%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP117^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:10:46 AM UTC 2026
% Result : Theorem 1.52s 0.54s
% Output : Refutation 1.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP117^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:55:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.52/0.54 % (2585357)Will run a generic schedule for satisfiability detection.
% 1.52/0.54 % (2585391)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3398201027:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.52/0.54 % (2585390)% WARNING: option uhcvi not known.
% 1.52/0.54 % (2585390)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2176749122:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.52/0.54 % (2585389)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=361583740_2999 on theBenchmark for (2999ds/0Mi)
% 1.52/0.54 % (2585392)dis+10_1_sil=32000:sp=arity:random_seed=3069667771:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.52/0.54 % (2585393)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2604021640:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.52/0.54 % (2585395)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1021984615:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.52/0.54 % (2585394)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2408247813:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.52/0.54 % (2585390)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.52/0.54 % (2585393)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.52/0.54 % Exception at run slice level% (2585390)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.52/0.54
% 1.52/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.52/0.54 % (2585392)Instruction limit reached!
% 1.52/0.54 % (2585392)------------------------------
% 1.52/0.54 % (2585392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585392)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585392)Termination reason: Instruction limit
% 1.52/0.54 % (2585392)Termination phase: Saturation
% 1.52/0.54 % (2585392)Time elapsed: 0.046 s
% 1.52/0.54 % (2585392)Peak memory usage: 12 MB
% 1.52/0.54 % (2585392)Instructions burned: 104 (million)
% 1.52/0.54 % (2585393)Instruction limit reached!
% 1.52/0.54 % (2585393)------------------------------
% 1.52/0.54 % (2585393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585393)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585393)Termination reason: Instruction limit
% 1.52/0.54 % (2585393)Termination phase: Saturation
% 1.52/0.54 % (2585393)Time elapsed: 0.052 s
% 1.52/0.54 % (2585393)Peak memory usage: 13 MB
% 1.52/0.54 % (2585393)Instructions burned: 116 (million)
% 1.52/0.54 % (2585409)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2430148941:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.52/0.54 % (2585394)Instruction limit reached!
% 1.52/0.54 % (2585394)------------------------------
% 1.52/0.54 % (2585394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585394)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585394)Termination reason: Instruction limit
% 1.52/0.54 % (2585394)Termination phase: Saturation
% 1.52/0.54 % (2585394)Time elapsed: 0.061 s
% 1.52/0.54 % (2585394)Peak memory usage: 13 MB
% 1.52/0.54 % (2585394)Instructions burned: 132 (million)
% 1.52/0.54 % (2585410)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=272967144:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.52/0.54 % (2585411)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1332519267:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.52/0.54 % (2585395)Instruction limit reached!
% 1.52/0.54 % (2585395)------------------------------
% 1.52/0.54 % (2585395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585395)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585395)Termination reason: Instruction limit
% 1.52/0.54 % (2585395)Termination phase: Saturation
% 1.52/0.54 % (2585395)Time elapsed: 0.079 s
% 1.52/0.54 % (2585395)Peak memory usage: 14 MB
% 1.52/0.54 % (2585395)Instructions burned: 159 (million)
% 1.52/0.54 % (2585413)ott-21_1_sil=16000:fs=off:random_seed=1439508882:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.52/0.54 % Exception at run slice level
% 1.52/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.52/0.54 % (2585411)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.52/0.54 % (2585416)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3032474927:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.52/0.54 % (2585418)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1181650323:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.52/0.54 % (2585411)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.52/0.54 % (2585410)Instruction limit reached!
% 1.52/0.54 % (2585410)------------------------------
% 1.52/0.54 % (2585410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585410)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585410)Termination reason: Instruction limit
% 1.52/0.54 % (2585410)Termination phase: Saturation
% 1.52/0.54 % (2585410)Time elapsed: 0.061 s
% 1.52/0.54 % (2585410)Peak memory usage: 13 MB
% 1.52/0.54 % (2585410)Instructions burned: 133 (million)
% 1.52/0.54 % (2585421)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=214275614:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.52/0.54 % Exception at run slice level
% 1.52/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.52/0.54 % (2585413)Instruction limit reached!
