22/0.38 ($true = ((member @ product_prod @ a @ real @ sK102 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))))),
% 0.22/0.38 inference(cnf_transformation,[],[f1457])).
% 0.22/0.38 thf(f1946,plain,(
% 0.22/0.38 (thesis != $true)),
% 0.22/0.38 inference(cnf_transformation,[],[f939])).
% 0.22/0.38 thf(f1997,plain,(
% 0.22/0.38 ( ! [X0 : a,X1 : real] : ((((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (product_Pair @ a @ real @ x @ y)) @ e)) != $true) | (thesis = $true) | (((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) != $true)) )),
% 0.22/0.38 inference(cnf_transformation,[],[f1539])).
% 0.22/0.38 thf(f2176,definition,(
% 0.22/0.38 spl179_6 <=> (thesis = $true)),
% 0.22/0.38 introduced(definition,[new_symbols(definition,[spl179_6])],[avatar_definition])).
% 0.22/0.38 thf(f2179,plain,(
% 0.22/0.38 ~spl179_6),
% 0.22/0.38 inference(avatar_split_clause,[],[f1946,f2176])).
% 0.22/0.38 thf(f2293,definition,(
% 0.22/0.38 spl179_30 <=> ! [X0 : a,X1 : real] : ((((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (product_Pair @ a @ real @ x @ y)) @ e)) != $true) | (((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) != $true))),
% 0.22/0.38 introduced(definition,[new_symbols(definition,[spl179_30])],[avatar_definition])).
% 0.22/0.38 thf(f2294,plain,(
% 0.22/0.38 ( ! [X0 : a,X1 : real] : ((((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (product_Pair @ a @ real @ x @ y)) @ e)) != $true) | (((member @ product_prod @ a @ real @ (product_Pair @ a @ real @ X0 @ X1) @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))) != $true)) ) | ~spl179_30),
% 0.22/0.38 inference(avatar_component_clause,[],[f2293])).
% 0.22/0.38 thf(f2295,plain,(
% 0.22/0.38 spl179_30 | spl179_6),
% 0.22/0.38 inference(avatar_split_clause,[],[f1997,f2176,f2293])).
% 0.22/0.38 thf(f2313,definition,(
% 0.22/0.38 spl179_34 <=> ($true = ((member @ product_prod @ a @ real @ sK102 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))))),
% 0.22/0.38 introduced(definition,[new_symbols(definition,[spl179_34])],[avatar_definition])).
% 0.22/0.38 thf(f2315,plain,(
% 0.22/0.38 ($true = ((member @ product_prod @ a @ real @ sK102 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))) | ~spl179_34),
% 0.22/0.38 inference(avatar_component_clause,[],[f2313])).
% 0.22/0.38 thf(f2316,plain,(
% 0.22/0.38 spl179_34),
% 0.22/0.38 inference(avatar_split_clause,[],[f1859,f2313])).
% 0.22/0.38 thf(f2373,definition,(
% 0.22/0.38 spl179_46 <=> ($true = ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ sK102 @ (product_Pair @ a @ real @ x @ y)) @ e)))),
% 0.22/0.38 introduced(definition,[new_symbols(definition,[spl179_46])],[avatar_definition])).
% 0.22/0.38 thf(f2375,plain,(
% 0.22/0.38 ($true = ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ sK102 @ (product_Pair @ a @ real @ x @ y)) @ e))) | ~spl179_46),
% 0.22/0.38 inference(avatar_component_clause,[],[f2373])).
% 0.22/0.38 thf(f2376,plain,(
% 0.22/0.38 spl179_46),
% 0.22/0.38 inference(avatar_split_clause,[],[f1858,f2373])).
% 0.22/0.38 thf(f2498,plain,(
% 0.22/0.38 ( ! [X0 : product_prod @ a @ real] : (($true != ((ord_less @ real @ (real_V2000881966t_dist @ product_prod @ a @ real @ X0 @ (product_Pair @ a @ real @ x @ y)) @ e))) | ($true != ((member @ product_prod @ a @ real @ X0 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f))))) ) | ~spl179_30),
% 0.22/0.38 inference(superposition,[],[f2294,f1654])).
% 0.22/0.38 thf(f2611,plain,(
% 0.22/0.38 ($true != $true) | ($true != ((member @ product_prod @ a @ real @ sK102 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))) | (~spl179_30 | ~spl179_46)),
% 0.22/0.38 inference(superposition,[],[f2498,f2375])).
% 0.22/0.38 thf(f2612,plain,(
% 0.22/0.38 ($true != ((member @ product_prod @ a @ real @ sK102 @ (lower_261390618igraph @ a @ top_top @ set @ a @ f)))) | (~spl179_30 | ~spl179_46)),
% 0.22/0.38 inference(trivial_inequality_removal,[],[f2611])).
% 0.22/0.38 thf(f2613,plain,(
% 0.22/0.38 $false | (~spl179_30 | ~spl179_34 | ~spl179_46)),
% 0.22/0.38 inference(forward_subsumption_resolution,[],[f2612,f2315])).
% 0.22/0.38 thf(f2614,plain,(
% 0.22/0.38 ~spl179_30 | ~spl179_34 | ~spl179_46),
% 0.22/0.38 inference(avatar_contradiction_clause,[],[f2613])).
% 0.22/0.38 cnf(s6, plain, ~spl179_6, inference(sat_conversion,[],[f2179])).
% 0.22/0.38 cnf(s30, plain, spl179_6 | spl179_30, inference(sat_conversion,[],[f2295])).
% 0.22/0.38 cnf(s36, plain, spl179_34, inference(sat_conversion,[],[f2316])).
% 0.22/0.38 cnf(s51, plain, spl179_46, inference(sat_conversion,[],[f2376])).
% 0.22/0.38 cnf(s73, plain, ~spl179_30 | ~spl179_34 | ~spl179_46, inference(sat_conversion,[],[f2614])).
% 0.22/0.38 cnf(s75, plain, ~spl179_30, inference(rat,[],[s73,s51,s36])).
% 0.22/0.38 cnf(s76, plain, spl179_6, inference(rat,[],[s30,s75])).
% 0.22/0.38 cnf(s80, plain, $false, inference(rat,[],[s6,s76])).
% 0.22/0.38 thf(f2615,plain,(
% 0.22/0.38 $false),
% 0.22/0.38 inference(avatar_sat_refutation,[],[s80])).
% 0.22/0.38 % SZS output end Proof for theBenchmark
% 0.22/0.38 % (4035547)------------------------------
% 0.22/0.38 % (4035547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.38 % (4035547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.38 % (4035547)CaDiCaL version: 2.1.3
% 0.22/0.38 % (4035547)Termination reason: Refutation
% 0.22/0.38 % (4035547)Time elapsed: 0.046 s
% 0.22/0.38 % (4035547)Peak memory usage: 15 MB
% 0.22/0.38 % (4035547)Instructions burned: 160 (million)
% 0.22/0.38 % (4035539)Success in time 0.096 s
% 0.22/0.38 % Vampire exiting
%------------------------------------------------------------------------------