% 1.52/0.54 % (2585413)------------------------------
% 1.52/0.54 % (2585413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585413)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585413)Termination reason: Instruction limit
% 1.52/0.54 % (2585413)Termination phase: Saturation
% 1.52/0.54 % (2585413)Time elapsed: 0.080 s
% 1.52/0.54 % (2585413)Peak memory usage: 14 MB
% 1.52/0.54 % (2585413)Instructions burned: 181 (million)
% 1.52/0.54 % (2585423)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=681527689:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.52/0.54 % (2585424)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3261780231:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 1.52/0.54 % (2585424)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.52/0.54 % Exception at run slice level
% 1.52/0.54 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.52/0.54 % (2585427)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1682699529:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.52/0.54 % (2585421) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2585357-2585421"...
% 1.52/0.54 % (2585421)...printing done.
% 1.52/0.54 % (2585427)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.52/0.54 % (2585421)Refutation found. Thanks to Tanya!
% 1.52/0.54 % SZS status Theorem for theBenchmark
% 1.52/0.54 % SZS output start Proof for theBenchmark
% 1.52/0.54 thf(type_def_5, type, extend1814228343nnreal: $tType).
% 1.52/0.54 thf(type_def_6, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 1.52/0.54 thf(type_def_7, type, sigma_measure: $tType > $tType).
% 1.52/0.54 thf(type_def_8, type, real: $tType).
% 1.52/0.54 thf(type_def_9, type, set: $tType > $tType).
% 1.52/0.54 thf(type_def_10, type, nat: $tType).
% 1.52/0.54 thf(type_def_11, type, int: $tType).
% 1.52/0.54 thf(type_def_12, type, n: $tType).
% 1.52/0.54 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 1.52/0.54 thf(func_def_0, type, ring_1: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_1, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_3, type, one: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_5, type, ring_char_0: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_6, type, neg_numeral: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_8, type, finite_finite: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_9, type, monoid_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_10, type, countable: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_11, type, ab_group_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_12, type, semigroup_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_13, type, complete_Sup: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_14, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_15, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_16, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_17, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_19, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_20, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_21, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_22, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_23, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_24, type, comple187826305attice: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_25, type, comple1035589618norder: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_26, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_27, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_28, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_29, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_30, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 1.52/0.54 thf(func_def_31, type, complete_Sup_Sup: !>[X0: $tType]:((set @ X0 > X0))).
% 1.52/0.54 thf(func_def_32, type, complete_completion: !>[X0: $tType]:((sigma_measure @ X0 > sigma_measure @ X0))).
% 1.52/0.54 thf(func_def_33, type, counta609264050t_into: !>[X0: $tType]:((set @ X0 > nat > X0))).
% 1.52/0.54 thf(func_def_34, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.52/0.54 thf(func_def_35, type, one_one: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_36, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.52/0.54 thf(func_def_37, type, zero_zero: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_38, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.52/0.54 thf(func_def_39, type, lebesgue_lborel: !>[X0: $tType]:(sigma_measure @ X0)).
% 1.52/0.54 thf(func_def_40, type, measure_null_sets: !>[X0: $tType]:((sigma_measure @ X0 > set @ set @ X0))).
% 1.52/0.54 thf(func_def_41, type, minkow1937162798nt_vec: !>[X0: $tType, X1: $tType]:((finite_Cartesian_vec @ int @ X0 > finite_Cartesian_vec @ X1 @ X0))).
% 1.52/0.54 thf(func_def_42, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.52/0.54 thf(func_def_43, type, top_top: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_44, type, sums: !>[X0: $tType]:(((nat > X0) > X0 > $o))).
% 1.52/0.54 thf(func_def_45, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.52/0.54 thf(func_def_46, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 1.52/0.54 thf(func_def_47, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 1.52/0.54 thf(func_def_48, type, sigma_emeasure: !>[X0: $tType]:((sigma_measure @ X0 > set @ X0 > extend1814228343nnreal))).
% 1.52/0.54 thf(func_def_49, type, sigma_sets: !>[X0: $tType]:((sigma_measure @ X0 > set @ set @ X0))).
% 1.52/0.54 thf(func_def_50, type, sigma_space: !>[X0: $tType]:((sigma_measure @ X0 > set @ X0))).
% 1.52/0.54 thf(func_def_51, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.52/0.54 thf(func_def_52, type, r: (finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n)).
% 1.52/0.54 thf(func_def_53, type, s: set @ finite_Cartesian_vec @ real @ n).
% 1.52/0.54 thf(func_def_54, type, t: (finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n)).
% 1.52/0.54 thf(func_def_55, type, t2: (finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n)).
% 1.52/0.54 thf(func_def_56, type, f: (nat > finite_Cartesian_vec @ int @ n)).
% 1.52/0.54 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.52/0.54 thf(func_def_62, type, db1: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.52/0.54 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.52/0.54 thf(func_def_65, type, vIMP: ($o > $o > $o)).
% 1.52/0.54 thf(func_def_66, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.52/0.54 thf(func_def_67, type, vAND: ($o > $o > $o)).
% 1.52/0.54 thf(func_def_68, type, vOR: ($o > $o > $o)).
% 1.52/0.54 thf(func_def_69, type, db2: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_70, type, vNOT: ($o > $o)).
% 1.52/0.54 thf(func_def_71, type, sK0: !>[X0: $tType]:((sigma_measure @ X0 > (nat > set @ X0) > nat))).
% 1.52/0.54 thf(func_def_72, type, sK1: !>[X0: $tType]:((sigma_measure @ X0 > (nat > set @ X0) > nat))).
% 1.52/0.54 thf(func_def_73, type, sK2: !>[X0: $tType]:((sigma_measure @ X0 > (nat > set @ X0) > nat))).
% 1.52/0.54 thf(func_def_74, type, sK3: !>[X0: $tType, X1: $tType]:((sigma_measure @ X1 > (X0 > set @ X1) > X0))).
% 1.52/0.54 thf(func_def_75, type, sK4: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.52/0.54 thf(func_def_76, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.52/0.54 thf(func_def_77, type, sK6: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > sigma_measure @ X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_78, type, sK7: !>[X0: $tType]:((set @ X0 > set @ sigma_measure @ X0 > sigma_measure @ X0))).
% 1.52/0.54 thf(func_def_79, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > sigma_measure @ X0) > (X1 > sigma_measure @ X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_80, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_81, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_82, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 1.52/0.54 thf(func_def_83, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_84, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 1.52/0.54 thf(func_def_85, type, sK14: !>[X0: $tType]:(X0)).
% 1.52/0.54 thf(func_def_86, type, sK15: !>[X0: $tType]:((set @ X0 > X0))).
% 1.52/0.54 thf(func_def_87, type, sK16: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 1.52/0.54 thf(func_def_88, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > (X0 > $o) > X1))).
% 1.52/0.54 thf(func_def_89, type, sK18: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 1.52/0.54 thf(func_def_90, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 1.52/0.54 thf(func_def_91, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 1.52/0.54 thf(func_def_92, type, sK21: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 1.52/0.54 thf(func_def_93, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_94, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 1.52/0.54 thf(func_def_95, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 1.52/0.54 thf(func_def_96, type, sK25: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > set @ X0) > X0 > X1))).
% 1.52/0.54 thf(func_def_97, type, sK26: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.52/0.54 thf(func_def_98, type, sF27: sigma_measure @ finite_Cartesian_vec @ real @ n).
% 1.52/0.54 thf(func_def_99, type, sF28: sigma_measure @ finite_Cartesian_vec @ real @ n).
% 1.52/0.54 thf(func_def_100, type, sF29: set @ finite_Cartesian_vec @ int @ n).
% 1.52/0.54 thf(func_def_101, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 1.52/0.54 thf(func_def_102, type, sK31: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 1.52/0.54 thf(func_def_103, type, sK32: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 1.52/0.54 thf(func_def_104, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 1.52/0.54 thf(func_def_105, type, sK34: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 1.52/0.54 thf(func_def_106, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > X0 > X1))).
% 1.52/0.54 thf(func_def_107, type, sK36: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 1.52/0.54 thf(func_def_108, type, sK37: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_109, type, sK38: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_110, type, sK39: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_111, type, sK40: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 1.52/0.54 thf(func_def_112, type, sK41: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_113, type, sK42: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 1.52/0.54 thf(func_def_114, type, sK43: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_115, type, sK44: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_116, type, sK45: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_117, type, sK46: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 1.52/0.54 thf(func_def_118, type, sK47: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 1.52/0.54 thf(func_def_119, type, sK48: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 1.52/0.54 thf(func_def_120, type, sK49: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 1.52/0.54 thf(func_def_121, type, sK50: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 1.52/0.54 thf(func_def_122, type, sK51: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 1.52/0.54 thf(func_def_123, type, sK52: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 1.52/0.54 thf(func_def_124, type, sK53: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 1.52/0.54 thf(func_def_125, type, sK54: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 1.52/0.54 thf(func_def_126, type, sK55: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 1.52/0.54 thf(func_def_127, type, sK56: !>[X0: $tType]:((set @ X0 > X0))).
% 1.52/0.54 thf(func_def_128, type, sK57: !>[X0: $tType, X1: $tType]:((set @ X0 > X1 > (X0 > X1) > X0))).
% 1.52/0.54 thf(func_def_129, type, sK58: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1))).
% 1.52/0.54 thf(func_def_131, type, sK60: nat).
% 1.52/0.54 thf(f1,axiom,(
% 1.52/0.54 ! [X2 : finite_Cartesian_vec @ int @ n] : (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ X2))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ X2))))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_emeasure__T_H)).
% 1.52/0.54 thf(f11,axiom,(
% 1.52/0.54 (t = (^[X0 : finite_Cartesian_vec @ int @ n] : ((image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X1 : finite_Cartesian_vec @ real @ n] : ((minus_minus @ finite_Cartesian_vec @ real @ n @ X1 @ (minkow1937162798nt_vec @ n @ real @ X0)))) @ (t2 @ X0)))))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_T_H__def)).
% 1.52/0.54 thf(f12,axiom,(
% 1.52/0.54 (f = ((counta609264050t_into @ finite_Cartesian_vec @ int @ n @ top_top @ set @ finite_Cartesian_vec @ int @ n)))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f__def)).
% 1.52/0.54 thf(f13,axiom,(
% 1.52/0.54 ! [X0 : finite_Cartesian_vec @ int @ n] : (((t @ X0)) = ((vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X1 : finite_Cartesian_vec @ real @ n] : ((plus_plus @ finite_Cartesian_vec @ real @ n @ X1 @ (minkow1937162798nt_vec @ n @ real @ X0)))) @ (t2 @ X0))))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_T_H__altdef)).
% 1.52/0.54 thf(f15,axiom,(
% 1.52/0.54 (t2 = (^[X0 : finite_Cartesian_vec @ int @ n] : ((inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_T__def)).
% 1.52/0.54 thf(f72,axiom,(
% 1.52/0.54 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (((minus_minus @ set @ X0 @ X1 @ (minus_minus @ set @ X0 @ X1 @ X2))) = ((inf_inf @ set @ X0 @ X1 @ X2)))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Diff__Diff__Int)).
% 1.52/0.54 thf(f119,axiom,(
% 1.52/0.54 ! [X0 : $tType,X1 : $tType] : (vimage @ X1 @ X0 = (^[X2 : (X1 > X0), X3 : set @ X0] : ((collect @ X1 @ (^[X4 : X1] : ((member @ X0 @ (X2 @ X4) @ X3)))))))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_vimage__def)).
% 1.52/0.54 thf(f382,conjecture,(
% 1.52/0.54 ((^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ X0))))) = (^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ X0))))))),
% 1.52/0.54 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.52/0.54 thf(f383,negated_conjecture,(
% 1.52/0.54 ~ ((^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ X0))))) = (^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ X0))))))),
% 1.52/0.54 inference(negated_conjecture,[status(cth)],[f382])).
% 1.52/0.54 thf(f400,plain,(
% 1.52/0.54 (t = (^[X0 : finite_Cartesian_vec @ int @ n] : ((image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X1 : finite_Cartesian_vec @ real @ n] : ((minus_minus @ finite_Cartesian_vec @ real @ n @ X1 @ (minkow1937162798nt_vec @ n @ real @ X0)))) @ (t2 @ X0)))))),
% 1.52/0.54 inference(rectify,[],[f11])).
% 1.52/0.54 thf(f401,plain,(
% 1.52/0.54 (t = (^[Y0 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ (t2 @ Y0))))),
% 1.52/0.54 inference(fool_elimination,[],[f400])).
% 1.52/0.54 thf(f402,plain,(
% 1.52/0.54 ! [X0 : finite_Cartesian_vec @ int @ n] : (((t @ X0)) = ((vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[X1 : finite_Cartesian_vec @ real @ n] : ((plus_plus @ finite_Cartesian_vec @ real @ n @ X1 @ (minkow1937162798nt_vec @ n @ real @ X0)))) @ (t2 @ X0))))),
% 1.52/0.54 inference(rectify,[],[f13])).
% 1.52/0.54 thf(f403,plain,(
% 1.52/0.54 ! [X0 : finite_Cartesian_vec @ int @ n] : (((t @ X0)) = ((vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (t2 @ X0))))),
% 1.52/0.54 inference(fool_elimination,[],[f402])).
% 1.52/0.54 thf(f406,plain,(
% 1.52/0.54 (t2 = (^[Y0 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y0))))),
% 1.52/0.54 inference(fool_elimination,[],[f15])).
% 1.52/0.54 thf(f565,plain,(
% 1.52/0.54 ! [X0 : $tType,X1 : $tType] : (vimage @ X1 @ X0 = (^[X2 : (X1 > X0), X3 : set @ X0] : ((collect @ X1 @ (^[X4 : X1] : ((member @ X0 @ (X2 @ X4) @ X3)))))))),
% 1.52/0.54 inference(rectify,[],[f119])).
% 1.52/0.54 thf(f566,plain,(
% 1.52/0.54 ! [X0 : $tType,X1 : $tType] : (vimage @ X1 @ X0 = (^[Y0 : X1 > X0]: ((^[Y1 : set @ X0]: (collect @ X1 @ (^[Y2 : X1]: (member @ X0 @ (Y0 @ Y2) @ Y1)))))))),
% 1.52/0.54 inference(fool_elimination,[],[f565])).
% 1.52/0.54 thf(f1072,plain,(
% 1.52/0.54 ~ ((^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ X0))))) = (^[X1 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ X1))))))),
% 1.52/0.54 inference(rectify,[],[f383])).
% 1.52/0.54 thf(f1073,plain,(
% 1.52/0.54 ~ ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) = (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 1.52/0.54 inference(fool_elimination,[],[f1072])).
% 1.52/0.54 thf(f1074,plain,(
% 1.52/0.54 ! [X0 : finite_Cartesian_vec @ int @ n] : (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ X0))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ X0))))),
% 1.52/0.54 inference(rectify,[],[f1])).
% 1.52/0.54 thf(f1084,plain,(
% 1.52/0.54 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 1.52/0.54 inference(flattening,[],[f1073])).
% 1.52/0.54 thf(f1377,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ X0))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ X0))))) )),
% 1.52/0.54 inference(cnf_transformation,[],[f1074])).
% 1.52/0.54 thf(f1387,plain,(
% 1.52/0.54 (t = (^[Y0 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ (t2 @ Y0))))),
% 1.52/0.54 inference(cnf_transformation,[],[f401])).
% 1.52/0.54 thf(f1388,plain,(
% 1.52/0.54 (f = ((counta609264050t_into @ finite_Cartesian_vec @ int @ n @ top_top @ set @ finite_Cartesian_vec @ int @ n)))),
% 1.52/0.54 inference(cnf_transformation,[],[f12])).
% 1.52/0.54 thf(f1389,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((t @ X0)) = ((vimage @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (t2 @ X0))))) )),
% 1.52/0.54 inference(cnf_transformation,[],[f403])).
% 1.52/0.54 thf(f1391,plain,(
% 1.52/0.54 (t2 = (^[Y0 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y0))))),
% 1.52/0.54 inference(cnf_transformation,[],[f406])).
% 1.52/0.54 thf(f1452,plain,(
% 1.52/0.54 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : ((((inf_inf @ set @ X0 @ X1 @ X2)) = ((minus_minus @ set @ X0 @ X1 @ (minus_minus @ set @ X0 @ X1 @ X2))))) )),
% 1.52/0.54 inference(cnf_transformation,[],[f72])).
% 1.52/0.54 thf(f1507,plain,(
% 1.52/0.54 ( ! [X1 : $tType,X0 : $tType] : ((vimage @ X1 @ X0 = (^[Y0 : X1 > X0]: ((^[Y1 : set @ X0]: (collect @ X1 @ (^[Y2 : X1]: (member @ X0 @ (Y0 @ Y2) @ Y1)))))))) )),
% 1.52/0.54 inference(cnf_transformation,[],[f566])).
% 1.52/0.54 thf(f1774,plain,(
% 1.52/0.54 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 1.52/0.54 inference(cnf_transformation,[],[f1084])).
% 1.52/0.54 thf(f1777,plain,(
% 1.52/0.54 (t = (^[Y0 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y1))) @ Y0))))),
% 1.52/0.54 inference(definition_unfolding,[],[f1387,f1391])).
% 1.52/0.54 thf(f1778,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ ((^[Y0 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y1))) @ Y0))) @ X0))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ ((^[Y0 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y0))) @ X0))))) )),
% 1.52/0.54 inference(definition_unfolding,[],[f1377,f1777,f1391])).
% 1.52/0.54 thf(f1785,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : (((((^[Y0 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ Y0))) @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y1))) @ Y0))) @ X0)) = (((^[Y0 : finite_Cartesian_vec @ real @ n > finite_Cartesian_vec @ real @ n]: ((^[Y1 : set @ finite_Cartesian_vec @ real @ n]: (collect @ finite_Cartesian_vec @ real @ n @ (^[Y2 : finite_Cartesian_vec @ real @ n]: (member @ finite_Cartesian_vec @ real @ n @ (Y0 @ Y2) @ Y1)))))) @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ ((^[Y0 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y0))) @ X0))))) )),
% 1.52/0.54 inference(definition_unfolding,[],[f1389,f1777,f1507,f1391])).
% 1.52/0.54 thf(f1821,plain,(
% 1.52/0.54 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y1))) @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ top_top @ set @ finite_Cartesian_vec @ int @ n @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y2 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y2 @ (minkow1937162798nt_vec @ n @ real @ Y1))) @ ((^[Y2 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y2))) @ Y1))) @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ top_top @ set @ finite_Cartesian_vec @ int @ n @ Y0)))))),
% 1.52/0.54 inference(definition_unfolding,[],[f1774,f1391,f1388,f1777,f1388])).
% 1.52/0.54 thf(f1842,definition,(
% 1.52/0.54 (sF27 = lebesgue_lborel @ finite_Cartesian_vec @ real @ n)),
% 1.52/0.54 introduced(definition,[new_symbols(definition,[sF27])],[function_definition])).
% 1.52/0.54 thf(f1843,plain,(
% 1.52/0.54 (lebesgue_lborel @ finite_Cartesian_vec @ real @ n = sF27)),
% 1.52/0.54 inference(reorient_equations,[],[f1842])).
% 1.52/0.54 thf(f1844,definition,(
% 1.52/0.54 (sF28 = ((complete_completion @ finite_Cartesian_vec @ real @ n @ sF27)))),
% 1.52/0.54 introduced(definition,[new_symbols(definition,[sF28])],[function_definition])).
% 1.52/0.54 thf(f1845,plain,(
% 1.52/0.54 (((complete_completion @ finite_Cartesian_vec @ real @ n @ sF27)) = sF28)),
% 1.52/0.54 inference(reorient_equations,[],[f1844])).
% 1.52/0.54 thf(f1846,definition,(
% 1.52/0.54 (sF29 = top_top @ set @ finite_Cartesian_vec @ int @ n)),
% 1.52/0.54 introduced(definition,[new_symbols(definition,[sF29])],[function_definition])).
% 1.52/0.54 thf(f1847,plain,(
% 1.52/0.54 (top_top @ set @ finite_Cartesian_vec @ int @ n = sF29)),
% 1.52/0.54 inference(reorient_equations,[],[f1846])).
% 1.52/0.54 thf(f1848,plain,(
% 1.52/0.54 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y1))) @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ ((^[Y1 : finite_Cartesian_vec @ int @ n]: (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y2 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y2 @ (minkow1937162798nt_vec @ n @ real @ Y1))) @ ((^[Y2 : finite_Cartesian_vec @ int @ n]: (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ Y2))) @ Y1))) @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0)))))),
% 1.52/0.54 inference(definition_folding,[],[f1821,f1847,f1845,f1843,f1847,f1845,f1843])).
% 1.52/0.54 thf(f1849,plain,(
% 1.52/0.54 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0))))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0)))) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0)))))))),
% 1.52/0.54 inference(beta-eta_normalization,[],[f1848])).
% 1.52/0.54 thf(f2320,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((collect @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (member @ finite_Cartesian_vec @ real @ n @ (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0)) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))) = ((image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))) )),
% 1.52/0.54 inference(beta-eta_normalization,[],[f1785])).
% 1.52/0.54 thf(f2327,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))) )),
% 1.52/0.54 inference(beta-eta_normalization,[],[f1778])).
% 1.52/0.54 thf(f2348,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((collect @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (member @ finite_Cartesian_vec @ real @ n @ (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0)) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))))) = ((image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))))) )),
% 1.52/0.54 inference(forward_demodulation,[],[f2320,f1452])).
% 1.52/0.54 thf(f2353,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))))) )),
% 1.52/0.54 inference(forward_demodulation,[],[f2327,f1452])).
% 1.52/0.54 thf(f2364,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ sF27) @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ sF27) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))))) )),
% 1.52/0.54 inference(forward_demodulation,[],[f2353,f1843])).
% 1.52/0.54 thf(f2374,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0))) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))))) )),
% 1.52/0.54 inference(forward_demodulation,[],[f2364,f1845])).
% 1.52/0.54 thf(f2382,plain,(
% 1.52/0.54 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0))))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (collect @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (member @ finite_Cartesian_vec @ real @ n @ (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ X0)) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ X0)))))))))) )),
% 1.52/0.54 inference(forward_demodulation,[],[f2374,f2348])).
% 1.52/0.54 thf(f3279,plain,(
% 1.52/0.54 ((((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0))))) @ sK60)) != (((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y1 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y1 @ (minkow1937162798nt_vec @ n @ real @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0)))) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ Y0)))))) @ sK60)))),
% 1.52/0.54 inference(negative_extensionality,[],[f1849])).
% 1.52/0.54 thf(f3280,plain,(
% 1.52/0.54 (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60))))) != ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60)))) @ (inf_inf @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60)))))))),
% 1.52/0.54 inference(beta-eta_normalization,[],[f3279])).
% 1.52/0.54 thf(f3281,plain,(
% 1.52/0.54 (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60)))))) != ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (image @ finite_Cartesian_vec @ real @ n @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (minus_minus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60)))) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60))))))))),
% 1.52/0.54 inference(forward_demodulation,[],[f3280,f1452])).
% 1.52/0.54 thf(f3282,plain,(
% 1.52/0.54 (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60)))))) != ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ sF28 @ (collect @ finite_Cartesian_vec @ real @ n @ (^[Y0 : finite_Cartesian_vec @ real @ n]: (member @ finite_Cartesian_vec @ real @ n @ (plus_plus @ finite_Cartesian_vec @ real @ n @ Y0 @ (minkow1937162798nt_vec @ n @ real @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60))) @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (minus_minus @ set @ finite_Cartesian_vec @ real @ n @ s @ (r @ (counta609264050t_into @ finite_Cartesian_vec @ int @ n @ sF29 @ sK60))))))))))),
% 1.52/0.54 inference(forward_demodulation,[],[f3281,f2348])).
% 1.52/0.54 thf(f3283,plain,(
% 1.52/0.54 $false),
% 1.52/0.54 inference(forward_subsumption_resolution,[],[f3282,f2382])).
% 1.52/0.54 % SZS output end Proof for theBenchmark
% 1.52/0.54 % (2585421)------------------------------
% 1.52/0.54 % (2585421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.52/0.54 % (2585421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.52/0.54 % (2585421)CaDiCaL version: 2.1.3
% 1.52/0.54 % (2585421)Termination reason: Refutation
% 1.52/0.54 % (2585421)Time elapsed: 0.102 s
% 1.52/0.54 % (2585421)Peak memory usage: 15 MB
% 1.52/0.54 % (2585421)Instructions burned: 209 (million)
% 1.52/0.54 % (2585357)Success in time 0.313 s
% 1.52/0.54 % Vampire exiting
%------------------------------------------------------------------------------